Function

Problem 2501

מצא את תחום ההגדרה של $f(x)=|2x-3|+1$ ושרטט את הפונקציה בגרף. הצג גם את התמונה שלה.

See Solution

Problem 2502

Calculate the integral: $\int \frac{\cos (\ln (x))}{x} d x$ .

See Solution

Problem 2503

Derive the equation $2as = v^2 - u^2$ for final velocity $v$ , initial velocity $u$ , acceleration $a$ , and displacement $s$ .

See Solution

Problem 2504

Derive the formula for final velocity: $V_f = V_i + a t$ .

See Solution

Problem 2505

Find the derivative of $y=x^{3} \ln (x)$ with respect to $x$ : $\frac{d y}{d x}$ .

See Solution

Problem 2506

If $(a+2,63)=\left(-1, b^{3}-1\right)$ , find $\sqrt{a^{2}+b^{2}}=\ldots$ (a) 25 (b) 7 (c) 5 (d) $\pm 5$

See Solution

Problem 2507

What happens to speed in these cases?
1. Distance doubles, time same.
2. Distance quarters, time same.
3. Distance triples, time halves.
4. Distance and time constant.

See Solution

Problem 2508

Find the value of $x$ that minimizes the function $f(x)=(x+7)^{2}+4$ .

See Solution

Problem 2509

Define relative speed in these scenarios:
1. Car at $80 \mathrm{~km/h}$ , relative speed $80 \mathrm{~km/h}$ .
2. Relative speed $100 \mathrm{~km/h}$ , real speed $50 \mathrm{~km/h}$ .
3. Relative speed $20 \mathrm{~km/h}$ , real speed $100 \mathrm{~km/h}$ .
4. Relative speed $0$ , real speed $70 \mathrm{~km/h}$ . - For a car at $200 \mathrm{~km/h}$ , find relative speed to:
1. An observer at rest.
2. An observer moving at $100 \mathrm{~km/h}$ in the same direction.
3. An observer moving at $100 \mathrm{~km/h}$ in the opposite direction.

See Solution

Problem 2510

Define relative speed in these scenarios:
1. Speed $80 \mathrm{~km/h}$ , relative speed $80 \mathrm{~km/h}$ .
2. Relative speed $100 \mathrm{~km/h}$ , real speed $50 \mathrm{~km/h}$ .
3. Relative speed $20 \mathrm{~km/h}$ , real speed $100 \mathrm{~km/h}$ .
4. Relative speed $0$ , real speed $70 \mathrm{~km/h}$ .
For a car at $200 \mathrm{~km/h}$ :
1. Relative speed to a stationary observer?
2. Relative speed to a $100 \mathrm{~km/h}$ observer in the same direction?
3. Relative speed to a $100 \mathrm{~km/h}$ observer in the opposite direction?
4. Relative speed to a $200 \mathrm{~km/h}$ observer in the same direction?

See Solution

Problem 2511

מהו תחום ההגדרה של הפונקציה $g(x)=\sqrt{2x-4}$ ?

See Solution

Problem 2512

מצא את הגרף של הפונקציה $f(x)=\sqrt{3-x}$ .

See Solution

Problem 2513

Determine the domain of the function $f(x)=x^{2}+2x+3$ .

See Solution

Problem 2514

Find $g(f(x))$ for $g(x)=\sqrt{x-1}$ and $f(x)=\sqrt{3-x}$ .

See Solution

Problem 2515

Find $f(2)$ if $f(0)=86$ and $f(x)$ decreases by $80\%$ for each increase of $x$ by 1.

See Solution

Problem 2516

Graph the function $f(x)=1-2 \sqrt{x+1}$ .

See Solution

Problem 2517

Jamie Wong wants to build a portfolio with stocks L (40%) and M (60%). Calculate:
a. Expected return $r_{p}$ for each year (2013-2018). b. Average return $\bar{r}_{p}$ over 6 years. c. Standard deviation $\sigma_{r_{p}}$ over 6 years. d. Correlation of returns for stocks L and M. e. Benefits of diversification in the portfolio.

See Solution

Problem 2518

Jamie Wong's portfolio has stocks L (40%) and M (60%). Calculate: a) annual return $r_{p}$ , b) average return $\bar{r}_{p}$ , c) standard deviation $\sigma_{r_{p}}$ , d) correlation of returns, e) diversification benefits.

See Solution

Problem 2519

Calculate the rate of return for January using: $\frac{(E_{1}+W)-(E_{0}+D)}{E_{0}+D}$ with $E_0=1200$ , $D=800$ , $E_1=2300$ , $W=500$ .

See Solution

Problem 2520

If $x$ and $y$ are directly proportional and $x=15$ gives $y=20$ , find $y$ when $x=18$ .

