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Problem 64401

Consider the figure. a. Find the perimeter of the figure. Then find the approximate perimeter by using 3.14 for $\pi$ . b. Find the area of the figure. Then find the approximate area by using 3.14 for $\pi$ .

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Problem 64402

15 Original Total: $\$ 42$ Tip Percent: 15\%

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Problem 64403

Find the discriminant. $2 v^{2}-v=0$
How many real solutions does the equation have? no real one real two real solutions solution solutions Submit

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Problem 64404

In parallelogram EFGH, the measure of angle $F$ is $(3 x-10)^{\circ}$ and the measure of angle $G$ is $(5 x+22)^{\circ}$ . What is the measure of angle $G$ ? $42^{\prime \prime}$ $53^{\circ}$ $117^{\circ}$ $127^{\circ}$

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Problem 64405

-) Simplify the logarithmic expression. $3 \ln (x)-\ln (y)+\ln (2)$ A) $x=\ln \left(\frac{6 x}{y}\right)$ c) $x=\ln \left(\frac{2 x^{3}}{y}\right)$ B) $\ln \left(\frac{x^{3}}{2 y}\right)$ D) $\ln \left(\frac{x}{\sigma_{y}}\right)$

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Problem 64406

Sales: $\$ 42,500$ Commission Rate: $3 \%$ the amount of interest.

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Problem 64407

Question 34 of 39 Determine the concentrations of $\mathrm{MgCl}_{2}, \mathrm{Mg}^{2+}$ , and $\mathrm{Cl}^{-}$ in a solution prepared by dissolving $1.17 \times 10^{-4} \mathrm{~g} \mathrm{MgCl}_{2}$ in 1.25 L of water. Express all three concentrations in molarity. Additionally, express the concentrations of the ionic species in parts per million (ppm). $\left[\mathrm{MgCl}_{2}\right]=$ $\square$ $\begin{array}{l} {\left[\mathrm{MgCl}_{2}\right]=4 \mathrm{M}} \\ {\left[\mathrm{Mg}^{2}+\right]=\square \mathrm{M}} \end{array}$ $\square$ M $\left[\mathrm{Mg}^{2+}\right]=$ $\square$ ppm $\left[\mathrm{Cl}^{-}\right]=$ $\square$ M $\left[\mathrm{Cl}^{-}\right]=$ $\square$ ppm

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Problem 64408

Divide. If the polynomial does not divide evenly, include the remainder as a fraction. $\left(-3 k^{2}+24 k-61\right) \div(k-5)$ $\square$ Submit

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Problem 64409

Find the inverse of each function. 1) $y=\log _{3} \frac{3^{x}}{-4}$ 2) $y=\log _{4}\left(2^{x}+7\right)$ 3) $y=\frac{5^{x}+7}{-2}$ 4) $y=\left(\frac{\left(\frac{1}{5}\right)^{x}}{-4}\right)^{\frac{1}{3}}$ 5) $y=5 \log _{6} x^{3}$ 6) $y=\log _{3}(4 x+8)$ 7) $y=\log _{6} x^{5}+8$ 8) $y=\log _{4}\left(4 x^{3}\right)$ 9) $y=\log _{3}\left(-4 \cdot 2^{x}\right)$

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Problem 64410

What is $\sqrt{9 x^{0}+8 y^{0}+3}$ in its SIMPlest torm?

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Problem 64411

A party rental company has chairs and tables for rent. The total cost to rent 2 chairs and 6 tables is $\$ 42$ . The total cost to rent 5 chairs and 3 tables is $\$ 30$ . What is the cost to rent each chair and each table?
Cost to rent each chair: $\$$ $\square$ Cost to rent each table: $\$$ $\square$

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Problem 64412

14 Solve the system using substitution: $\left\{\begin{array}{l} 2 x-y=3 \\ x=-2 y-1 \end{array}\right.$
Solution - write as an ordered pair, $(x, y)$

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Problem 64413

Select all statements that are true. $\theta$ is in standard position. $(a, b)$ are the coordinates of a point on the terminal arm of $\theta$ If you know the values of a and $b$ , you can determine the value of $\theta$ If you know the value of $\theta$ , you can determine possible values for $a$ and $b$ .

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Problem 64414

12 The registration at a preschool is $\$ 125$ . Then, parents must also pay $\$ 475$ per month for tuition. A. What is the rate of change? $\square$ B. What is the initial value? $\square$ C. What is the independent variable? $\square$ D. What is the dependent variable? $\square$
Write an equation to represent the total cost after each month. $\square$

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Problem 64415

$x^{4}-13 x^{2}-12 x=0$

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Problem 64416

The line parallel to $y=\frac{2}{3} x+1$ that passes through the point $(3,6)$

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Problem 64417

Question Watch Video Show Examples
Arianna throws a ball up in the air. The graph below shows the height of the ball $h$ in meters after $t$ seconds. After how many seconds does the ball hit the ground?

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Problem 64418

Question Watch Video Show Examples
Ajay throws a ball up in the air. The graph below shows the height of the ball $h$ in meters after $t$ seconds. What is the ball's greatest height?

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Problem 64419

How many different roots does the polynomial function, $y=(x+4)(x-2)^{2}(x+7)$ have? A. 4 B. 3 C. 1 D. 2

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Problem 64420

MULTIPLE-CHOICE QUESTION
Since there is an OF before 50 , is 50 the part or the whole?
Whole
Part

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Problem 64421

Knowing that 50 is $\mathbf{O F}$ will it be the numerator (number on top) or the denominator (number on bottom)? $\square$ Numerator $\square$ Denominator

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Problem 64422

Simplify, using only positive exponents in your answer. $\frac{x^{-5}+y^{-4}}{x^{-4}+y^{-3}}$

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Problem 64423

5-77. A bond has a face value of $\$ 1,000$ , is redeemable in eight years, and pays interest of $\$ 100$ at the end of each of the eight years. If the bond can be purchased for $\$ 981$ , what is the rate of return if the bond is held until maturity? (5.3) (a) $10.65 \%$ (b) $12.65 \%$ (c) $10.35 \%$ (d) $11.65 \%$

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Problem 64424

問題 64 平面において, 原点を中心に $\frac{\pi}{6}$ 回転移動させてから, 直線 $y=-2 x$ に関して対称移動させても動かない点を求めよ。

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Problem 64425

What is the oxidation state of each element in $\mathrm{K}_{2} \mathrm{Cr}_{2} \mathrm{O}_{7}$ ?
K Cr
O $\square$

