Browse Equation problems Studdy Solved!

Problem 11101

$\sin ^{2} \theta+2 \cos ^{2} \theta-1=\cos ^{2} \theta$

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Problem 11102

Billie is planning to rent a car while on vacation. The equation $C=0.65 m+55$ models the relation between the cost in dollars, $C$ , per day and the number of miles, $m$ , she drives in one day. What is the cost on a day when Billie drives the car 0 miles? 200 miles?
Plot these two points to graph the equation.

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Problem 11103

Том, жижиг ачааны машины даац нийлээд 14 тонн бөгөөд 10 том, 22 жижиг ачааны машин байв. Жижиг машины даацыг $x$ гэвэл том машинуудын даац нийлээд хэд болох вэ?

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Problem 11104

Solve $4(2 n+5)=13 n$ Give your answer as a whole number or as a decimal.

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Problem 11105

Find a value for $x$ if $4 x^{2}+72=6 x^{2}$

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Problem 11106

Based on historical data in Oxnard college, we believe that $45 \%$ of freshmen do not visit their counselors regularly. For this year, you would like to obtain a new sample to estimate the proportiton of freshmen who do not visit their counselors regularly. You would like to be $98 \%$ confident that your estimate is within $3.5 \%$ of the true population proportion. How large of a sample size is required? Do not round mid-calculation. $n=$

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Problem 11107

TYT / Temel Matematik
5. \%40'ı tuz olan bir çözelti hazırlamak isteyen Alper'in, bunun için boş bir kaba 10 birimküp tuz ve bir miktar su koyup karıştırması gerekmektedir. Boş kaba tuzu doğru ölçüde koyan Alper, kaba yanlışlıkla doğru ölçünün 2 katı kadar su koyduğuna göre, oluşan çözeltinin yüzde kaçı tuz olur? A) 15 B) 20 C) 25 D) 30 E) 35

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Problem 11108

Contoh / Example 7 Cari julat nilai bagi $m$ jika persamaan kuadratik $x^{2}+m x+16=2(x+m)$ tidak mempunyai dua punca nyata. Find the range of values of $m$ if the quadratic equation $x^{2}+m x+16=2(x+m)$ does not have real roots.

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Problem 11109

1.(1) 288 dollars must be divided between three children proportionally of their ages. Children are 10, 11 and 15 years old. How many dollars will receive the eldest child?
2. (0.5) What percent of 1050 is 70 ?
3. (0.5) 80 is $4 \%$ of what number?
4. (0.5) Find 35 percent of 300

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Problem 11110

ب) اكتب المعادلة الثنربيعية في أبسط صورة الثي جذر اها هعا 2 ,

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Problem 11111

(30)

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Problem 11112

4 AMC 12 B Problems 8
Equilateral $\triangle A B C$ with side length 14 is rotated about its center by angle $\theta$ , where $0<\theta \leq 60^{\circ}$ , to form $\triangle D E F$ . See the figure. The area of hexagon $A D B E C F$ is $91 \sqrt{3}$ . What is $\tan \theta$ ? 如图所示, 边长为 14 的等边三角形 $\triangle A B C$ 绕其中心旋转 $\theta$ 度得到 $\triangle D E F$ , 其中 $0<\theta \leq 60^{\circ}$ 。若六边形 $A D B E C F$ 的面积为 $91 \sqrt{3}$ , 请问 $\tan \theta$ 的值是多少?

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Problem 11113

Цахилгааны тариф өдрийн хэрэглээ нэг киловатт нь 110 төгрөг, шөнийн хэрэглээ нэг киловатт нь 80 төгрөг байв. Доржийн энэ сарын өдөр, шөнийн нийт хэрэглээ нийлээд 204 киловатт болсон. Шөнийн нийт хэрэглээг х гэвэл төлбөр нь 80х болно. Тэгвэл өдрийн хэрэглээний нийт төлбөр нь ямар байх вэ?

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Problem 11114

1) Etant donnée l'équation $3 x^{2}-2 x+m-1=0$ , Déterminer $m$ pour que l'une des racines soit le triple de l'autre. 2) Les racines $x^{i}$ et $x^{i j}$ d'une équation du second ordre vérifient le système: $\left\{\begin{array}{c}x^{\prime}+x^{\prime \prime}-2 x^{\prime} x^{\prime \prime}=0 \\ m x^{\prime} x^{\prime \prime}-x^{\prime}-x^{\prime \prime}=2 m-1\end{array}\right.$ a) Former cette équation. b) Préciser la valeur de m pour laquelle, ces racines soient positives et soient les mesures des côtés de l'angle droit d'un triangle rectangle dont l'hypoténuse a pour mesure $\sqrt{2}$ . 3) On considère l'équation $(3 m+1) x^{2}-2(m-2) x+2-m=0$
Peut-on déterminer m pour que cette équation admette deux racines distinctes?

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Problem 11115

An object is travelling at a uniform speed in a circular path of radius 2.0 m . If the object's centripetal acceleration is found to be $3.0 \mathrm{~m} / \mathrm{s}^{2}$ , what time is required for the object to make two complete rotations?

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Problem 11116

Problem 1: When a cosmic ray (e.g. a proton) hits a molecule in the atmosphere, muons are created during the particle shower. Muons decay with a mean lifetime $\langle\tau\rangle=$ $2.20 \mu \mathrm{~s}$ . (a) What is the decay rate, $\Gamma$ , for the muon?
Let us now model our cosmic ray as a particle of mass M. Assume that the particle of mass $M$ decays into two particles of mass $m \neq M: M \rightarrow m m$ . (a) Write down the conservation of the quadrimomentum in the reference frame of the particle of mass $M$ (hint: the particle $M$ is at rest in its reference frame) (b) Using the conservation equation above, compute the energies and momentum of the two particles of mass $m$ after the decay. (c) Is there a maximum value for $m$ over which the decay is no longer admissible? If the answer is yes, write such value.