See Solution

Problem 2521

If $x$ and $y$ are direct and inverse proportions, find $y$ when $x=18$ and $x$ when $y=6$ .

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Problem 2522

A box of pencils is shared among $x$ children with each getting $n$ pencils in inverse proportion. If $x=25$ , $n=8$ . For $x=16$ , can they share equally? Explain.

See Solution

Problem 2523

Calculate the time to deposit 0.50 g of gold (atomic mass 197) using a current of 0.10 A and Faraday's constant $F = 96485 \mathrm{C}$ .

See Solution

Problem 2524

Convert $41^{\circ} F$ to $C$ and $5^{\circ} C$ to $F$ . Explain the relationship between the conversion formulas.

See Solution

Problem 2525

Find the volume between a cone and a cube, with the cone's base inscribed in the cube's face. Use edge length $s$ .

See Solution

Problem 2526

Find the formula for the function $f(x)$ : square $x$ , subtract 16, then take the square root.

See Solution

Problem 2527

Find the perimeter of a rectangle with area $100 \mathrm{~m}^{2}$ as a function of one side's length.

See Solution

Problem 2528

Find the area between $y=e^{x}$ , $y=x^{2}$ , from $x=0$ to $x=1$ .

See Solution

Problem 2529

Find the slant asymptotes of the curve given by the equation $y=\sqrt{x^{2}+4 x}$ .

See Solution

Problem 2530

Calculate $\log_2{128}$ .

See Solution

Problem 2531

A car travels south at 60 km/h and a plane flies east at 650 km/h. Find distances and separation at 1:30 PM.

See Solution

Problem 2532

Evaluate the integral: $\int \frac{1}{5 x^{2}-30 x+65} dx$

See Solution

Problem 2533

出租车费用为 $c(x)=3x+2.00$ ，斜率表示什么？ A. 每分钟费用增加 \$2.00 B. 总费用为 \$3.00 C. 每次费用为 \$2.00 D. 每分钟费用增加 \$3.00

See Solution

Problem 2534

Find points $(x, y)$ where $\nabla f(x, y)=(0,0)$ for $f(x, y)=\frac{x^{3}}{3}-\frac{y^{3}}{3}+3xy$ and classify them.

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Problem 2535

Evaluate the following limits as $x$ approaches 0:
1. $\lim _{x \rightarrow 0} \frac{(1+x) \sin x-x \cos x}{x^{2}}$
2. $\lim _{x \rightarrow 0} \frac{e^{x^{2}}-\cos x}{x \sin x}$
3. $\lim _{x \rightarrow 0} \frac{\sin x-x e^{x}+x^{2}}{x(\cos x-1)}$
4. $\lim _{x \rightarrow 0}\left\{\frac{1}{\sin ^{2} x}-\frac{1}{x^{2}}\right\}$

See Solution

Problem 2536

A customer wants a 5-line ad for $\$ 45.00$ max. Suggest the best package based on the rates provided.

See Solution

Problem 2537

Commuters and parking spaces data: a) Find the correlation coefficient. b) Find critical values for $r$ . c) Check for significant correlation at 0.05 level. d) State the conclusion.
CPI and subway fare data: a) Find regression equation with CPI as $x$ . b) Predict subway fare for CPI = 182.5.

See Solution

Problem 2538

Calcule o valor $A$ usando a fórmula $A=\frac{P V_{A}^{*} i}{1-(1+i)^{-n}}$ com $P=40.000.000$ , $i=0,12$ e $n=5$ .

See Solution

Problem 2539

Integrate: $\int \frac{2 x+5}{\sqrt{4 x^{2}-20 x+29}} d x$ (15 pts, 1a: 5 pts)

See Solution

Problem 2540

极差为多少？计算 $\sqrt{8} \times \frac{1}{2}-(\sqrt{3})^{0}$ ，分解 $x^{2}+2xy+y^{2}$ ， $y$ 随 $x$ 的变化情况。

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Problem 2541

Calculate the surface area from revolving $x=\frac{1}{3}(y^{2}+2)^{3/2}$ around the x-axis for $1 \leq y \leq 2$ .

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Problem 2542

某公司有两个农产品基地，产量关系为 $y=2x+3$ 。求甲、乙基地存入仓库量及总量 $p$ 与天数 $x$ 的函数关系。

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Problem 2543

Maximize $Z=3x+4y$ graphically with constraints: $x+y \leq 4$ , $x \geq 0$ , $y \geq 0$ .

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Problem 2544

Find the coordinates of the minimum point of the graph of $x^{2}-7x+11$ .

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Problem 2545

Find the minimum number of '?' in a regex pattern that intersects with all given patterns. Example: patterns = ["ha???rrank", "?a? ke?bank"].

