Function

Problem 10101

Find the derivative of y=sin3xcos3xy=\sin 3x - \cos 3x at x=45x=45^{\circ}.

See Solution

Problem 10102

What is the final temperature of a 50.0 g glass piece after absorbing 5275 J of heat, starting at 20.0°C with a specific heat of 0.50 J/g°C?

See Solution

Problem 10103

Find the derivative of the function f(x)=xcos3xf(x)=\sqrt{x} \cos^{3} x. What is f(x)f^{\prime}(x)?

See Solution

Problem 10104

Find the composition of the functions f(x)=x2f(x)=x^{2} and g(x)=x3g(x)=x-3: calculate g(f(x))g(f(x)).

See Solution

Problem 10105

Find the length ll of a rectangle with area 25in225 \mathrm{in}^{2} for widths w=10w = 10 in and w=15w = 15 in. Rearrange A=lwA = lw.

See Solution

Problem 10106

A rectangle has area A=25in2A = 25 \mathrm{in}^2. If w=10w = 10 in, find ll. If w=15w = 15 in, find ll. Rearrange A=lwA = lw for ll.

See Solution

Problem 10107

Find a,b,c,da, b, c, d for f(x)f(x) to be continuous, where:
f(x)={x2+x2x1if x<1aif x=1b(xc)2if 1<x<4dif x=42x8if x>4 f(x) = \begin{cases} \frac{x^2+x-2}{x-1} & \text{if } x<1 \\ a & \text{if } x=1 \\ b(x-c)^2 & \text{if } 1<x<4 \\ d & \text{if } x=4 \\ 2x-8 & \text{if } x>4 \end{cases}

See Solution

Problem 10108

Find the value of f(7)f(7) for the function f(x)=2x26f(x)=2 x^{2}-6.

See Solution

Problem 10109

Find the derivative of the function y=sinx+cosxxy=\frac{\sin x+\cos x}{x}.

See Solution

Problem 10110

Find the domain restriction for the function f(x)=1x3f(x) = \frac{1}{x-3}. Explain your reasoning.

See Solution

Problem 10111

Find the derivative f(π)f^{\prime}(\pi) for the function f(x)=11+cosxf(x)=\frac{1}{1+\cos x}.

See Solution

Problem 10112

Write a cost function for a ski resort that charges \$20 plus \$4.25 per hour. Identify the correct variable.

See Solution

Problem 10113

Find the linear cost function C(x)C(x) given a fixed cost of \$300 and that producing 60 items costs \$3,300.

See Solution

Problem 10114

Find the average cost per item given the cost function C(x)=18x+1400C(x)=18x+1400 for producing 100 items. What is the average cost?

See Solution

Problem 10115

Determine the slope, mm, of the tangent line to the curve y=7+5x22x3y=7+5 x^{2}-2 x^{3} at x=ax=a.

See Solution

Problem 10116

Decompose the function 1+xcos(x)1+x \cos (x) into its even and odd parts.

See Solution

Problem 10117

Find the linear depreciation function for a car priced at \$25,250, expected to be worth \$14,234 in 4 years. Also, estimate its value in 6 years and find the depreciation rate.

See Solution

Problem 10118

Calculate the specific heat of a liquid given that 47.1 J47.1 \mathrm{~J} raises 13.8 g13.8 \mathrm{~g} by 1.79C1.79^{\circ} \mathrm{C}.

See Solution

Problem 10119

Find the value of csc(1305)\csc (-1305).

See Solution

Problem 10120

Compute Δy/Δx\Delta y / \Delta x for y=4x7y=4x-7 over [2,6][2,6] and find the instantaneous rate of change at x=2x=2.

See Solution

Problem 10121

Evaluate the piecewise function f(x)f(x) where f(9)f(-9) and find f(4)f(4).

See Solution

Problem 10122

Find the critical points of f(x,y)=x2+2xy+2y28x+2yf(x, y)=x^{2}+2xy+2y^{2}-8x+2y and classify each as max, min, or saddle.

See Solution

Problem 10123

A cyclist took 3 h to cycle from Town X to Town Y at 12 km/h. If speed increases by 3 km/h, how long will the journey take?

See Solution

Problem 10124

A moving company delivers to two sites. What is the probability of the shortest route using the factorial rule? Calculate 2!2!.

See Solution

Problem 10125

Find f+gf+g, fgf-g, fgfg, and fg\frac{f}{g} for given functions f(x)f(x) and g(x)g(x) in three cases.

See Solution

Problem 10126

Find f+gf+g, fgf-g, fgfg, and fg\frac{f}{g} for f(x)=3x+4f(x)=3x+4 and g(x)=2x1g(x)=2x-1.

See Solution

Problem 10127

Find critical points of t(x,y)=x312xy+y3t(x, y)=x^{3}-12xy+y^{3} and classify as max, min, or saddle.

See Solution

Problem 10128

Minimize the cost function C(x,y)=3000+600x2+700y2C(x, y) = 3000 + 600x^2 + 700y^2 for pounds of sulfur (xx) and lead (yy) removed daily.

See Solution

Problem 10129

Find the following for f(x)=2x5f(x)=2x-5 and g(x)=4x2g(x)=4x^{2}: a. f+gf+g, b. fgf-g, c. fgfg, d. fg\frac{f}{g}.

See Solution

Problem 10130

Find prices p1p_{1} and p2p_{2} for Ultra Mini and Big Stack such that q1=0q_{1}=0 and q2=0q_{2}=0 using given demand functions.