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Problem 11117

$\varepsilon x$ if $y_{1}(x)=e^{x}$ is a solk for $y^{\prime \prime}-2 y^{\prime}+y=0$ , find the general solu

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Problem 11118

Q. 3 If $\$ 350,000$ is to grow to $\$ 700,000$ over an 8 -year period, at what annual interest rate must it be invested, given that interest is computed quarterly?

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Problem 11119

5. The number of real solutions for $x^{3}+x^{2}+x+1$ is

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Problem 11120

(d) [2 Points] On $1 / 6 / 2022$ " ABC " Company purchased equipment for $\$ 260,000$ . The equipment has an estimated useful life and salvage value of 20 years and $\$ 20,000$ , respectively. At the end of the financial period, the accountant recorded the adjusting entry for the depreciation by debiting depreciation expense $\$ 12,000$ and crediting equipment $\$ 12,000$

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Problem 11121

Аав, ээж, хүү гурав өндрөө хэмжив. Ээжийн өндрийг $x$ гэвэл аав ээжээс 15 смээр өндөр, харин хүү эжээсээ 46 см-ээр намхан байсан бол аав, ээж, хүү гурвын өндрийн нийлбэрийг ол.

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Problem 11122

b. $\tan x \cos x \sin x-1=0$ where $0^{\circ} \leq x \leq 360^{\circ}$

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Problem 11123

$y^{-}+2 x y-y^{4} e^{\left(3 x^{2}+2 x\right)^{11}}=0$

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Problem 11124

2. Prove: $1+\tan ^{2} \theta=\frac{1}{\cos ^{2} \theta}$ (4 marks)

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Problem 11125

The vector parametric equation for the line through the points $(-3,-4,-2)$ and $(-3,1,-1)$ is $L(t)=\square$

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Problem 11126

Use the like-bases property and exponents to solve the equation $100000^{n}=1000$ $n=$

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Problem 11127

ІЭгшитгэл зохиож бод:
Энхжин өглөө, өдөр, орой гэсэн гурван удаа өрөөнийхөө дулааныг хэмжихэд өглөө 19 хэм, өдөр оройноос 7 хэмээр дулаан байсан ба тэдгээрийг нэмэхэд 62 гарав. Эндээс орой хэдэн хэм дулаан байсныг ол.

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Problem 11128

1. $2 \cos x \cos y=\cos (x+y)+\cos (x-y)$

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Problem 11129

Гурвалжны хоёр өнцөг нь $54^{\circ}, 98^{\circ}$ бол гурав дахь өнцгийг ол.

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Problem 11130

Find the equation of the tangent line at the given point on the following curve. $x^{2}+y^{2}=25,(-3,4)$
The equation of the tangent line to the point $(-3,4)$ is $y=$ $\square$

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Problem 11131

If $\$ 2,000$ is depositied into a bank by a customer and the required reserve ratio is $10 \%$ , the bank's Actual reserves increase $\$ 2000$ Required reserves increase $\$ 200$ Excess reserves increase $\$ 1800$ All the above changes in reserves will occur

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Problem 11132

10) If $x^{2}+\frac{1}{x^{2}}=18$ , find the value of $x-\frac{1}{x}$ .

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Problem 11133

6. Jane borrows $\$ 20500$ from her bank to purchase a car. The bank offers her an interest rate of $4.75 \%$ for 4 years. A) Calculate the monthly payment. (2 marks) $\begin{array}{l} \text { the monthly payment. (2 marks) } \quad 4 \times 12=48 \\ \frac{4.75}{17 \times 100}= \end{array}$ B) Calculate the total amount of interest paid over the life of the loan. (2 marks)
7. Mac borrows $\$ 16750$ at $1.25 \%$ over 5 years to purchase a car. A) Calculate his monthly payment. (2 marks) B) State the amount of interest paid in the first month. (1 mark)
8. Laurie wishes to buy a new vehicle from a Manitoba dealership for $\$ 18800$ before taxes. She has $\$ 5000$ saved for a down payment. A) Calculate the amount Laurie needs to borrow to purchase the vehicle. ( 2 marks) B) Laurie can get a loan for 4 years at $3.5 \%$ . Calculate the amount of interest in the first month's payment. (2 marks)

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Problem 11134

4. Find the value of $k$ so that the line passing through $(2,-3)$ and $(5, k)$ has a slope of $-\frac{4}{3}$ .

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Problem 11135

5. Suppose a line has a slope of $\frac{k}{5}$ . Find the value of $k$ so that each of the following is true: a. The line is parallel to a line with slope $-\frac{1}{2}$ b. The line is perpendicular to a line with slope $-\frac{1}{2}$

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Problem 11136

$-4(3 x+2)=16$

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Problem 11137

not $X$ $P(\operatorname{not} X)=$
Subtract. $1-P(x)=\frac{2}{5}$

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Problem 11138

Inis question: 1 point(S) possible
Apply the law of sines to the following: $a=\sqrt{5}, \mathrm{c}=2 \sqrt{5}, \mathrm{~A}=30^{\circ}$ . What is the value of $\sin \mathrm{C}$ ? What is the measure of C ? Based on its angle measures, what kind of triangle is triangle ABC ?
What is the value of $\sin C$ ? $\square$ (Type an exact answer, using radicals as needed.) What is the measure of $C$ ? - (Type an integer or a decimal )
Based on its angle measures, what kind of triangle is triangle $A B C$ ? Choose the correct answer below. Right Triangle Obtuse Triangle Acute Triangle