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Problem 2546

Find values of $a$ , $b$ , and $c$ for $f(x)=x^{3}+5$ based on given pairs: $a=f(0)$ , $b=f^{-1}(32)$ , $c=f(7)$ . Select correct option.

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Problem 2547

Find the ordered pair $(x, y)$ that completes the pattern: $(0, 0)$ , $(1, 8)$ , $(2, 16)$ , $(4, 32)$ .

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Problem 2548

Calculate the average rate of change of $f(x)=2 x^{4}-3 x$ from $x=-1$ to $x=2$ .

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Problem 2549

What is the selling price for 6 blueberry muffins if the cost per muffin is \$0.54, food cost is 30\%, and a 10\% discount is applied?

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Problem 2550

Find the acute related angle for an angle in standard position of $120^{\circ}$ . Options: $60^{\circ}$ , $225^{\circ}$ , $-45^{\circ}$ , $-225^{\circ}$ .

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Problem 2551

Find the correct expression for $\tan \theta$ for point $P(x, y)$ on a terminal arm of angle $\theta$ in the second quadrant. Options: $\frac{y}{r}$ , $\frac{x}{r}$ , $\frac{-x}{y}$ , $\frac{y}{-x}$ .

See Solution

Problem 2552

Find $\frac{d y}{d x}$ in terms of $t$ for $x=\sin(t)$ and $y=\cos^2(t)$ . Simplify your expression.

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Problem 2553

Find $\frac{d y}{d x}$ in terms of $t$ for the equations $x=\sin^3 t$ and $y=\cos^4 t$ .

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Problem 2554

Find and simplify $\frac{d y}{d x}$ using the parametric equations $x=\sin(t)$ and $y=\cos^2(t)$ .

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Problem 2555

Find $\frac{d y}{d x}$ in terms of $t$ for the equations $x=\sin(t)$ , $y=\cos^2(t)$ .

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Problem 2556

Johanna fährt mit $22 \mathrm{~km/h}$ . Wann muss sie starten, um um 7:45 an der $15 \mathrm{~km}$ entfernten Schule zu sein?

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Problem 2557

What is the value of $g(x) - f(x)$ for the functions $f(x)=5$ and $g(x)=5x$ ? Choose from: a. $g(5)$ , b. $f(5)$ , c. $f(2x)$ , d. $g(x-1)$ .

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Problem 2558

Identify the correct function $m(x)$ , which is three times the input minus 15. Choose from the options provided.

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Problem 2559

Identify the line with a steeper slope and higher $y$ -intercept than $y=f(x)=a x+b$ from options a. $y=10 x+5.5$ or b. $y=3 x+7.5$ .

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Problem 2560

Find a linear function with a greater slope and $y$ -intercept than $y=f(x)=a x+b$ given points (-1, 5), (1, 9), (3, 13), (5, 17). Options: a. $y=10 x+5.5$ , b. $y=3 x+7.5$ .

See Solution

Problem 2561

Find the rate of change of sales $S(t) = 10,000 + 2000t - 200t^2$ at $t=0$ , $t=4$ , and $t=8$ weeks.

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Problem 2562

Evaluate the integral: $\int \frac{3 a x}{b^{2}+c^{2} x^{2}} \, dx$

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Problem 2563

An airplane accelerates at $3.20 \mathrm{~m} / \mathrm{s}^{2}$ for $32.8 \mathrm{~s}$ . Find the distance before takeoff.

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Problem 2564

Determine the pattern connecting the pairs: (12, 9), (7, 4), (2, ?), (6, 5), (4, 5), (9, 10).

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Problem 2565

Find $g(-6)$ for the function $g(x)=10x-6$ .

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Problem 2566

Find the zero of the function $f(x)=2(2)^{x}-16$ . Enter a number.

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Problem 2567

Find the two-year par yield given zero rates of 5.10\%, 5.00\%, 4.80\%, and 4.75\%. Show discounted cash flows. Round to 4 decimal places.

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Problem 2568

Monthly sales (in thousands) for a music store are given by $S(t)=\frac{200}{t^{2}+36}$ . Find $S(2)$ , $S'(2)$ , and estimate sales for month 3.

See Solution

Problem 2569

Find the price per television set, $p$ , for maximum profit using $C(x)=60,000+60x$ and $p=200-\frac{x}{50}$ .

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Problem 2570

Monthly sales for a record album are given by $S(t)=\frac{200 t}{t^{2}+36}$ . Find: a) $S(2)$ , b) $S^{\prime}(2)$ , c) estimate sales in month 3 using (a) and (b).

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Problem 2571

Find the values of: (a) $\sin \frac{\pi}{3}$ , (b) $\cos \frac{2 \pi}{3}$ , and $\tan \frac{7 \pi}{4}$ in surd form.