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Problem 64426

Percent Proportion mULIIFLE-LnUILe yUCJIIUN
Write and solve a proportion to answer the question.
1. What percent of 5 is 3 ?
2. 25 is what percent of 20 ?
3. What number is $80 \%$ of 60 ?
4. $10 \%$ of 40.5 is what number?
5. $0.1 \%$ of what number is 4 ?
6. $\frac{1}{2}$ is $25 \%$ of what number? $\frac{\text { Part }}{\text { Whole }(\text { Total })}=\frac{\%}{100}$
Part (clue word IS) $\qquad$ Whole (clue word OF) $\qquad$ Percent (\%) $\qquad$ Unknown $x$ (What) $\qquad$ $\frac{1}{60}=\frac{100}{80}$ $\frac{x}{60}=\frac{80}{100}$ $\frac{80}{60}=\frac{1}{100}$ $\frac{60}{2}=\frac{80}{100}$

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Problem 64427

2. Определить, не вычисляя, знак интеграла: а) $\int_{1}^{2}\left(x^{2}-4 x+3\right) d x$ б) $\int_{\frac{\pi}{2}}^{\pi} x \sin x d x$

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Problem 64428

the function defined by $f(x)=\frac{3 e^{2 x}}{5 x}$ . Give the interval(s) for which $f$ is increasing and decreasing. Also, give the $x$ :e of any extrema (maximum or minimum values, (2 points each)
7creasing $\qquad$ ecreasing $\qquad$ aximum(s) $\qquad$ inimum(s) $\qquad$

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Problem 64429

Ex: Find $\frac{d w}{d t}$ at $t=0$ for $\begin{aligned} \omega=\ln \left(x^{2}+y^{2}+z^{2}\right), x & =\operatorname{los} t \\ y & =\sin t \\ z & =4 \sqrt{t} . \end{aligned}$

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Problem 64430

(d) Give any five features of MS. Excel that
10. Below are the letter grades of 20 students in a class.
A, B, C, C, C, C, B, B, A, D, A, C, C, A, B, F, C, C, A, B (a) Construct a categorical frequency distribution for the above data. (b) Construct simple bar chart for the above data.
11. The birth weights (kilograms) of 30 children were recorded as follows:
Construct: (a) grouped frequency distribution (b) histogram. (c) Frequency polygon (d) Less than cumulative frequency (ogive) curve (e) More than cumulative frequency (ogive) curve for the above data.

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Problem 64431

A 5.0 kg block is pushed 1.0 m at a constant velocity up a vertical wall by a constant force applied at an angle of $29.0^{\circ}$ with the horizontal, as shown in the figure.
The acceleration of gravity is $9.81 \mathrm{~m} / \mathrm{s}^{2}$ .
Drawing not to scale. If the coefficient of kinetic friction between the block and the wall is 0.30 , find a) the work done by the force on the block.
Answer in units of J .

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Problem 64432

What is $\cos 28^{\circ} ?$ A. $\frac{15}{17}$ B. $\frac{8}{17}$ c. $\frac{8}{15}$ D. $\frac{15}{8}$

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Problem 64433

7) $y^{\prime}-y \operatorname{tg} x=\cos x$

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Problem 64434

Select all of the options which are true of the perpendicular bisector of line AB . ``` It is a fixed distance from line AB It meets line AB at 90 It passes through A It meets line AB at 180 It passes through B It does not meet line AB ``` It passes through the midpoint of line AB

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Problem 64435

$36 x^{2}-y^{2}+144 x+8 y+119=0$ (a) Find the standard form of the equation of $\frac{(y-4)^{2}}{9}-\frac{(x+2)^{2}}{4}=1$

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Problem 64436

$f(x)=\left\{\begin{array}{l} \frac{\sin (3 x)}{\sin (5 x)} \text{ if } x \neq 0 \\ \frac{a}{b} \text{ if } x=0 \end{array}\right.$
$g(x)=\left(x^{3}+2 x+1\right) \ln (x)$
المطلوب: إيجاد مجموعة تعريف الدوال $f(x)$ و $g(x)$ .