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Problem 11139

ring.pearson.com/?courseld=12901720\#/
Learning Goal: To understand the meaning and possible applications of the work-energy theorem.
In this problem, you will use your prior knowledge to derive one of the most important relationships in mechanics: the work-energy theorem. We will start with a special case: a particle of mass $m$ moving in the $x$ direction at constant acceleration $a$ . During a certain interval of time, the particle accelerates from $v_{\mathrm{i}}$ to $v_{\mathrm{f}}$ , undergoing displacement $s$ given by $s=x_{\mathrm{f}}-x_{\mathrm{i}}$ . $a=\frac{v_{f}^{2}-v_{i}^{2}}{2 s}$
Submit Previous Answers
Correct
Part B
Find the net force $F$ acting on the particle. Express your answer in terms of $m$ and $a$ . View Available Hint(s)

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Problem 11140

THINKING - don't forget your concluding statements Peter invested in a GIC that paid $3.25 \%$ simple interest. In 36 months, he earned $\$ 485$ interest. $\begin{array}{l} =485 \\ =? \end{array}$ $\begin{array}{l} =3.25 \\ =36 \end{array}$

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Problem 11141

$\begin{array}{l} \text { رد الة عدون عيار تها كائلى } \\ f(\mathrm{x})=\frac{2 \mathrm{x}-1}{\mathrm{x}-1} \\ \text { D. } 1 \\ 2 \end{array}$ $\begin{array}{l} f(x)=a+\frac{b}{x-1} \quad 4 b, a+1-4 \\ \text { التعرين الثاند : ( } 06 \text { نتاط) } \end{array}$ $\begin{array}{l} 5 x-1=0 \\ \mathrm{x}+3=2 \mathrm{x}+6+\mathrm{x} \\ (x-4)(x+8)=0 \\ 2 \text { - أتشر نم حلل المبرأت التثلية: } \\ A=(\mathrm{x}-3)(2 \mathrm{x}+1)+(\mathrm{x}-3)(\mathrm{x}+5) \\ B=(\mathrm{x}+2)^{2}+(\mathrm{x}+2)(\mathrm{x}-5) \\ 3 \text { - الىهد حلا اللشراهحت المثلبة: } \\ 3 x+4 \leq x+9 \\ x^{2}+3 x+-12 \geq x^{2}+8 x+3 \\ \frac{x+3}{2} \leq \frac{x+5}{3} \end{array}$

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Problem 11142

Express as a single logarithmic expression. You do NOT need to expand exponents. Assume all expressions represent positive numbers. $\log _{9}(x+8)+\log _{9}(x-7)=\log _{9}(\square)$ Question Help: Video Written Example Submit Question

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Problem 11143

Glide Path A pilot has just started on the glide path for landing at an airport with a runway of length 9000 feet. The angles of depression from the plane to the ends of the runway are $17.5^{\circ}$ and $18.8^{\circ}$ . (a) Draw a diagram that visually represents the problem. (b) Find the air distance the plane must travel until touching down on the near end of the runway. (c) Find the ground distance the plane must travel until touching down. (d) Find the altitude of the plane when the pilot begins the descent.

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Problem 11144

Au démarrage, un scooter passe de 0 à $36 \mathrm{~km} \cdot \mathrm{~h}$ -1 en 10 s . Son accélération moyenne ést de : (Au démarrage, un scooter passe de 0 à $36 \mathrm{~km} . \mathrm{h}-1$ en 10 secondes. Son accélération moyenne est de) :
Sélectionnez une option : $: 3.6 \mathrm{~m} \cdot \mathrm{~s}^{-2}$ $: 3,6 \mathrm{~km} \cdot \mathrm{~h}^{-2}$ $: 1,0 \mathrm{~ms}^{-2}$

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Problem 11145

For the following exercises, solve exactly on $[0,2 \pi)$ .
13. $2 \cos \theta=\sqrt{2}$
14. $2 \cos \theta=-1$
15. $2 \sin \theta=-1$
16. $2 \sin \theta=-\sqrt{3}$
17. $2 \sin (3 \theta)=1$
18. $2 \sin (2 \theta)=\sqrt{3}$
19. $2 \cos (3 \theta)=-\sqrt{2}$
20. $\cos (2 \theta)=-\frac{\sqrt{3}}{2}$
21. $2 \sin (\pi \theta)=1$
22. $2 \cos \left(\frac{\pi}{5} \theta\right)=\sqrt{3}$
For the following exercises, find all exact solutions on $[0,2 \pi)$ .

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Problem 11146

Virginia Beach City Public Schools Math $7>$ Convert customary and metric units using proportions DPY
Which proportion could you use to convert 5 kilograms to grams? $\frac{10 \text { grams }}{1 \text { kilogram }}=\frac{? \text { grams }}{5 \text { kilograms }} \quad \frac{1,000 \text { grams }}{1 \text { kilogram }}=\frac{? \text { grams }}{5 \text { kilograms }}$
Convert. 5 kilograms = $\square$ grams Submit

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Problem 11147

You spend $\$ 28$ on ingredients to make cookies. You charge $\$ 4$ per container of cookies. How many containers do you need to sell to earn $\$ 20$ in profit? CLEAR CHECK
Write an equation to represent the problem. Let $c$ represent the number of containers of cookies you need to sell. $\square$ $\square$ $\square$
How many containers of cookies do you need to sell? You need to sell $\square$ containers of cookies.

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Problem 11148

Find the measure of $x$ . $x=[?$

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Problem 11149

$x y^{\prime}+2 x y+2 y=x e^{-2}$

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Problem 11150

Using the formula $V=l w h$ , and given $l=8 \mathrm{~cm}, w=7 \mathrm{~cm}$ , and $h=2.5 \mathrm{~cm}$ which equation is set up correctly?