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Problem 2572

A shop sells $T$ -shirts for R 25 each with monthly fixed costs of R 2,000. Complete the formula: $c=25n+\ldots$ .

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Problem 2573

Diberikan fungsi $f(x)=2x-1$ dan $g(x)=\sqrt{2x-5}$ . Temukan: a. Hasil kali $f(x) \cdot g(x)$ . b. Domain dari $f(x) \cdot g(x)$ .

See Solution

Problem 2574

Solve for $x$ if $2 \sin x \cos x = \sin x$ .

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Problem 2575

Diberi $W$ berubah langsung dengan $x^{2}$ dan songsang dengan $z$ . Jika $W=20$ untuk $x=5$ , $z=2$ , cari $z$ untuk $W=160$ , $x=40$ .

See Solution

Problem 2576

Solve $\sin 2 x=\cos (x-30)$ for $-90^{\circ} \leq x<90^{\circ}$ .

See Solution

Problem 2577

Masa $t$ jam untuk memasang mesin berubah songsang dengan bilangan pekerja $w$ . Jika 4 pekerja memerlukan 165 minit, (a) ungkapkan $t$ dalam $w$ . (b) Berapa minit yang diambil oleh 10 pekerja?

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Problem 2578

(a) Ungkapkan $t$ dalam sebutan $w$ . (b) Nyatakan masa yang diambil oleh 10 orang pekerja untuk memasang sebuah mesin dalam minit.

See Solution

Problem 2579

Diketahui $f(x)=2x+1$ dan $g(x)=4-x^{2}$ . Hitung: a. $(f \circ g)(x)$ b. $(g \circ f)(x)$

See Solution

Problem 2580

Tentukan $f(g(x))$ untuk $f(x)=\frac{x-1}{x+1}, x \neq-1$ dan $g(x)=\frac{1}{x}$ .

See Solution

Problem 2581

Diketahui $(f \circ g)(x)=x^{2}+2 x-3$ dan $f(x)=x+3$ . Temukan $g(x)$ dan nilai $g(-2)$ .

See Solution

Problem 2582

Tentukan $(f \circ g)(5)$ untuk $f(x)=x+2$ dan $g(x)=\frac{2 x-1}{x+4}, x \neq-4$ .

See Solution

Problem 2583

Find the general solution for $\sin (x-30)=\cos 2x$ .

See Solution

Problem 2584

Find the range of the functions $f(x)=\sin \left(x-30^{\circ}\right)$ and $g(x)=1038$ .

See Solution

Problem 2585

Find values of $a$ and $b$ for $f(x)=a \cos b \theta$ and $g(x)=c \tan \theta$ intersecting at $P(58^\circ, 1.6)$ and $Q$ .

See Solution

Problem 2586

Find the free extrema of the function $z=-2x^{2}+22y^{2}-192y+x^{2}y$ .

See Solution

Problem 2587

Find the free extremes of the function $z=3 x^{2}-8 y^{2}+64 y-y x^{2}$ .

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Problem 2588

Một ô tô đi từ tỉnh $A$ đến tỉnh $B$ . Sau 1 giờ, ô tô đã đi $\frac{2}{5}$ quãng đường. Hỏi thời gian để đi hết quãng đường $A B$ ?

See Solution

Problem 2589

A 3-digit number divided by the sum of its digits equals 26. Reversing the digits exceeds it by 198. Find the ten's digit.

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Problem 2590

已知函数 $f(x)$ 满足 $f(x+1)=\left\{\begin{array}{ll}a x+a, & x \leq-1 \\ \ln (x+1), & x>-1\end{array}\right.$ ，函数 $g(x)=f(x)-f(-x)$ 有5个零点，求 $a$ 的取值范围。选项为： A. $\left(-\frac{1}{e}, 0\right)$ B. $\left(0, \frac{1}{e}\right)$ C. $\left(-\frac{1}{e}, \frac{1}{e}\right)$ D. $\left(\frac{1}{e},+\infty\right)$

See Solution

Problem 2591

Find the linear function that passes through the points $(-2, 8)$ , $(1, 5)$ , $(3, 13)$ , and $(5, 29)$ .

See Solution

Problem 2592

Identify a function that fits the points $(-2, 8)$ , $(1, 5)$ , $(3, 13)$ , and $(5, 29)$ .

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Problem 2593

Tentukan titik minimum dari fungsi kuadratik $f(x)=x^{2}-6x+5$ . Koordinatnya adalah $(1,5)$ .

See Solution

Problem 2594

Tentukan titik minimum dari fungsi kuadratik $f(x)=x^{2}-6x+5$ .