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Problem 64437

```latex فرض کنید می‌خواهیم تعداد اصابت گلوله‌های سه نوع سلاح انفرادی را با هم مقایسه کنیم. اصابت گلوله‌های هر کدام از این سلاح‌ها در پنج روز به شرح زیر بوده است:
\begin{align} \text{A:} & \quad 26, 19, 21, 10, 24 \\ \text{B:} & \quad 19, 22, 28, 16, 30 \\ \text{C:} & \quad 22, 18, 13, 21, 21 \\ \end{align}
در سطح معنی‌دار ۵ درصد آزمون کنید که آیا اختلاف معنی‌داری بین میانگین‌های تعداد اصابت گلوله‌های سه نوع اسلحه وجود دارد یا خیر؟ برای این منظور چهار مرحله آزمون تحلیل واریانس را تکمیل نمایید.
۱. تعریف فرض‌ها: - فرض صفر ( $H_0$ ): میانگین تعداد اصابت گلوله‌ها برای هر سه نوع سلاح برابر است. - فرض یک ( $H_1$ ): حداقل یکی از میانگین‌ها با دیگران متفاوت است.
۲. آماره آزمون: - جدول تحلیل واریانس: \begin{tabular}{|c|c|c|c|c|} \hline \text{منبع تغییرات} & \text{مجموع توان‌های دوم} & \text{درجه آزادی} & \text{میانگین توان‌های دوم} & \text{آماره آزمون} \\ \hline \text{تیمارها} & \text{SS(tr)} = 18 & & \text{MS(tr)} = \ldots & F = \ldots \\ \text{خطا} & \text{SSE} = \ldots & & \text{MSE} = \ldots & \\ \hline \text{جمع} & \text{SST} = 586 & & & \\ \hline \end{tabular}
۳. مقدار بحرانی:
۴. تصمیم‌گیری: - با توجه به مقدار آماره آزمون و مقدار بحرانی، تصمیم بگیرید که آیا فرض صفر رد می‌شود یا خیر.

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Problem 64438

Suppose that $\lim _{(x, y) \rightarrow(5,2)} f(x, y)=7$ . What can you say about the value of $f(5,2)$ ? We can say $f(5,2)=\infty$ . We can say $f(5,2)$ is an open point. We can say $\lim _{(x, y) \rightarrow(5,2)} f(x, y)=f(5,2)=7$ . We can say $\underset{(x, y) \rightarrow(5,2)}{ } f(x, y)=f(5,2)=\infty$ . In general, nothing can be said about the value of $f(5,2)$ .
What if $f$ is continuous? We can say $f(5,2)=\infty$ . We can say $f(5,2)$ is an open point. We can say $(x, y) \rightarrow(5,2)$ . We can say $\lim _{(x, y) \rightarrow(5,2)} f(x, y)=f(5,2)=\infty$ . In general, nothing can be said about the value of $f(5,2)$ .

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Problem 64439

Determine the set of points at which the function is continuous. $f(x, y)=\left\{\begin{array}{ll} \frac{x^{2} y^{3}}{2 x^{2}+y^{2}} & \text { if }(x, y) \neq(0,0) \\ 1 & \text { if }(x, y)=(0,0) \end{array}\right.$ $\{(x, y) \mid x>0$ and $y>0\}$ $\{(x, y) \mid(x, y) \neq(0,0)\}$ $\{(x, y) \mid x \in \mathbb{R}$ and $y \neq 0\}$ $\{(x, y) \mid x \in \mathbb{R}$ and $y \in \mathbb{R}\}$ $\{(x, y) \mid x \cdot y \neq 0\}$

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Problem 64440

Use implicit differentiation to find $\partial z / \partial x$ and $\partial z / \partial y$ . $\begin{array}{c} e^{3 z}=x y z \\ \frac{\partial z}{\partial x}=\square \\ \frac{\partial z}{\partial y}=\square \end{array}$ Submit Answer

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Problem 64441

Prob 1
1. A line was measured to have 5 tallies, 6 pins, and 63.5 links. How long is the line in feet?
2. A line was measured with a 50 m tape. There were 5 tallies, 8 pins, and the distance from the last pin to the end line was 2.25 m . Find the length of the line in meters.
3. A distance was measured and was recorded to have a value equivalent to 8 perches, 6 rods, and 45 varas. Compute the total distance in meters.

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Problem 64442

Find the indicated partial derivative. $\begin{array}{c} f(x, y, z)=e^{x y z^{5}} ; \quad f_{x y z} \\ f_{x y z}(x, y, z)=\square \end{array}$

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Problem 64443

Suppose $(1,1)$ is a critical point of a function $f$ with continuous second derivatives. In each case, what can you say about $f$ ? (a) $f_{x x}(1,1)=6, f_{x y}(1,1)=2, f_{y y}(1,1)=1$ The critical point $(1,1)$ is a local minimum. The critical point $(1,1)$ is a local maximum. The critical point $(1,1)$ is a saddle point. Nothing can be determined about the critical point $(1,1)$ . (b) $f_{x x}(1,1)=6, f_{x y}(1,1)=3, f_{y y}(1,1)=1$ The critical point $(1,1)$ is a local minimum. The critical point $(1,1)$ is a local maximum. The critical point $(1,1)$ is a saddle point. Nothing can be determined about the critical point $(1,1)$ .

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Problem 64444

3. б) $y=3 \log _{2} x$ .
Сравните числа: а) $\log _{\frac{3}{5}} 3,07$ и 1 ; б) $\log _{3} 10$ и $\lg 3$ .
4. Решите уравнения:

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Problem 64445

1. From the figure below, P is directed at an angle $\alpha$ from x -axis and the 200 N force is acting at a slope of 5 vertical to 12 horizontal. a. Find the value of F and $\alpha$ if $\mathrm{T}=450 \mathrm{~N}, \mathrm{P}=250 \mathrm{~N}, \beta=30^{\circ}$ , and the resultant is 300 N acting up along the y -axis. Answer: $F=484.92 \mathrm{~N}, \alpha=61.22$ 。 b. Find the value of F and $\alpha$ if $\mathrm{T}=450 \mathrm{~N}, \mathrm{P}=250 \mathrm{~N}, \beta=30^{\circ}$ and the resultant is zero. Answer: $F=264.85 \mathrm{~N}, \alpha=28.16$ 。
2. From Figure below, $P$ is directed at an angle $\alpha$ from $x$ -axis and the 200 N force is acting at a slope of 5 vertical to 12 horizontal. a. Find P and $\alpha$ if the resultant is 500 N upward to the right with a slope of 3 horizontal to 4 vertical. Answer: $P=490.68 \mathrm{~N}, \alpha=76.40$

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Problem 64446

7. Evaluate $\lim _{x \rightarrow 0}(2-x) \tan \left(\frac{\pi x}{2}\right)$ $\begin{array}{l} \lim _{x \rightarrow 0}(-2-x)^{\tan \left(\frac{\pi x}{2}\right)} \\ =(2-0)^{\tan \frac{\pi(0)}{2}} \\ =(2-0)^{\tan \frac{0}{2}} \\ =(2-0)^{\circ} \\ =1 \end{array}$

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Problem 64447