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Problem 11151

Which proportion could you use to convert 3.5 gallons to cups? $\frac{16 \text { cups }}{1 \text { gallon }}=\frac{? \text { cups }}{3.5 \text { gallons }} \quad \frac{16 \text { cups }}{1 \text { gallon }}=\frac{3.5 \text { gallons }}{? \text { cups }}$
Convert. 3.5 gallons $=$ $\square$ cups Submit

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Problem 11152

You buy painting supplies for $\$ 12$ , and you charge $\$ 3$ per person to paint faces. How many faces will you need to paint to earn $\$ 15$ in profit? CLEAR CHECK
Write an equation to represent the problem. Let $f$ represent the number of faces you need to paint. $\square$ f- $\square$
How many faces do you need to paint? You need to paint $\square$ faces.

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Problem 11153

$S O H \Rightarrow \sin x=\frac{0}{h} \quad C A H \Rightarrow \cos x=\frac{a}{h} \quad T O A \Rightarrow \tan x=0 / a$ (1)) Solve for the missing angle $\theta$ . a) b)

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Problem 11154

Find the measure of $x$ . $x=$ $\square$

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Problem 11155

6.4. 1) Скорость полета голубя 90 км/ч, ласточки 150 км/ч. Ласточка за определенное время пролетела 10 км. Какое расстояние пролетит голубь за это же время? 2) 8 метров шелка стоят столько же, сколько 63 метра шелка. Сколько метров шелка можно купить вместо 14 метров шелка? 3) В 17 л раствора содержится 6 л спирта. Сколько литров спирта содержится
в л раствора?

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Problem 11156

Solve the exponential equation. $4\left(10^{x}\right)=40,000$
Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The solution is $x=$ $\square$ (Simplify your answer. Use a comma to separate answers as needed.) B. There is no solution.

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Problem 11157

Write the equation of the line in fully simplified slope-intercept form.

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Problem 11158

The solution of the initial value problem $2 y^{\prime}+3 y=e^{-x} y(0)=5$ is

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Problem 11159

solve $2 \cosh (x) \cos (y) d x=\sinh (x) \sin (y) d y$

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Problem 11160

Given $\cos \theta=\frac{3 \sqrt{3}}{8}$ , what is $\sin \theta$ ? $\sin \theta=\frac{\sqrt{[?]}}{}$

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Problem 11161

1. Un resorte de constante elástica $\mathrm{k}=200 \mathrm{~N} / \mathrm{m}$ se comprime 0.3 m . ¿Cuánta energía potencial elástica almacena el resorte?

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Problem 11162

$-4 x^{2}+5 x+7=0$
Graph Taking the Completing Quadratic Square Root the Square Formula

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Problem 11163

Un objeto de 10 kg cae desde una altura de 20 metros. ¿Cuál será su velocidad al llegar al suelo, suponiendo que no hay fricción?

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Problem 11164

Un automóvil de 1200 kg acelera de 0 a 25 $\mathrm{m} / \mathrm{s}$ . ¿Cuál es la energía cinética del automóvil al alcanzar esta velocidad?

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Problem 11165

2. (II) Arlene is to walk across a "high wire" strung horizontally between two buildings 10.0 m apart. The sag in the rope when she is at the midpoint is $10.0^{\circ}$ , as shown in Fig. 4-39. If her mass is 50.0 kg , what is the tension in the rope at this point?

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Problem 11166

33. (II) A window washer pulls herself upward using the bucket-pulley apparatus shown in Fig. 4-40. (a) How hard must she pull downward to raise herself slowly at constant speed? (b) If she increases this force by $15 \%$ , what will her acceleration be? The mass of the person plus the bucket is 78 kg .
FIGURE $4-40$ Problem 33.

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Problem 11167

Question 14(Multiple Choice Worth 2 points) (Linear Relationships LC) Which linear equation shows a proportional relationship? $y=-2$ $y=3 x+1$ $y=\frac{3}{2} x$ $y=\frac{1}{2} x-3$

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Problem 11168

Use the Lat of Cosines to determine the indicated side $x$ in the following figure. (Rou $x=$ $\square$

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Problem 11169

$\frac{1.22}{1.22}=.0002(7.66)+.0029(12)+.34 x$

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Problem 11170

Use the Law of Cosines to determine the indi

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Problem 11171

Una persona mide la temperatura del agua y obtiene $25^{\circ}$ C. ¿Cuál es esta temperatura en grados Fahrenheit?

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Problem 11172

Use the Law of Cosines to determine the indicated a

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Problem 11173

39. (II) A skateboarder, with an initial speed of $2.0 \mathrm{~m} / \mathrm{s}$ , rolls virtually friction free down a straight incline of length 18 m in 3.3 s . At what angle $\theta$ is the incline oriented above the horizontal?

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Problem 11174

40. (II) At the instant a race began, a $65-\mathrm{kg}$ sprinter exerted a force of 720 N on the starting block at a $22^{\circ}$ angle with respect to the ground. (a) What was the horizontal acceleration of the sprinter? (b) If the force was exerted for 0.32 s , with what speed did the sprinter leave the starting block?

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Problem 11175

41. (II) A mass $m$ is at rest on a horizontal frictionless surface at $t=0$ . Then a constant force $F_{0}$ acts on it for a time $t_{0}$ . Suddenly the force doubles to $2 F_{0}$ and remains constant until $t=2 t_{0}$ . Determine the total distance traveled from $t=0$ to $t=2 t_{0}$ .

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Problem 11176

43. (II) A $27-\mathrm{kg}$ chandelier hangs from a ceiling on a vertical 3.4-m-long wire. (a) What horizontal force would be necessary to displace its position 0.15 m to one side? (b) What will be the tension in the wire?