See Solution

Problem 2595

Find the inverse $f^{-1}(x)$ of $f(x)=e^{2x-3}-2$ , its domain and range. Sketch $f$ and $f^{-1}$ . Also, find $(f \cdot g)(x)$ for $g(x)=\ln 3x$ .

See Solution

Problem 2596

Find the inverse $f^{-1}(x)$ of $f(x)=e^{2x-3}-2$ and its domain/range. Sketch $f$ and $f^{-1}$ . For $g(x)=\ln 3x$ , find $(f \cdot g)(x)$ .

See Solution

Problem 2597

Find the inverse $f^{-1}(x)$ of $f(x)=e^{2 x-3}-2$ , its domain and range. Sketch $f$ and $f^{-1}$ . Calculate $(f \cdot g)(x)$ for $g(x)=\ln 3 x$ .

See Solution

Problem 2598

Find the inverse $f^{-1}(x)$ of $f(x)=e^{2x-3}-2$ , its domain/range, sketch $f$ and $f^{-1}$ , and compute $(f \cdot g)(x)$ for $g(x)=\ln 3x$ .

See Solution

Problem 2599

Find the inverse $f^{-1}(x)$ of $f(x)=e^{2 x-3}-2$ and its domain/range. Sketch $f$ and $f^{-1}$ . For $g(x)=\ln 3 x$ , find $(f \cdot g)(x)$ .

See Solution

Problem 2600

Find a formula for the perimeter of a rectangle with area $100 \mathrm{~m}^{2}$ as a function of one side's length.

See Solution

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Function

Problem 2501

מצא את תחום ההגדרה של f(x)=∣2x−3∣+1f(x)=|2x-3|+1f(x)=∣2x−3∣+1 ושרטט את הפונקציה בגרף. הצג גם את התמונה שלה.

Problem 2502

Calculate the integral: ∫cos⁡(ln⁡(x))xdx\int \frac{\cos (\ln (x))}{x} d x∫xcos(ln(x))​dx.

Problem 2503

Derive the equation 2as=v2−u22as = v^2 - u^22as=v2−u2 for final velocity vvv, initial velocity uuu, acceleration aaa, and displacement sss.

Problem 2504

Derive the formula for final velocity: Vf=Vi+atV_f = V_i + a tVf​=Vi​+at.

Problem 2505

Find the derivative of y=x3ln⁡(x)y=x^{3} \ln (x)y=x3ln(x) with respect to xxx: dydx\frac{d y}{d x}dxdy​.

Problem 2506

If (a+2,63)=(−1,b3−1)(a+2,63)=\left(-1, b^{3}-1\right)(a+2,63)=(−1,b3−1), find a2+b2=…\sqrt{a^{2}+b^{2}}=\ldotsa2+b2​=… (a) 25 (b) 7 (c) 5 (d) ±5\pm 5±5

Problem 2507

What happens to speed in these cases? 1. Distance doubles, time same. 2. Distance quarters, time same. 3. Distance triples, time halves. 4. Distance and time constant.

Problem 2508

Find the value of xxx that minimizes the function f(x)=(x+7)2+4f(x)=(x+7)^{2}+4f(x)=(x+7)2+4.

Problem 2509

Problem 2510

Problem 2511

מהו תחום ההגדרה של הפונקציה g(x)=2x−4g(x)=\sqrt{2x-4}g(x)=2x−4​?

Problem 2512

מצא את הגרף של הפונקציה f(x)=3−xf(x)=\sqrt{3-x}f(x)=3−x​.

Problem 2513

Determine the domain of the function f(x)=x2+2x+3f(x)=x^{2}+2x+3f(x)=x2+2x+3.

Problem 2514

Find g(f(x))g(f(x))g(f(x)) for g(x)=x−1g(x)=\sqrt{x-1}g(x)=x−1​ and f(x)=3−xf(x)=\sqrt{3-x}f(x)=3−x​.

Problem 2515

Find f(2)f(2)f(2) if f(0)=86f(0)=86f(0)=86 and f(x)f(x)f(x) decreases by 80%80\%80% for each increase of xxx by 1.

Problem 2516

Graph the function f(x)=1−2x+1f(x)=1-2 \sqrt{x+1}f(x)=1−2x+1​.

Problem 2517

Problem 2518

Jamie Wong's portfolio has stocks L (40%) and M (60%). Calculate: a) annual return rpr_{p}rp​, b) average return rˉp\bar{r}_{p}rˉp​, c) standard deviation σrp\sigma_{r_{p}}σrp​​, d) correlation of returns, e) diversification benefits.

Problem 2519

Calculate the rate of return for January using: (E1+W)−(E0+D)E0+D\frac{(E_{1}+W)-(E_{0}+D)}{E_{0}+D}E0​+D(E1​+W)−(E0​+D)​ with E0=1200E_0=1200E0​=1200, D=800D=800D=800, E1=2300E_1=2300E1​=2300, W=500W=500W=500.