11. movir cosrs In the United States, the average movie ticket price (in dollars) since 1974 can be modeled by $0.131 x+1.89$ where $x$ is the number of years since 1974. What values of $x$ should you use to find the ticket prices in 1974. 1984. 1994, and 2004 ? Find the ticket prices for those years.
11. $\qquad$

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Problem 64448

Exercice 1. 1) Montrer en utilisant la définition que $\lim _{x \rightarrow 1} 4 x+2=6, \lim _{x \rightarrow 0} x^{3}+x+2=2, \lim _{x \rightarrow+\infty} \frac{1}{x^{3}+1}=0$ 2) Montrer que les limites $\lim _{x \rightarrow 1} E(x), \lim _{x \rightarrow 0} \cos \frac{1}{x}$ n'existent pas.
Exercice 2. Calculer les limites suivantes:
1. $\lim _{x \rightarrow 0} \frac{\tan x-\sin x}{x^{3}}$ ,
2. $\lim _{x \rightarrow \frac{\pi}{2}} \frac{e^{\cos x}-1}{x-\frac{\pi}{2}}$ ,
3. $\lim _{x \rightarrow 0} \frac{x}{a} E$ $-1-2 x)$ ,
5. $\lim _{x \rightarrow+\infty}\left(\sqrt{x^{2}+2 x-1}-2 x\right)$ , 6. $\lim _{x \rightarrow+\infty}\left(1+\frac{1}{x}\right)^{x}$ ,
7. $\lim _{x \rightarrow-\infty}\left(\frac{x-1}{x+1}\right)^{x}$ .
Exercice 3. Soit $f: \mathbb{R} \longrightarrow \mathbb{R}$ , une fonction définie par $f(x)=\left\{\begin{array}{ll} x & \text { si }|x| \leqslant 1 \\ x^{2}+a x+b & \text { si }|x|>1 \end{array}\right.$
Où $a, b \in \mathbb{R}$ . Déterminer les valeurs de $a$ et $b$ pour que $f$ soit continue sur $\mathbb{R}$ . Exercice 4. Soit $f: \mathbb{R} \longrightarrow \mathbb{R}$ la fonction définie par $f(x)=\left\{\begin{array}{l} 1 \text { si } x \in \mathbb{Q} \\ 0 \text { si } \notin \mathbb{Q} . \end{array}\right.$
Montrer que $f$ est discontinue en tout point de $\mathbb{R}$ . Exercice 5. Soit $f$ une fonction définie par $f:[a, b] \rightarrow[a, b]$ , telle que $\left|f\left(x_{1}\right)-f\left(x_{2}\right)\right|<\left|x_{1}-x_{2}\right|, \quad \forall x_{1}, x_{2} \in[a, b], \quad\left(x_{1} \neq x_{2}\right) .$ 1) Montrer que $f$ est continue sur $[a, b]$ . 2) Montrer que l'équation $f(x)=x$ admet une solution unique.
Exercice 6. Étudier dans chacun des cas suivants si la fonction $f$ est prolongeable par continuité sur $\mathbb{R}$ . 1) $f: x \longrightarrow \frac{1-\cos \sqrt{|x|}}{|x|}$ , 2) $f: x \longrightarrow \sin (x) \cdot \sin \left(\frac{1}{x}\right)$ , 3) $f: x \longrightarrow \frac{x^{3}+1}{x^{2}+3 x+2}$ , 4) $f: x \longrightarrow 1-\cos \left(1-\cos \frac{1}{x-2}\right)$ , 5) $f: x \longrightarrow \frac{\sin |x-4|}{x-4}$ , 6) $f: x \longrightarrow \frac{1}{1-x}-\frac{2}{1-x^{2}}$ .

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Problem 64449

e) $\sum_{n=1}^{\infty} \frac{7^{n}}{4^{n}-3}$

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Problem 64450

Ready Graph Systems of Linear Equations - Quiz - Level H
Two groups are hiking on a glacier. Group B starts 1 mile ahead of Group A and walks 2 miles per hour. To catch up to Group B, Group A walks 3 miles per hour. $x$ : hours since the start of the hike $y$ : miles from the start of the trail Which equation shows Group A's distance from the start? $y=3 x$ $y=x+1$ $y=x+3$ $y=3 x+1$

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Problem 64451

1) Développe $(\sqrt{5}+1)^{2}$ et $(\sqrt{5}-1)^{2}$ . En déduire une expression plus simple de $A=\sqrt{6+2 \sqrt{5}} \quad \text { et } B=\sqrt{6-2 \sqrt{5}}$

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Problem 64452

32500 صندوق، 2000 دئر 2000 بنك ، 525 نور وميار، 875 عمولة وكلاء الشراء، 2500 جمارك مشتريات، 3500 مردود المبيعات، 2000 ايجار، 625 خصم مسموح به، 32500 مصاريف نتل مبيعات، 1250 عمولة وكلاء البيع، 14000 أنات، 175000 عملاء، 1750 مردود مشتريات، 4000 مسحوبات، 13635 خصم مكتسب، 1125 فواند داننة، 6000 أوراق مالية ، 8750أوراق دفع، 1300 مصروف دعاية وإعلان ، 13625 موردون، 127500 راس المال. إذا علمت أن بضاعة أخر المدة قدرت ب 35875 المطلوب: 1. إعداد قائمة الدخل (قَائمة نتيجة الاعمال) عن السنة المنتهية في 2018/12/31

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Problem 64453

(10) The sequences $a_{n}=\frac{e^{n}+e^{-n}}{e^{2 n}+1}$ (a) converges to 0 (b) converges to 1 (c) converges to $\frac{1}{2}$ (d) diverges (11) $\int_{2}^{\infty} \frac{d x}{\sqrt{x^{3}-1}}$ (a) converges by direct comparison with $\int_{2}^{\infty} \frac{d x}{x^{3 / 2}}$ (b) diverges by direct comparison with $\int_{2}^{\infty} \frac{d x}{x^{3}}$ (c) converges by limit comparison with $\int_{2}^{\infty} \frac{d x}{x^{3 / 2}}$ (d) diverges by limit comparison with $\int_{2}^{\infty} \frac{d x}{x^{3}}$ (12) The series $\sum_{n=1}^{\infty} \ln \left(1+\frac{1}{n^{2}}\right)$ (a) converges to $\ln 2$ (b) diverges by L.C.T. with $\sum_{n=1}^{\infty} \frac{1}{n}$ (c) converges L.C.T. with $\sum_{n=1}^{\infty} \frac{1}{n^{2}}$ (d) divegres by D.C.T with $\sum_{n=1}^{\infty} \frac{1}{n}$ (13) $\int_{3}^{\infty} \frac{\ln ^{2} x}{x^{3}} d x$ (a) converges by direct comparison with $\int_{3}^{\infty} \frac{d x}{x^{3}}$ (b) diverges by direct comparison with $\int_{3}^{\infty} \frac{d x}{x}$ C. converges by direct comparison with $\int_{3}^{\infty} \frac{d x}{x^{2}}$ (d) diverges by direct comparison with $\int_{3}^{\infty} \frac{d x}{\sqrt{x}}$

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Problem 64454

Evaluate the definite integral. $\begin{array}{l} \int_{0}^{1}\left(5 x^{2}-4 x+7\right) d x \\ \int_{0}^{1}\left(5 x^{2}-4 x+7\right) d x= \end{array}$ (Simplify your answer.)

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Problem 64455

2024-12
1. $\sum_{k=1}^{\infty} \frac{\sqrt{k}+3}{2 \sqrt{k}+1}$ $2 \sum_{k=1}^{\infty} \frac{k^{2}+k}{7 k+1}$
3. $\sum_{k=1}^{\infty} \frac{5 k+4}{4 k+3}$
4. $\sum_{k=1}^{\infty} \frac{k+4}{k^{2}+5}$
5. $\sum_{k=1}^{\infty} \frac{1}{\sqrt{k+7}}$ a. 3 and 5 b. 1 and 3 c. 2 and 4

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Problem 64456

浙江科技大学考试试卷
4. The state of plane stress at a point with respect to the $x y$ -axes is shown in Figure. Determine the principal stresses and principal planes. Show the results on a sketch of an element aligned with the principal directions. (25 points）