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Problem 11177

3 Formula 1 point Return Submit
A climber is working on climbing 5 meter boulder as fast as he can. The climber does 2,351 Joules of work in climbing this boulder and it takes him 7 seconds to do it. What is the climbers power output in watts? $K E=(1 / 2)^{} m^{} v^{\wedge} 2$
GPE=mgh $\mathrm{W}=\mathrm{F}^{*} \mathrm{~d}$ All Bookmarks $s$ 1 2 3 4 5 6 7

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Problem 11178

45. (II) The block shown in Fig. $4-45$ has mass $m=7.0 \mathrm{~kg}$ and lies on a fixed smooth frictionless plane tilted at an angle $\theta=22.0^{\circ}$ to the horizontal. (a) Determine the acceleration of the block as it slides down the plane. (b) If the block starts from rest 12.0 m up the plane from its base, what will be the block's speed when it reaches the bottom of the incline?
FIGURE 4-45 Block on inclined plane. Problems 45 and 46.

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Problem 11179

Find all real solutions of the equation $3(t-5)^{2}-7=17$
Write out the exact answers (no decimal values), with answers separated by a comma. $t=$

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Problem 11180

(II) A block is given an initial speed of $5.2 \mathrm{~m} / \mathrm{s}$ up the $22.0^{\circ}$ plane shown in Fig. 4-45. (a) How far up the plane will it go? (b) How much time elapses before it returns to its starting point? Ignore friction.

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Problem 11181

Solve the equation. Write the answer in terms of the natural logarithm. $5 e^{0.2 x}=6$
The solution set is $\square$ \}. (Type an exact answer. Simplify your answer. Use a comma to separate answers as needed.

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Problem 11182

47. (II) An object is hanging by a string from your rearview mirror. While you are accelerating at a constant rate from rest to $28 \mathrm{~m} / \mathrm{s}$ in 5.0 s , what angle $\theta$ does the string make with the vertical? See Fig. 4-46.

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Problem 11183

Solve for $z$ . $2 z^{2}=98$
Write each solution as an integer, proper fraction, or improper fraction in simplest form. If there are multiple solutions, separate them with commas. $z=$

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Problem 11184

48. (II) A $2.0-\mathrm{kg}$ purse is dropped from the top of the Leaning Tower of Pisa and falls 55 m before reaching the ground with a speed of $27 \mathrm{~m} / \mathrm{s}$ . What was the average force of air resistance?

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Problem 11185

49. (II) Bob traverses a chasm by stringing a rope between a tree on one side of the chasm and a tree on the opposite side, 25 m away, Fig. 4-47. Assume the rope can provide a tension force of up to 31 kN before breaking, and use a "safety factor" of 10 (that is, the rope should only be required to undergo a tension force of 3.1 kN ). (a) If Bob's mass is 72.0 kg , determine the distance $x$ that the rope must sag at a point halfway across if it is to be within its recommended safety range. (b) If the rope sags by only one-fourth the distance found in ( $a$ ), determine the tension force in the rope. Will the rope break?
FIGURE 4-47 Problem 49.

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Problem 11186

0. (II) As shown in Fig. 4-48, five balls (masses 2.00, 2.05, 2.10, $2.15,2.20 \mathrm{~kg}$ ) hang from a crossbar. Each mass is supported by "5-lb test" fishing line which will break when its tension force exceeds 22.2 N ( $=5.00 \mathrm{lb}$ ). When this device is placed in an elevator, which accelerates upward, only the lines attached to the 2.05 and 2.00 kg masses do not break. Within what range is the elevator's acceleration?
FIGURE 4-48 Problem 50.

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Problem 11187

51. (II) A high-speed 14 -car Italian train has a mass of 640 metric tons $(640,000 \mathrm{~kg})$ . It can exert a maximum force of 400 kN horizontally against the tracks, whereas at maximum constant velocity $(300 \mathrm{~km} / \mathrm{h})$ , it exerts a force of about 150 kN . Calculate (a) its maximum acceleration, and (b) estimate the total force of friction and air resistance at top speed.

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Problem 11188

52. (II) A $450-\mathrm{kg}$ piano is being unloaded from a truck by rolling it down a ramp inclined at $15^{\circ}$ . There is negligible friction and the ramp is 4.0 m long. Two workers slow the rate at which the piano moves by pushing with a combined force of 1020 N parallel to the ramp. If the piano starts from rest, how fast is it moving at the bottom?

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Problem 11189

53. (II) Uphill escape ramps are sometimes provided to the side of steep downhill highways for trucks with overheated brakes. For a simple $11^{\circ}$ upward ramp, what length would be needed to stop a runaway truck traveling $140 \mathrm{~km} / \mathrm{h}$ ? Note the large size of your calculated length. (If sand is used for the bed of the ramp, its length can be reduced by a factor of about 2 .)

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Problem 11190

54. (II) A child on a sled reaches the bottom of a hill with a velocity of $10.0 \mathrm{~m} / \mathrm{s}$ and travels 25.0 m along a horizontal straightaway to a stop. If the child and sled together have a mass of 60.0 kg , what is the average retarding force on the sled on the horizontal straightaway?

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Problem 11191

58. (III) Suppose the pulley in Fig. 4-50 is suspended by a cord C. Determine the tension in this cord after the masses are released and before one hits the ground. Ignore the mass of the pulley and cords.