Problem 2520

If xxx and yyy are directly proportional and x=15x=15x=15 gives y=20y=20y=20, find yyy when x=18x=18x=18.

Problem 2521

If xxx and yyy are direct and inverse proportions, find yyy when x=18x=18x=18 and xxx when y=6y=6y=6.

Problem 2522

A box of pencils is shared among xxx children with each getting nnn pencils in inverse proportion. If x=25x=25x=25, n=8n=8n=8. For x=16x=16x=16, can they share equally? Explain.

Problem 2523

Calculate the time to deposit 0.50 g of gold (atomic mass 197) using a current of 0.10 A and Faraday's constant F=96485CF = 96485 \mathrm{C}F=96485C.

Problem 2524

Convert 41∘F41^{\circ} F41∘F to CCC and 5∘C5^{\circ} C5∘C to FFF. Explain the relationship between the conversion formulas.

Problem 2525

Find the volume between a cone and a cube, with the cone's base inscribed in the cube's face. Use edge length sss.

Problem 2526

Find the formula for the function f(x)f(x)f(x): square xxx, subtract 16, then take the square root.

Problem 2527

Find the perimeter of a rectangle with area 100 m2100 \mathrm{~m}^{2}100 m2 as a function of one side's length.

Problem 2528

Find the area between y=exy=e^{x}y=ex, y=x2y=x^{2}y=x2, from x=0x=0x=0 to x=1x=1x=1.

Problem 2529

Find the slant asymptotes of the curve given by the equation y=x2+4xy=\sqrt{x^{2}+4 x}y=x2+4x​.

Problem 2530

Calculate log⁡2128\log_2{128}log2​128.

Problem 2531

A car travels south at 60 km/h and a plane flies east at 650 km/h. Find distances and separation at 1:30 PM.

Problem 2532

Evaluate the integral: ∫15x2−30x+65dx\int \frac{1}{5 x^{2}-30 x+65} dx∫5x2−30x+651​dx

Problem 2533

出租车费用为 c(x)=3x+2.00c(x)=3x+2.00c(x)=3x+2.00，斜率表示什么？ A. 每分钟费用增加 \$2.00 B. 总费用为 \$3.00 C. 每次费用为 \$2.00 D. 每分钟费用增加 \$3.00

Problem 2534

Find points (x,y)(x, y)(x,y) where ∇f(x,y)=(0,0)\nabla f(x, y)=(0,0)∇f(x,y)=(0,0) for f(x,y)=x33−y33+3xyf(x, y)=\frac{x^{3}}{3}-\frac{y^{3}}{3}+3xyf(x,y)=3x3​−3y3​+3xy and classify them.

Problem 2535

Problem 2536

A customer wants a 5-line ad for $45.00\$ 45.00$45.00 max. Suggest the best package based on the rates provided.

Problem 2537

Commuters and parking spaces data: a) Find the correlation coefficient. b) Find critical values for rrr. c) Check for significant correlation at 0.05 level. d) State the conclusion. CPI and subway fare data: a) Find regression equation with CPI as xxx. b) Predict subway fare for CPI = 182.5.

Problem 2538

Calcule o valor AAA usando a fórmula A=PVA∗i1−(1+i)−nA=\frac{P V_{A}^{*} i}{1-(1+i)^{-n}}A=1−(1+i)−nPVA∗​i​ com P=40.000.000P=40.000.000P=40.000.000, i=0,12i=0,12i=0,12 e n=5n=5n=5.

Problem 2539

Integrate: ∫2x+54x2−20x+29dx\int \frac{2 x+5}{\sqrt{4 x^{2}-20 x+29}} d x∫4x2−20x+29​2x+5​dx (15 pts, 1a: 5 pts)

Problem 2540

极差为多少？计算 8×12−(3)0\sqrt{8} \times \frac{1}{2}-(\sqrt{3})^{0}8​×21​−(3​)0，分解 x2+2xy+y2x^{2}+2xy+y^{2}x2+2xy+y2，yyy 随 xxx 的变化情况。

Problem 2541

Calculate the surface area from revolving x=13(y2+2)3/2x=\frac{1}{3}(y^{2}+2)^{3/2}x=31​(y2+2)3/2 around the x-axis for 1≤y≤21 \leq y \leq 21≤y≤2.

Problem 2542

מצא את תחום ההגדרה של $f(x)=|2x-3|+1$ ושרטט את הפונקציה בגרף. הצג גם את התמונה שלה.

Calculate the integral: $\int \frac{\cos (\ln (x))}{x} d x$ .