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Problem 64457

What is the output, or $y$ -value, when you input $x=7$ into the function: $\begin{array}{l} y=4 x+1 \\ y=\square \end{array}$

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Problem 64458

3. $\log _{2}^{2} x+(x-1) \log _{2} x=6-2 x$

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Problem 64459

10. Use simplex method to solve $\begin{aligned} \text { Maximize } z & =7 x_{1}+5 x_{2} \\ \text { Subjected to } & 2 x_{1}+x_{2} \leq 10 \\ & 4 x_{1}+3 x_{2} \leq 24 \\ & x_{1} \geq 0, x_{2} \geq 0 \end{aligned}$

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Problem 64460

Question Id : 109899 9 of
Which inequality statements are represented by the number line graph? Choose two. $x>2$ $x \geq 2$ $x \leq 2$ $2 \leq x$ $2 \geq x$ $2<x$

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Problem 64461

$(4-i)(2+5 i)$ a. $2(4+9 i)$ c. $3+18 i$ b. $(13+18 i)$ d. $(8+18 i)$

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Problem 64462

1 Die Punkte $A(1|2| 1), B(-2|4| 1)$ und $C(4|1|-1)$ legen eine Ebene fest. Geben Sie für die Ebene eine a) Parametergleichung b) Koordinatengleichung an.

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Problem 64463

Question Id : 387568
Which set of numbers is in the solution set of the inequality $x<14$ ?
A $\{3,7,9,10,12\}$
B $\{15,18,20,21,23\}$
C $\{17,21,24,25,31\}$
D $\{23,27,29,30,36\}$

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Problem 64464

3. $\log _{2}^{2} x+(x-1) \log _{2} x=6-2 x$

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Problem 64465

Problem B Find all $x \in \mathbb{R}$ that solve this equation: $x^{4}+x^{2}-x-1=1-x-x^{2}-x^{4}$

See Solution

Problem 64466

Question Progress Homework Progress 23 / 45 Marks
Mary invests $£ 12000$ in a savings account. The account pays $1.5 \%$ compound interest per year. Work out the value of her investment after 2 years.

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Problem 64467

15 ცნობილია, რომ C წერტილი ძევს წრფეზე, 0 C D X რომლის განტოლებაა y=x და დაშორებულია A(6; 1) წერტილიდან 5 ერ- თეულის ტოლი მანძილით. იპოვეთ C წერტილის კოორდინატები.

See Solution

Problem 64468

$\left(5 w^{2}-w+6\right)+\left(-2 w^{2}+7 w+4\right)$

See Solution

Problem 64469

If $\left[\begin{array}{lll}3 & 7 & 1\end{array}\right] \cdot\left[\begin{array}{l}5 \\ 3 \\ 6\end{array}\right]=\left[x_{1}\right]$ , what is the value of $x_{1}$ ? If the matrix operation is not possible, write "none".

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Problem 64470

15 из 45 Следующий 37:32 II
Ученый изучает популяцию белок в определенном регионе в течение нескольких лет. Изначально там 24 белки, и популяция белок удваивается каждый год.
Какая функция лучше всего представляет количество белок в регионе в концехлет? Обоснуйте свой ответ.
A $f(x)=x^{2}-24$ , поскольку функция растет на одинаковую разницу каждый год и лучше всего представляется линейной функцией.
5 $f(x)=24\left(2^{x}\right)$ , поскольку функция ежегодно увеличивается в 2 раза и лучше всего ее можно представить экспоненциальной функцией.
C $f(x)=2 x+24$ , поскольку функция ежегодно увеличивается на постоянный коэффициент 2 и лучше всего представляется линейной функцией.
Д $f(x)=2\left(24^{x}\right)$ , поскольку функция ежегодно увеличивается в 2 раза и лучше всего ее можно представить экспоненциальной функцией.

See Solution

Problem 64471

2. Determine all values of $x$ on the interval $0^{\circ} \leq x \leq 360^{\circ}$ that satisfy $\cos (2 x)=0$ .

See Solution

Problem 64472

Mr. Ishimoto ordered $x$ new math books and $y$ new workbooks for his class. The totat weight of the box of books cannot be more than 50 pounds. If each math book weighs 3.2 pounds and each workbook weighs 0.8 pounds, which inequality represents the maximum numberfof each type of book that can be shipped in a single box? $3.2 x+0.8 y<50$ $3.2 x+0.8 y \leq 50$ $0.8 x+3.2 y<50$ $0.8 x+3.2 y \leq 50$

See Solution

Problem 64473

6. Solve the equation $5 \cos (2 \alpha)+3=0$ for all values of $\alpha$ on the interval $0^{\circ} \leq \alpha \leq 360^{\circ}$ . Round all answers to the nearest tenth of a degree.

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Problem 64474

Simplify the expression. Write your answe $y^{2}(-4 y+5)-6 y^{2}$

See Solution

Problem 64475

Wvich function nas the greatest $y$ -intercept? $01.01: 57$ II
B
D The values in the table reflect a linear equation. \begin{tabular}{|c|c|c|c|c|} \hline $x$ & -1 & 1 & 2 & 5 \\ \hline $y$ & -1 & 3 & 5 & 11 \\ \hline \end{tabular} D）L

See Solution

Problem 64476

Match each polynomial function to its graph. $\begin{array}{l} f(x)=x^{4}+15 x^{3}+81 x^{2}+185 x+150=(x+5)^{2}(x+3)(x+2) \\ g(x)=x^{2}+2 \end{array}$ $f(x)=x^{4}+15 x^{3}+81 x^{2}+185 x+150 \quad g(x)=x^{2}+2$

See Solution

Problem 64477

25 и3 45 Следующий 01:06:22
Прокат велосипедов на пляже стоит $\$ 5$ плюс $\$ 2$ в час. Напишите функцию для моделирования этой ситуации и постройте ее график ниже.
Прокат велосипедов Рэй Отменить
Переделать Перезагрузить D2LL

See Solution

Problem 64478

Question
Express $(x-11)^{2}$ as a trinomial in standard form.
Answer Attempt 1 out of 2

See Solution

Problem 64479

Find the sine, cosine, and tangent of $\angle G$ .
Write your answer in simplified, rationalized form. Do not round. $\begin{array}{l} \sin (G)=\square \\ \cos (G)=\square \\ \tan (G)=\square \end{array}$

See Solution

Problem 64480

5. A car begins driving from a stationary position. It accelerates at $4 \mathrm{~m} / \mathrm{s}^{2}$ for 10 seconds, then travels at a steady speed for another 10 seconds, all in the same direction. How much distance has it covered since it started driving? Answer: 600 m