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Problem 11192

3) Solve the following trigonometric equations within the domain $[0,2 \pi]$ . Round to the nearest tenth and use radians. $\text { a) } \begin{array}{l} 2 \sin ^{2} x-1=0 \\ \frac{2 \sin ^{3} x}{2}=\frac{1}{2} \\ \sin x= \pm \frac{1}{\sqrt{2}} \\ \text { or } \end{array}$ $(\sqrt{2} \sin x-1)(\sqrt{2} \sin x+1)$ $\sqrt{2} \sin x=1 \quad \sqrt{2} \sin x=-1$ $\sin x=\frac{1}{\sqrt{2}} \quad \sin x=-\frac{1}{\sqrt{2}}$ $x=\frac{\pi}{4} \quad x=\frac{\pi}{4}$ $\begin{array}{ll} \text { b) } \csc ^{2} x+2 \csc x-3=0 \\ \csc ^{2} x-1 \csc x+3 \csc x-3=0 \\ \csc x(\csc x-1) & 3(\csc x-1)=0 \\ \csc x+3=0 & \csc x-1=0 \\ \csc x=-3 & \csc x=1 \\ \frac{1}{\sin _{x}}=-3 & \frac{1}{\sin x}=1 \\ \sin x=\frac{1}{-3} & \sin x=\frac{1}{1} \\ \sin ^{-1} x=0.340 & x=\frac{\pi}{2} \end{array}$ c) $\cos x-\cos 2 x=1 / 2$

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Problem 11193

Part A Complete and balance each of the following hydrocarbon combustion reactions. $\mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{CH}_{2} \mathrm{CH}_{3}+\mathrm{O}_{2} \rightarrow$ $2 \mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{CH}_{2} \mathrm{CH}_{3}+13 \mathrm{O}_{2} \rightarrow 8 \mathrm{CO}_{2}+10 \mathrm{H}_{2} \mathrm{O}$ $\mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{CH}_{2} \mathrm{CH}_{3}+11 \mathrm{O}_{2} \rightarrow 6 \mathrm{CO}_{2}+10 \mathrm{H}_{2} \mathrm{O}$ $2 \mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{CH}_{2} \mathrm{CH}_{3}+11 \mathrm{O}_{2} \rightarrow 8 \mathrm{CO}_{2}+8 \mathrm{H}_{2} \mathrm{O}$ $\mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{CH}_{2} \mathrm{CH}_{3}+13 \mathrm{O}_{2} \rightarrow 6 \mathrm{CO}_{2}+8 \mathrm{H}_{2} \mathrm{O}$

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Problem 11194

What is the concentration of $\mathrm{H}^{+}$ in a $0.54 \mathrm{~mol} / \mathrm{L}$ oxalic acid solution?
Oxalic acid is weak. Therefore, this is an equilibrium problem! $\begin{array}{l} \mathrm{HOOCCOOH}(\mathrm{aq})+\mathrm{H}_{2} \mathrm{O}(\mathrm{I}) \prod \mathrm{H}_{3} \mathrm{O}^{+}(\mathrm{aq})+\mathrm{HOOCCOO}^{-}(\mathrm{aq}) \\ K a= \\ \begin{array}{lllll} \hline & \mathrm{HOOCCOOH} & \mathrm{H}_{3} \mathrm{O}+ & \text { HOOCCOO } \\ \hline \mathrm{I}(\mathrm{~mol} / \mathrm{L}) & 0.54 & 0 & 0 \\ \mathrm{C}(\mathrm{~mol} / \mathrm{L}) & -\mathrm{x} & +\mathrm{x} & +\mathrm{x} \\ \mathrm{E}(\mathrm{~mol} / \mathrm{L}) & 0.54-\mathrm{x} & \mathrm{x} & \mathrm{x} \\ & & 5.6 \times 10^{-2}= & \end{array} \end{array}$

See Solution

Problem 11195

7. (12 points) Solve the exponential equation $7^{2 x+3}=3^{x+1}$ .

See Solution

Problem 11196

find A, B, C, and D using S SI = A + B S- Sti Partial fractions + C + D S 2 +1

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Problem 11197

$-4|w-16|+9=-39$ A) $w=\{-4,-28\}$ cowboy boo B) $w=\{4,28\}$ hot rollers C) $w=\{-4,28\}$ snow pants D) $w=\{-28,28\}$ hair nets E) $w=\{-28,4\}$ clown shoes

See Solution

Problem 11198

Ive the equation beior $\begin{array}{c} 2|3 r-9|-1=23 \\ \begin{array}{c} r=\{-7,7\} \\ r=\{1,7\} \\ \text { t) } r=\{-7,1\} \\ \text { D) } r=\{-1,7\} \\ \text { posting on on Twitter } \\ \text { D) } \quad \text { singing waffles karaoke } \end{array} \end{array}$

See Solution

Problem 11199

$|8 v-12|=68$ A) $v=\{-10,7\}$ lifting weights

See Solution

Problem 11200

For the following right triangle, find the side length $x$ .

See Solution

Equation

Problem 11101

sin⁡2θ+2cos⁡2θ−1=cos⁡2θ\sin ^{2} \theta+2 \cos ^{2} \theta-1=\cos ^{2} \thetasin2θ+2cos2θ−1=cos2θ

Problem 11102

Problem 11103

Том, жижиг ачааны машины даац нийлээд 14 тонн бөгөөд 10 том, 22 жижиг ачааны машин байв. Жижиг машины даацыг xxx гэвэл том машинуудын даац нийлээд хэд болох вэ?

Problem 11104

Solve 4(2n+5)=13n4(2 n+5)=13 n4(2n+5)=13n Give your answer as a whole number or as a decimal.

Problem 11105

Find a value for xxx if 4x2+72=6x24 x^{2}+72=6 x^{2}4x2+72=6x2

Problem 11106

Problem 11107

Problem 11108

Contoh / Example 7 Cari julat nilai bagi mmm jika persamaan kuadratik x2+mx+16=2(x+m)x^{2}+m x+16=2(x+m)x2+mx+16=2(x+m) tidak mempunyai dua punca nyata. Find the range of values of mmm if the quadratic equation x2+mx+16=2(x+m)x^{2}+m x+16=2(x+m)x2+mx+16=2(x+m) does not have real roots.