Derive the equation $2as = v^2 - u^2$ for final velocity $v$ , initial velocity $u$ , acceleration $a$ , and displacement $s$ .

Derive the formula for final velocity: $V_f = V_i + a t$ .

Find the derivative of $y=x^{3} \ln (x)$ with respect to $x$ : $\frac{d y}{d x}$ .

If $(a+2,63)=\left(-1, b^{3}-1\right)$ , find $\sqrt{a^{2}+b^{2}}=\ldots$ (a) 25 (b) 7 (c) 5 (d) $\pm 5$

What happens to speed in these cases?
1. Distance doubles, time same.
2. Distance quarters, time same.
3. Distance triples, time halves.
4. Distance and time constant.

Find the value of $x$ that minimizes the function $f(x)=(x+7)^{2}+4$ .

מהו תחום ההגדרה של הפונקציה $g(x)=\sqrt{2x-4}$ ?

מצא את הגרף של הפונקציה $f(x)=\sqrt{3-x}$ .

Determine the domain of the function $f(x)=x^{2}+2x+3$ .

Find $g(f(x))$ for $g(x)=\sqrt{x-1}$ and $f(x)=\sqrt{3-x}$ .

Find $f(2)$ if $f(0)=86$ and $f(x)$ decreases by $80\%$ for each increase of $x$ by 1.

Graph the function $f(x)=1-2 \sqrt{x+1}$ .

Jamie Wong's portfolio has stocks L (40%) and M (60%). Calculate: a) annual return $r_{p}$ , b) average return $\bar{r}_{p}$ , c) standard deviation $\sigma_{r_{p}}$ , d) correlation of returns, e) diversification benefits.

Calculate the rate of return for January using: $\frac{(E_{1}+W)-(E_{0}+D)}{E_{0}+D}$ with $E_0=1200$ , $D=800$ , $E_1=2300$ , $W=500$ .

If $x$ and $y$ are directly proportional and $x=15$ gives $y=20$ , find $y$ when $x=18$ .

If $x$ and $y$ are direct and inverse proportions, find $y$ when $x=18$ and $x$ when $y=6$ .

A box of pencils is shared among $x$ children with each getting $n$ pencils in inverse proportion. If $x=25$ , $n=8$ . For $x=16$ , can they share equally? Explain.

Calculate the time to deposit 0.50 g of gold (atomic mass 197) using a current of 0.10 A and Faraday's constant $F = 96485 \mathrm{C}$ .

Convert $41^{\circ} F$ to $C$ and $5^{\circ} C$ to $F$ . Explain the relationship between the conversion formulas.

Find the volume between a cone and a cube, with the cone's base inscribed in the cube's face. Use edge length $s$ .

Find the formula for the function $f(x)$ : square $x$ , subtract 16, then take the square root.

Find the perimeter of a rectangle with area $100 \mathrm{~m}^{2}$ as a function of one side's length.

Find the area between $y=e^{x}$ , $y=x^{2}$ , from $x=0$ to $x=1$ .

Find the slant asymptotes of the curve given by the equation $y=\sqrt{x^{2}+4 x}$ .

Calculate $\log_2{128}$ .

Evaluate the integral: $\int \frac{1}{5 x^{2}-30 x+65} dx$

出租车费用为 $c(x)=3x+2.00$ ，斜率表示什么？ A. 每分钟费用增加 \$2.00 B. 总费用为 \$3.00 C. 每次费用为 \$2.00 D. 每分钟费用增加 \$3.00

Find points $(x, y)$ where $\nabla f(x, y)=(0,0)$ for $f(x, y)=\frac{x^{3}}{3}-\frac{y^{3}}{3}+3xy$ and classify them.

A customer wants a 5-line ad for $\$ 45.00$ max. Suggest the best package based on the rates provided.

Commuters and parking spaces data: a) Find the correlation coefficient. b) Find critical values for $r$ . c) Check for significant correlation at 0.05 level. d) State the conclusion.
CPI and subway fare data: a) Find regression equation with CPI as $x$ . b) Predict subway fare for CPI = 182.5.

Calcule o valor $A$ usando a fórmula $A=\frac{P V_{A}^{*} i}{1-(1+i)^{-n}}$ com $P=40.000.000$ , $i=0,12$ e $n=5$ .

Integrate: $\int \frac{2 x+5}{\sqrt{4 x^{2}-20 x+29}} d x$ (15 pts, 1a: 5 pts)

极差为多少？计算 $\sqrt{8} \times \frac{1}{2}-(\sqrt{3})^{0}$ ，分解 $x^{2}+2xy+y^{2}$ ， $y$ 随 $x$ 的变化情况。

Calculate the surface area from revolving $x=\frac{1}{3}(y^{2}+2)^{3/2}$ around the x-axis for $1 \leq y \leq 2$ .