See Solution

Problem 64481

Simplify the expression $\left(\frac{3 a^{5} b^{5}}{a b^{2}}\right)^{2}$ A $9 a^{8} b^{6}$
B $6 a^{8} b^{6}$
C $6 a^{16} b^{9}$
D $9 a^{6} b^{5}$

See Solution

Problem 64482

Solve for $x$ . Round to the nearest tenth, if necessary.

See Solution

Problem 64483

5. Find the domain of the function: $f(x)=\frac{x-6}{(x+4)(x-8)}$ $(-4, \infty)$ $(-4,8) \cup(-8, \propto$ $(-\infty,-4) \cup(-4$ $(-\infty,-4) \cup(-4$ ,
Clear All

See Solution

Problem 64484

$\frac{\left(2 x^{6}\right)^{3}}{\left(8 x^{5}\right)^{2}}$
Write your answer using only positive exponents.

See Solution

Problem 64485

49. A flat surface that extends forever in all directions is called a $\qquad$ a. Line b. Point c. Ray d. Plane

See Solution

Problem 64486

8. Sketch a graph where $f(4)$ does not exist but $\lim _{x \rightarrow 4} \quad f(x)$ does exist.

See Solution

Problem 64487

Unit 3 17) Scientists want to find out if playing video games with violent content makes kids more prone to violar behavior. The scientists might have children come into a lab and have a certain number play a highty, violent video game, another group play a somewhat violent video game, and then a last group play a game with no violence. The scientists would then watch the kids play with other children and record any violent behavior. This is an example of an $\qquad$ study. a. experimental b. observational 18) The average size sultcase that can fit under an airplane seat is 15.25 inches. The margin of error is $\pm 2.5$ inches. Which of the following would not fit under the airplane seat? a. 12.5 b. 13 c. 17 d. 17.5
For \#19-20 indicate which sampling technique is described. 19) Kevin wants to find out the opinions of college students about the availability of parking spaces. He surveys students as they walk by his car. a. simple random b. stratified random c. systematic random d. cluster e. convenience 20) A teacher wants to survey 10 of her 30 students. She places their names on popsicle sticks and draws the sticks out of the cup to see who will take the survey. a. simple random b. stratified random c. systematic random d. cluster e. convenience 21) Is this question an Open Question or a Closed Question: What is your favorite flavor of ice cream? a. Open Question b. Closed Question
For \#22-23 use the table that represents the average number of inches of precipitation per month in Seattle to answer the questions. \begin{tabular}{|c|c|} \hline Month & \begin{tabular}{c} Average Rainfall per \\ Month (inches) \end{tabular} \\ \hline January & 4.81 \\ \hline February & 3.43 \\ \hline March & 3.51 \\ \hline April & 2.77 \\ \hline May & 2.16 \\ \hline June & 1.63 \\ \hline July & 0.79 \\ \hline August & 0.97 \\ \hline September & 1.52 \\ \hline October & 3.41 \\ \hline November & 7.05 \\ \hline December & 5.85 \\ \hline \end{tabular} 22) What is the median of the data? a. 3.16 b. 3.09 c. 4.16 d. 1.56 23) What is the IQR of the data? a. 4.16 b. 1.56 c. 2.59 d. 3.16

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Problem 64488

9. For which values of the parameter $c \in \mathbb{R}$ is the vector $(1,1, c)$ a linear combination of the vectors $(2,1,3),(1,2,4),(3,0,2),(2,-2,-2)$ ?

See Solution

Problem 64489

9. Claire invests $\$ 1900$ in an account with a $3.2 \%$ annual interestrate compounded continuously. If she does not make any other deposits or withdraws, how much will be in Claire's account after 6 months? 36 months?
10. Uma borrows $\$ 2900$ with a $0.9 \%$ annual simple interest rate. If Uma does not make any payments, how much will Uma owe after 18 months? 3 years?
11. Pedro borrows $\$ 300$ with a $5.3 \%$ annual interest rate compounded continuously. If he does not make any payments, how much will Pedro owe after 1 year? 2 years?
12. Gianna invests $\$ 9800$ in an account with a $0.5 \%$ annual interest rate compounded semiannually, making no other deposits or withdrawals. What will Gianna's account balance be after 5 years? 10 years?

See Solution

Problem 64490

What is the sum of the given polynomials in standard form? $\left(x^{2}-3 x\right)+\left(-2 x^{2}+5 x-3\right)$ $-3 x^{2}+8 x-3$ $-x^{2}-2 x-3$ $3 x^{2}-8 x+3$ $-x^{2}+2 x-3$

See Solution

Problem 64491

13. Jane wants to invest $\$ 2000$ at a bank offering three different accounts. Account $A$ earns $1.2 \%$ annual simple interest, Account B earns $1.2 \%$ interest compounded annually, and Account $C$ earns $1.2 \%$ interest compounded continuously. If no other deposits or withdrawals are made, compare the balances of the accounts after each period of time. a.) 1 year b. 2 years c. 5 years
14. Jessen wants to invest $\$ 10,000$ at a bank offering three different accounts. Account $A$ earns $3.1 \%$ annual simple interest, Account B earns $3.1 \%$ interest compounded annually, and Account C earns $3.1 \%$ interest compounded continuously. If no other deposits or withdrawals are made, compare the balances of the accounts after each period of time. a. 1 year b. 5 years c. 10 years

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Problem 64492

1. An electrician wishes to cut a nichrome wire $\left(p=1.00 \times 10^{-6} \Omega \cdot m\right)$ that has $10.0 \Omega$ of resistance. The wire has a cross-sectional area of $1.65 \times 10^{-8} \mathrm{~m}^{2}$ . Approximately what length of wire has a resistance equal to $10.0 \Omega$ ? (3)

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Problem 64493

QUESTION 10 - 1 POINT Let $y$ be defined implicitly by the equation $-4 x^{2}+7 y^{4}-2 x-3 y=44$
Use implicit differentiation to find $\frac{d y}{d x}$ .
Provide your answer below: $\frac{d y}{d x}=$ $\square$

See Solution

Problem 64494

Write an equation of a line perpendicular to the line $4 x-3 y=15$ and passes through the point $(8,-5)$ .

See Solution