Problem 11109

1.(1) 288 dollars must be divided between three children proportionally of their ages. Children are 10, 11 and 15 years old. How many dollars will receive the eldest child?2. (0.5) What percent of 1050 is 70 ?3. (0.5) 80 is 4%4 \%4% of what number?4. (0.5) Find 35 percent of 300

Problem 11110

ب) اكتب المعادلة الثنربيعية في أبسط صورة الثي جذر اها هعا 2 ,

Problem 11111

(30)

Problem 11112

Problem 11113

Problem 11114

Problem 11115

An object is travelling at a uniform speed in a circular path of radius 2.0 m . If the object's centripetal acceleration is found to be 3.0 m/s23.0 \mathrm{~m} / \mathrm{s}^{2}3.0 m/s2, what time is required for the object to make two complete rotations?

Problem 11116

Problem 11117

εx\varepsilon xεx if y1(x)=exy_{1}(x)=e^{x}y1​(x)=ex is a solk for y′′−2y′+y=0y^{\prime \prime}-2 y^{\prime}+y=0y′′−2y′+y=0, find the general solu

Problem 11118

Q. 3 If $350,000\$ 350,000$350,000 is to grow to $700,000\$ 700,000$700,000 over an 8 -year period, at what annual interest rate must it be invested, given that interest is computed quarterly?

Problem 11119

5. The number of real solutions for x3+x2+x+1x^{3}+x^{2}+x+1x3+x2+x+1 is

Problem 11120

Problem 11121

Problem 11122

b. tan⁡xcos⁡xsin⁡x−1=0\tan x \cos x \sin x-1=0tanxcosxsinx−1=0 where 0∘≤x≤360∘0^{\circ} \leq x \leq 360^{\circ}0∘≤x≤360∘

Problem 11123

y−+2xy−y4e(3x2+2x)11=0y^{-}+2 x y-y^{4} e^{\left(3 x^{2}+2 x\right)^{11}}=0y−+2xy−y4e(3x2+2x)11=0

Problem 11124

2. Prove: 1+tan⁡2θ=1cos⁡2θ1+\tan ^{2} \theta=\frac{1}{\cos ^{2} \theta}1+tan2θ=cos2θ1​ (4 marks)

Problem 11125

The vector parametric equation for the line through the points (−3,−4,−2)(-3,-4,-2)(−3,−4,−2) and (−3,1,−1)(-3,1,-1)(−3,1,−1) is L(t)=□L(t)=\squareL(t)=□

Problem 11126

Use the like-bases property and exponents to solve the equation 100000n=1000100000^{n}=1000100000n=1000 n=n=n=

Problem 11127

Problem 11128

1. 2cos⁡xcos⁡y=cos⁡(x+y)+cos⁡(x−y)2 \cos x \cos y=\cos (x+y)+\cos (x-y)2cosxcosy=cos(x+y)+cos(x−y)

Problem 11129

Гурвалжны хоёр өнцөг нь 54∘,98∘54^{\circ}, 98^{\circ}54∘,98∘ бол гурав дахь өнцгийг ол.

Problem 11130

Find the equation of the tangent line at the given point on the following curve. x2+y2=25,(−3,4)x^{2}+y^{2}=25,(-3,4)x2+y2=25,(−3,4)The equation of the tangent line to the point (−3,4)(-3,4)(−3,4) is y=y=y= □\square□

Problem 11131

If $2,000\$ 2,000$2,000 is depositied into a bank by a customer and the required reserve ratio is 10%10 \%10%, the bank's Actual reserves increase $2000\$ 2000$2000 Required reserves increase $200\$ 200$200 Excess reserves increase $1800\$ 1800$1800 All the above changes in reserves will occur

Problem 11132

10) If x2+1x2=18x^{2}+\frac{1}{x^{2}}=18x2+x21​=18, find the value of x−1xx-\frac{1}{x}x−x1​.

Problem 11133

Problem 11134

4. Find the value of kkk so that the line passing through (2,−3)(2,-3)(2,−3) and (5,k)(5, k)(5,k) has a slope of −43-\frac{4}{3}−34​.

Problem 11135

5. Suppose a line has a slope of k5\frac{k}{5}5k​. Find the value of kkk so that each of the following is true: a. The line is parallel to a line with slope −12-\frac{1}{2}−21​ b. The line is perpendicular to a line with slope −12-\frac{1}{2}−21​

Problem 11136

−4(3x+2)=16-4(3 x+2)=16−4(3x+2)=16

Problem 11137

not XXX P(not⁡X)=P(\operatorname{not} X)=P(notX)=Subtract. 1−P(x)=251-P(x)=\frac{2}{5}1−P(x)=52​

Problem 11138

Problem 11139

Problem 11140

THINKING - don't forget your concluding statements Peter invested in a GIC that paid 3.25%3.25 \%3.25% simple interest. In 36 months, he earned $485\$ 485$485 interest. =485=?\begin{array}{l} =485 \\ =? \end{array}=485=?​ =3.25=36\begin{array}{l} =3.25 \\ =36 \end{array}=3.25=36​

Problem 11141

Problem 11142

Problem 11143

Problem 11144

Problem 11145

Problem 11146

Problem 11147

Problem 11148

Find the measure of xxx. x=[?x=[?x=[?

Problem 11149

xy′+2xy+2y=xe−2x y^{\prime}+2 x y+2 y=x e^{-2}xy′+2xy+2y=xe−2

Problem 11150

$\sin ^{2} \theta+2 \cos ^{2} \theta-1=\cos ^{2} \theta$

Том, жижиг ачааны машины даац нийлээд 14 тонн бөгөөд 10 том, 22 жижиг ачааны машин байв. Жижиг машины даацыг $x$ гэвэл том машинуудын даац нийлээд хэд болох вэ?

Solve $4(2 n+5)=13 n$ Give your answer as a whole number or as a decimal.

Find a value for $x$ if $4 x^{2}+72=6 x^{2}$

Contoh / Example 7 Cari julat nilai bagi $m$ jika persamaan kuadratik $x^{2}+m x+16=2(x+m)$ tidak mempunyai dua punca nyata. Find the range of values of $m$ if the quadratic equation $x^{2}+m x+16=2(x+m)$ does not have real roots.