某公司有两个农产品基地，产量关系为 $y=2x+3$ 。求甲、乙基地存入仓库量及总量 $p$ 与天数 $x$ 的函数关系。

Maximize $Z=3x+4y$ graphically with constraints: $x+y \leq 4$ , $x \geq 0$ , $y \geq 0$ .

Find the coordinates of the minimum point of the graph of $x^{2}-7x+11$ .

Find values of $a$ , $b$ , and $c$ for $f(x)=x^{3}+5$ based on given pairs: $a=f(0)$ , $b=f^{-1}(32)$ , $c=f(7)$ . Select correct option.

Find the ordered pair $(x, y)$ that completes the pattern: $(0, 0)$ , $(1, 8)$ , $(2, 16)$ , $(4, 32)$ .

Calculate the average rate of change of $f(x)=2 x^{4}-3 x$ from $x=-1$ to $x=2$ .

Find the acute related angle for an angle in standard position of $120^{\circ}$ . Options: $60^{\circ}$ , $225^{\circ}$ , $-45^{\circ}$ , $-225^{\circ}$ .

Find the correct expression for $\tan \theta$ for point $P(x, y)$ on a terminal arm of angle $\theta$ in the second quadrant. Options: $\frac{y}{r}$ , $\frac{x}{r}$ , $\frac{-x}{y}$ , $\frac{y}{-x}$ .

Find $\frac{d y}{d x}$ in terms of $t$ for $x=\sin(t)$ and $y=\cos^2(t)$ . Simplify your expression.

Find $\frac{d y}{d x}$ in terms of $t$ for the equations $x=\sin^3 t$ and $y=\cos^4 t$ .

Find and simplify $\frac{d y}{d x}$ using the parametric equations $x=\sin(t)$ and $y=\cos^2(t)$ .

Find $\frac{d y}{d x}$ in terms of $t$ for the equations $x=\sin(t)$ , $y=\cos^2(t)$ .

Johanna fährt mit $22 \mathrm{~km/h}$ . Wann muss sie starten, um um 7:45 an der $15 \mathrm{~km}$ entfernten Schule zu sein?

What is the value of $g(x) - f(x)$ for the functions $f(x)=5$ and $g(x)=5x$ ? Choose from: a. $g(5)$ , b. $f(5)$ , c. $f(2x)$ , d. $g(x-1)$ .

Identify the correct function $m(x)$ , which is three times the input minus 15. Choose from the options provided.

Identify the line with a steeper slope and higher $y$ -intercept than $y=f(x)=a x+b$ from options a. $y=10 x+5.5$ or b. $y=3 x+7.5$ .

Find a linear function with a greater slope and $y$ -intercept than $y=f(x)=a x+b$ given points (-1, 5), (1, 9), (3, 13), (5, 17). Options: a. $y=10 x+5.5$ , b. $y=3 x+7.5$ .

Find the rate of change of sales $S(t) = 10,000 + 2000t - 200t^2$ at $t=0$ , $t=4$ , and $t=8$ weeks.

Evaluate the integral: $\int \frac{3 a x}{b^{2}+c^{2} x^{2}} \, dx$

An airplane accelerates at $3.20 \mathrm{~m} / \mathrm{s}^{2}$ for $32.8 \mathrm{~s}$ . Find the distance before takeoff.

Find $g(-6)$ for the function $g(x)=10x-6$ .

Find the zero of the function $f(x)=2(2)^{x}-16$ . Enter a number.

Monthly sales (in thousands) for a music store are given by $S(t)=\frac{200}{t^{2}+36}$ . Find $S(2)$ , $S'(2)$ , and estimate sales for month 3.

Find the price per television set, $p$ , for maximum profit using $C(x)=60,000+60x$ and $p=200-\frac{x}{50}$ .

Monthly sales for a record album are given by $S(t)=\frac{200 t}{t^{2}+36}$ . Find: a) $S(2)$ , b) $S^{\prime}(2)$ , c) estimate sales in month 3 using (a) and (b).

Find the values of: (a) $\sin \frac{\pi}{3}$ , (b) $\cos \frac{2 \pi}{3}$ , and $\tan \frac{7 \pi}{4}$ in surd form.

A shop sells $T$ -shirts for R 25 each with monthly fixed costs of R 2,000. Complete the formula: $c=25n+\ldots$ .

Diberikan fungsi $f(x)=2x-1$ dan $g(x)=\sqrt{2x-5}$ . Temukan: a. Hasil kali $f(x) \cdot g(x)$ . b. Domain dari $f(x) \cdot g(x)$ .

Solve for $x$ if $2 \sin x \cos x = \sin x$ .