Problem 64495

Order the expressions by choosing $>,<$ , or $=$ . $\begin{array}{ll} 2^{4} \times 2^{2} & \square \end{array} 2^{8}$
$x$

See Solution

Problem 64496

1- Calcule a integral iterada: a) $\int_{\frac{1}{3}}^{\frac{1}{2}} \int_{0}^{\pi} \int_{0}^{1} z x^{2} \cos (x y) d z d y d x$ (2,5 valores)

See Solution

Problem 64497

Factor completely. $y^{2}+13 y-14$ $\square$
Savbanswer

See Solution

Problem 64498

Bài 13: Để phòng chống dịch Covid - 19. Tỉnh Bà Rịa-Vũng Tàu đã thành lập các đội phản úng nhanh bao gồm 16 bác sĩ hồi sức cấp cứu, 24 bác sĩ đa khoa và 40 điều dưỡng viên. Hỏi có thề thành lập nhiều nhất bao nhiêu đội phản ứng nhanh, trong đó các bác sĩ và điều dưỡng viên chia đều vào mỗi đội.

See Solution

Problem 64499

Mised number Improper fraction \begin{tabular}{|l|c|l|} \hline A. & $2 \frac{4}{5}$ & $14 / 5$ \\ \hline B. & $4 \frac{3}{4}$ & \\ \hline C. & $3 \frac{1}{4}$ & \\ \hline D. & $6 \frac{3}{8}$ & \\ \hline \end{tabular}

See Solution

Problem 64500

Graph the function. $f(x)=3 \sqrt{x-2}$
Plot four points on the graph of the function: the le

See Solution

Math

Problem 64401

Consider the figure. a. Find the perimeter of the figure. Then find the approximate perimeter by using 3.14 for π\piπ. b. Find the area of the figure. Then find the approximate area by using 3.14 for π\piπ.

Problem 64402

15 Original Total: $42\$ 42$42 Tip Percent: 15\%

Problem 64403

Find the discriminant. 2v2−v=02 v^{2}-v=02v2−v=0How many real solutions does the equation have? no real one real two real solutions solution solutions Submit

Problem 64404

Problem 64405

Problem 64406

Sales: $42,500\$ 42,500$42,500 Commission Rate: 3%3 \%3% the amount of interest.

Problem 64407

Problem 64408

Divide. If the polynomial does not divide evenly, include the remainder as a fraction. (−3k2+24k−61)÷(k−5)\left(-3 k^{2}+24 k-61\right) \div(k-5)(−3k2+24k−61)÷(k−5) □\square□ Submit

Problem 64409

Problem 64410

What is 9x0+8y0+3\sqrt{9 x^{0}+8 y^{0}+3}9x0+8y0+3​ in its SIMPlest torm?

Problem 64411

Problem 64412

14 Solve the system using substitution: {2x−y=3x=−2y−1\left\{\begin{array}{l} 2 x-y=3 \\ x=-2 y-1 \end{array}\right.{2x−y=3x=−2y−1​Solution - write as an ordered pair, (x,y)(x, y)(x,y)

Problem 64413

Problem 64414

Problem 64415

x4−13x2−12x=0x^{4}-13 x^{2}-12 x=0x4−13x2−12x=0

Problem 64416

The line parallel to y=23x+1y=\frac{2}{3} x+1y=32​x+1 that passes through the point (3,6)(3,6)(3,6)

Problem 64417

Question Watch Video Show ExamplesArianna throws a ball up in the air. The graph below shows the height of the ball hhh in meters after ttt seconds. After how many seconds does the ball hit the ground?

Problem 64418

Question Watch Video Show ExamplesAjay throws a ball up in the air. The graph below shows the height of the ball hhh in meters after ttt seconds. What is the ball's greatest height?

Problem 64419

How many different roots does the polynomial function, y=(x+4)(x−2)2(x+7)y=(x+4)(x-2)^{2}(x+7)y=(x+4)(x−2)2(x+7) have? A. 4 B. 3 C. 1 D. 2

Problem 64420

MULTIPLE-CHOICE QUESTIONSince there is an OF before 50 , is 50 the part or the whole?WholePart

Problem 64421

Knowing that 50 is OF\mathbf{O F}OF will it be the numerator (number on top) or the denominator (number on bottom)? □\square□ Numerator □\square□ Denominator

Problem 64422

Simplify, using only positive exponents in your answer. x−5+y−4x−4+y−3\frac{x^{-5}+y^{-4}}{x^{-4}+y^{-3}}x−4+y−3x−5+y−4​

Problem 64423

Problem 64424

問題 64 平面において, 原点を中心に π6\frac{\pi}{6}6π​ 回転移動させてから, 直線 y=−2xy=-2 xy=−2x に関して対称移動させても動かない点を求めよ。

Problem 64425

What is the oxidation state of each element in K2Cr2O7\mathrm{K}_{2} \mathrm{Cr}_{2} \mathrm{O}_{7}K2​Cr2​O7​ ?K CrO □\square□

Problem 64426

Problem 64427

2. Определить, не вычисляя, знак интеграла: а) ∫12(x2−4x+3)dx\int_{1}^{2}\left(x^{2}-4 x+3\right) d x∫12​(x2−4x+3)dx б) ∫π2πxsin⁡xdx\int_{\frac{\pi}{2}}^{\pi} x \sin x d x∫2π​π​xsinxdx

Problem 64428

the function defined by f(x)=3e2x5xf(x)=\frac{3 e^{2 x}}{5 x}f(x)=5x3e2x​. Give the interval(s) for which fff is increasing and decreasing. Also, give the xxx :e of any extrema (maximum or minimum values, (2 points each)7creasing \qquad ecreasing \qquad aximum(s) \qquad inimum(s) \qquad

Problem 64429

Ex: Find dwdt\frac{d w}{d t}dtdw​ at t=0t=0t=0 for ω=ln⁡(x2+y2+z2),x=los⁡ty=sin⁡tz=4t.\begin{aligned} \omega=\ln \left(x^{2}+y^{2}+z^{2}\right), x & =\operatorname{los} t \\ y & =\sin t \\ z & =4 \sqrt{t} . \end{aligned}ω=ln(x2+y2+z2),xyz​=lost=sint=4t​.​

Problem 64430

Problem 64431

Problem 64432

What is cos⁡28∘?\cos 28^{\circ} ?cos28∘? A. 1517\frac{15}{17}1715​ B. 817\frac{8}{17}178​ c. 815\frac{8}{15}158​ D. 158\frac{15}{8}815​

Problem 64433

7) y′−ytg⁡x=cos⁡xy^{\prime}-y \operatorname{tg} x=\cos xy′−ytgx=cosx

Problem 64434

Select all of the options which are true of the perpendicular bisector of line AB . ``` It is a fixed distance from line AB It meets line AB at 90 It passes through A It meets line AB at 180 It passes through B It does not meet line AB ``` It passes through the midpoint of line AB

Problem 64435

36x2−y2+144x+8y+119=036 x^{2}-y^{2}+144 x+8 y+119=036x2−y2+144x+8y+119=0 (a) Find the standard form of the equation of (y−4)29−(x+2)24=1\frac{(y-4)^{2}}{9}-\frac{(x+2)^{2}}{4}=19(y−4)2​−4(x+2)2​=1

Problem 64436

Problem 64437

Problem 64438

Problem 64439

Problem 64440

Problem 64441

Problem 64442

Find the indicated partial derivative. f(x,y,z)=exyz5;fxyzfxyz(x,y,z)=□\begin{array}{c} f(x, y, z)=e^{x y z^{5}} ; \quad f_{x y z} \\ f_{x y z}(x, y, z)=\square \end{array}f(x,y,z)=exyz5;fxyz​fxyz​(x,y,z)=□​

Problem 64443

Problem 64444

3. б) y=3log⁡2xy=3 \log _{2} xy=3log2​x.Сравните числа: а) log⁡353,07\log _{\frac{3}{5}} 3,07log53​​3,07 и 1 ; б) log⁡310\log _{3} 10log3​10 и lg⁡3\lg 3lg3.4. Решите уравнения:

Problem 64445

Problem 64446

Problem 64447