1.(1) 288 dollars must be divided between three children proportionally of their ages. Children are 10, 11 and 15 years old. How many dollars will receive the eldest child?
2. (0.5) What percent of 1050 is 70 ?
3. (0.5) 80 is $4 \%$ of what number?
4. (0.5) Find 35 percent of 300

An object is travelling at a uniform speed in a circular path of radius 2.0 m . If the object's centripetal acceleration is found to be $3.0 \mathrm{~m} / \mathrm{s}^{2}$ , what time is required for the object to make two complete rotations?

$\varepsilon x$ if $y_{1}(x)=e^{x}$ is a solk for $y^{\prime \prime}-2 y^{\prime}+y=0$ , find the general solu

Q. 3 If $\$ 350,000$ is to grow to $\$ 700,000$ over an 8 -year period, at what annual interest rate must it be invested, given that interest is computed quarterly?

5. The number of real solutions for $x^{3}+x^{2}+x+1$ is

b. $\tan x \cos x \sin x-1=0$ where $0^{\circ} \leq x \leq 360^{\circ}$

$y^{-}+2 x y-y^{4} e^{\left(3 x^{2}+2 x\right)^{11}}=0$

2. Prove: $1+\tan ^{2} \theta=\frac{1}{\cos ^{2} \theta}$ (4 marks)

The vector parametric equation for the line through the points $(-3,-4,-2)$ and $(-3,1,-1)$ is $L(t)=\square$

Use the like-bases property and exponents to solve the equation $100000^{n}=1000$ $n=$

1. $2 \cos x \cos y=\cos (x+y)+\cos (x-y)$

Гурвалжны хоёр өнцөг нь $54^{\circ}, 98^{\circ}$ бол гурав дахь өнцгийг ол.

Find the equation of the tangent line at the given point on the following curve. $x^{2}+y^{2}=25,(-3,4)$
The equation of the tangent line to the point $(-3,4)$ is $y=$ $\square$

If $\$ 2,000$ is depositied into a bank by a customer and the required reserve ratio is $10 \%$ , the bank's Actual reserves increase $\$ 2000$ Required reserves increase $\$ 200$ Excess reserves increase $\$ 1800$ All the above changes in reserves will occur

10) If $x^{2}+\frac{1}{x^{2}}=18$ , find the value of $x-\frac{1}{x}$ .

4. Find the value of $k$ so that the line passing through $(2,-3)$ and $(5, k)$ has a slope of $-\frac{4}{3}$ .

5. Suppose a line has a slope of $\frac{k}{5}$ . Find the value of $k$ so that each of the following is true: a. The line is parallel to a line with slope $-\frac{1}{2}$ b. The line is perpendicular to a line with slope $-\frac{1}{2}$

$-4(3 x+2)=16$

not $X$ $P(\operatorname{not} X)=$
Subtract. $1-P(x)=\frac{2}{5}$

THINKING - don't forget your concluding statements Peter invested in a GIC that paid $3.25 \%$ simple interest. In 36 months, he earned $\$ 485$ interest. $\begin{array}{l} =485 \\ =? \end{array}$ $\begin{array}{l} =3.25 \\ =36 \end{array}$

Find the measure of $x$ . $x=[?$

$x y^{\prime}+2 x y+2 y=x e^{-2}$

Using the formula $V=l w h$ , and given $l=8 \mathrm{~cm}, w=7 \mathrm{~cm}$ , and $h=2.5 \mathrm{~cm}$ which equation is set up correctly?

$S O H \Rightarrow \sin x=\frac{0}{h} \quad C A H \Rightarrow \cos x=\frac{a}{h} \quad T O A \Rightarrow \tan x=0 / a$ (1)) Solve for the missing angle $\theta$ . a) b)

Find the measure of $x$ . $x=$ $\square$

The solution of the initial value problem $2 y^{\prime}+3 y=e^{-x} y(0)=5$ is

solve $2 \cosh (x) \cos (y) d x=\sinh (x) \sin (y) d y$

Given $\cos \theta=\frac{3 \sqrt{3}}{8}$ , what is $\sin \theta$ ? $\sin \theta=\frac{\sqrt{[?]}}{}$

1. Un resorte de constante elástica $\mathrm{k}=200 \mathrm{~N} / \mathrm{m}$ se comprime 0.3 m . ¿Cuánta energía potencial elástica almacena el resorte?

$-4 x^{2}+5 x+7=0$
Graph Taking the Completing Quadratic Square Root the Square Formula

Un automóvil de 1200 kg acelera de 0 a 25 $\mathrm{m} / \mathrm{s}$ . ¿Cuál es la energía cinética del automóvil al alcanzar esta velocidad?

2. (II) Arlene is to walk across a "high wire" strung horizontally between two buildings 10.0 m apart. The sag in the rope when she is at the midpoint is $10.0^{\circ}$ , as shown in Fig. 4-39. If her mass is 50.0 kg , what is the tension in the rope at this point?

Question 14(Multiple Choice Worth 2 points) (Linear Relationships LC) Which linear equation shows a proportional relationship? $y=-2$ $y=3 x+1$ $y=\frac{3}{2} x$ $y=\frac{1}{2} x-3$

Use the Lat of Cosines to determine the indicated side $x$ in the following figure. (Rou $x=$ $\square$

$\frac{1.22}{1.22}=.0002(7.66)+.0029(12)+.34 x$

Una persona mide la temperatura del agua y obtiene $25^{\circ}$ C. ¿Cuál es esta temperatura en grados Fahrenheit?

39. (II) A skateboarder, with an initial speed of $2.0 \mathrm{~m} / \mathrm{s}$ , rolls virtually friction free down a straight incline of length 18 m in 3.3 s . At what angle $\theta$ is the incline oriented above the horizontal?