Problem 64448

Problem 64449

e) ∑n=1∞7n4n−3\sum_{n=1}^{\infty} \frac{7^{n}}{4^{n}-3}∑n=1∞​4n−37n​

Problem 64450

Problem 64451

1) Développe (5+1)2(\sqrt{5}+1)^{2}(5​+1)2 et (5−1)2(\sqrt{5}-1)^{2}(5​−1)2. En déduire une expression plus simple de A=6+25 et B=6−25A=\sqrt{6+2 \sqrt{5}} \quad \text { et } B=\sqrt{6-2 \sqrt{5}}A=6+25​​ et B=6−25​​

Consider the figure. a. Find the perimeter of the figure. Then find the approximate perimeter by using 3.14 for $\pi$ . b. Find the area of the figure. Then find the approximate area by using 3.14 for $\pi$ .

15 Original Total: $\$ 42$ Tip Percent: 15\%

Find the discriminant. $2 v^{2}-v=0$
How many real solutions does the equation have? no real one real two real solutions solution solutions Submit

Sales: $\$ 42,500$ Commission Rate: $3 \%$ the amount of interest.

Divide. If the polynomial does not divide evenly, include the remainder as a fraction. $\left(-3 k^{2}+24 k-61\right) \div(k-5)$ $\square$ Submit

What is $\sqrt{9 x^{0}+8 y^{0}+3}$ in its SIMPlest torm?

14 Solve the system using substitution: $\left\{\begin{array}{l} 2 x-y=3 \\ x=-2 y-1 \end{array}\right.$
Solution - write as an ordered pair, $(x, y)$

$x^{4}-13 x^{2}-12 x=0$

The line parallel to $y=\frac{2}{3} x+1$ that passes through the point $(3,6)$

Question Watch Video Show Examples
Arianna throws a ball up in the air. The graph below shows the height of the ball $h$ in meters after $t$ seconds. After how many seconds does the ball hit the ground?

Question Watch Video Show Examples
Ajay throws a ball up in the air. The graph below shows the height of the ball $h$ in meters after $t$ seconds. What is the ball's greatest height?

How many different roots does the polynomial function, $y=(x+4)(x-2)^{2}(x+7)$ have? A. 4 B. 3 C. 1 D. 2

MULTIPLE-CHOICE QUESTION
Since there is an OF before 50 , is 50 the part or the whole?
Whole
Part

Knowing that 50 is $\mathbf{O F}$ will it be the numerator (number on top) or the denominator (number on bottom)? $\square$ Numerator $\square$ Denominator

Simplify, using only positive exponents in your answer. $\frac{x^{-5}+y^{-4}}{x^{-4}+y^{-3}}$

問題 64 平面において, 原点を中心に $\frac{\pi}{6}$ 回転移動させてから, 直線 $y=-2 x$ に関して対称移動させても動かない点を求めよ。

What is the oxidation state of each element in $\mathrm{K}_{2} \mathrm{Cr}_{2} \mathrm{O}_{7}$ ?
K Cr
O $\square$

2. Определить, не вычисляя, знак интеграла: а) $\int_{1}^{2}\left(x^{2}-4 x+3\right) d x$ б) $\int_{\frac{\pi}{2}}^{\pi} x \sin x d x$

the function defined by $f(x)=\frac{3 e^{2 x}}{5 x}$ . Give the interval(s) for which $f$ is increasing and decreasing. Also, give the $x$ :e of any extrema (maximum or minimum values, (2 points each)
7creasing $\qquad$ ecreasing $\qquad$ aximum(s) $\qquad$ inimum(s) $\qquad$

Ex: Find $\frac{d w}{d t}$ at $t=0$ for $\begin{aligned} \omega=\ln \left(x^{2}+y^{2}+z^{2}\right), x & =\operatorname{los} t \\ y & =\sin t \\ z & =4 \sqrt{t} . \end{aligned}$

What is $\cos 28^{\circ} ?$ A. $\frac{15}{17}$ B. $\frac{8}{17}$ c. $\frac{8}{15}$ D. $\frac{15}{8}$

7) $y^{\prime}-y \operatorname{tg} x=\cos x$

$36 x^{2}-y^{2}+144 x+8 y+119=0$ (a) Find the standard form of the equation of $\frac{(y-4)^{2}}{9}-\frac{(x+2)^{2}}{4}=1$

Find the indicated partial derivative. $\begin{array}{c} f(x, y, z)=e^{x y z^{5}} ; \quad f_{x y z} \\ f_{x y z}(x, y, z)=\square \end{array}$

3. б) $y=3 \log _{2} x$ .
Сравните числа: а) $\log _{\frac{3}{5}} 3,07$ и 1 ; б) $\log _{3} 10$ и $\lg 3$ .
4. Решите уравнения:

e) $\sum_{n=1}^{\infty} \frac{7^{n}}{4^{n}-3}$

1) Développe $(\sqrt{5}+1)^{2}$ et $(\sqrt{5}-1)^{2}$ . En déduire une expression plus simple de $A=\sqrt{6+2 \sqrt{5}} \quad \text { et } B=\sqrt{6-2 \sqrt{5}}$

Evaluate the definite integral. $\begin{array}{l} \int_{0}^{1}\left(5 x^{2}-4 x+7\right) d x \\ \int_{0}^{1}\left(5 x^{2}-4 x+7\right) d x= \end{array}$ (Simplify your answer.)

浙江科技大学考试试卷
4. The state of plane stress at a point with respect to the $x y$ -axes is shown in Figure. Determine the principal stresses and principal planes. Show the results on a sketch of an element aligned with the principal directions. (25 points）

What is the output, or $y$ -value, when you input $x=7$ into the function: $\begin{array}{l} y=4 x+1 \\ y=\square \end{array}$

3. $\log _{2}^{2} x+(x-1) \log _{2} x=6-2 x$

Question Id : 109899 9 of
Which inequality statements are represented by the number line graph? Choose two. $x>2$ $x \geq 2$ $x \leq 2$ $2 \leq x$ $2 \geq x$ $2<x$

$(4-i)(2+5 i)$ a. $2(4+9 i)$ c. $3+18 i$ b. $(13+18 i)$ d. $(8+18 i)$

1 Die Punkte $A(1|2| 1), B(-2|4| 1)$ und $C(4|1|-1)$ legen eine Ebene fest. Geben Sie für die Ebene eine a) Parametergleichung b) Koordinatengleichung an.

Question Id : 387568
Which set of numbers is in the solution set of the inequality $x<14$ ?
A $\{3,7,9,10,12\}$
B $\{15,18,20,21,23\}$
C $\{17,21,24,25,31\}$
D $\{23,27,29,30,36\}$

3. $\log _{2}^{2} x+(x-1) \log _{2} x=6-2 x$

Problem B Find all $x \in \mathbb{R}$ that solve this equation: $x^{4}+x^{2}-x-1=1-x-x^{2}-x^{4}$

Question Progress Homework Progress 23 / 45 Marks
Mary invests $£ 12000$ in a savings account. The account pays $1.5 \%$ compound interest per year. Work out the value of her investment after 2 years.

$\left(5 w^{2}-w+6\right)+\left(-2 w^{2}+7 w+4\right)$

If $\left[\begin{array}{lll}3 & 7 & 1\end{array}\right] \cdot\left[\begin{array}{l}5 \\ 3 \\ 6\end{array}\right]=\left[x_{1}\right]$ , what is the value of $x_{1}$ ? If the matrix operation is not possible, write "none".

2. Determine all values of $x$ on the interval $0^{\circ} \leq x \leq 360^{\circ}$ that satisfy $\cos (2 x)=0$ .

6. Solve the equation $5 \cos (2 \alpha)+3=0$ for all values of $\alpha$ on the interval $0^{\circ} \leq \alpha \leq 360^{\circ}$ . Round all answers to the nearest tenth of a degree.

Simplify the expression. Write your answe $y^{2}(-4 y+5)-6 y^{2}$