See Solution

Problem 10131

A motorist traveled from Town A to B, averaging 54 km/h54 \mathrm{~km/h}. If the first 13\frac{1}{3} was at 45 km/h45 \mathrm{~km/h} and he traveled 480 km after, find the speed for the last 23\frac{2}{3}.

See Solution

Problem 10132

Find the sums, differences, products, and quotients of the following functions:
1. f(x)=3x+4,g(x)=2x1f(x)=3x+4, g(x)=2x-1
2. f(x)=2x5,g(x)=4x2f(x)=2x-5, g(x)=4x^2
3. f(x)=x4,g(x)=xf(x)=x-4, g(x)=\sqrt{x}

See Solution

Problem 10133

Prove the trigonometric equation: θsin(1n)x1x2=tan1(x)\theta \sin \left(\frac{1}{n}\right) \frac{x}{\sqrt{1-x^{2}}} = \tan^{-1}(x).

See Solution

Problem 10134

Given matrix AA and vectors uu and vv, find T(u)T(u) and T(v)T(v) where T(x)=AxT(x) = A x.

See Solution

Problem 10135

Find f(4)f^{\prime}(-4) for f(x)=4x23xf(x)=4 x^{2}-3 x using the difference quotient and limit as h0h \rightarrow 0.

See Solution

Problem 10136

Find the following for f(x)=x4f(x)=x-4 and g(x)=xg(x)=\sqrt{x}: a. f+gf+g, b. fgf-g, c. fgfg, d. fg\frac{f}{g}.

See Solution

Problem 10137

Find (fg)(x)(f \circ g)(x), (gf)(x)(g \circ f)(x), and (fg)(3)(f \circ g)(3) for f(x)=2xf(x)=2x, g(x)=x+5g(x)=x+5.

See Solution

Problem 10138

Given the matrix AA and vectors uu and vv, find T(u)T(u) and T(v)T(v) where T(x)=AxT(x)=Ax. Simplify your answers.

See Solution

Problem 10139

EXN.1.SL.TZO.8 [9 marks] The following diagram shows the graph of y=2+x3y=-2+\sqrt{x-3} for x3x \geq 3. (a) Describe a sequence of transformations that transforms the graph of y=xy=\sqrt{x} for x0x \geq 0 to the graph of y=2+x3y=-2+\sqrt{x-3} for x3x \geq 3. [3 marks]
A function ff is defined by f(x)=2+x3f(x)=-2+\sqrt{x-3} for x3x \geq 3. (b) State the range of ff. [1 marks] (c) Find an expression for f1(x)f^{-1}(x), stating its domain. [5 marks]

See Solution

Problem 10140

1. In Exercises 53-60, use transformations to describe how the graph of the function is related to a basic trigonometric graph. Graph two periods.
53. y=sin(x+π)y=\sin (x+\pi)
54. y=3+2cosxy=3+2 \cos x
55. y=cos(x+π/2)+4y=-\cos (x+\pi / 2)+4
56. y=23sin(xπ)y=-2-3 \sin (x-\pi)
57. y=tan2xy=\tan 2 x
58. y=2cot3xy=-2 \cot 3 x
59. y=2secx2y=-2 \sec \frac{x}{2}
60. y=cscπxy=\csc \pi x

See Solution

Problem 10141

Let gg be a.function defined for all x0x \neq 0, such that g(5)=3g(5)=-3, and the derivative of gg is given by g(x)=x2x2xg^{\prime}(x)=\frac{x^{2}-x-2}{x} for all x0x \neq 0. A. Find all values of xx for which the graph of gg has a horizontal tangent, and determine whether gg has a local maximum a local minimum, or neither at each of these values. Justify your answers. B. On what intervals, if any, is the graph of gg concave up? Justify your answer. C. Write an equation for the line tangent to the graph of gg at x=5x=5. D. Does the line tangent to the graph of gg at x=5x=5 lie above or below the graph of gg for x>5x>5 ? Why?

See Solution

Problem 10142

Question 1 (a) Rationalize the denominator and simplify 23113+331+3\frac{2 \sqrt{3}-1}{1-\sqrt{3}}+\frac{3 \sqrt{3}}{1+\sqrt{3}}. [5 marks] (b) If w=4+7iw=4+7 i, express w+1ww+\frac{1}{w} in the form a+bia+b i where aa and bb are real. [5 marks]
Question 2 Given that f(x)=x+5f(x)=\sqrt{x+5} and g(x)=ln(x+5)g(x)=\ln (x+5). (i) Sketch the graph of f(x)f(x). (ii) State the domain and range of f(x)f(x). (iii) Find f1(x)f^{-1}(x) and (gf1)(x)\left(g \circ f^{-1}\right)(x). [10 marks] Question 3 (a) Given that the 5th 5^{\text {th }} term of an arithmetic progression is 21 and its 10th 10^{\text {th }} term is 41 , find (i) the common difference, dd and the first term, aa. (ii) the sum of first 20th 20^{\text {th }} term. [7 marks] (b) Expand (23x)8(2-3 x)^{8} in ascending power of xx up to the term in x3x^{3}. [3 marks]
Question 4 (a) Given that A=(2132)\mathbf{A}=\left(\begin{array}{cc}2 & -1 \\ 3 & 2\end{array}\right) and B=(a1b1)\mathbf{B}=\left(\begin{array}{ll}a & 1 \\ b & 1\end{array}\right) where aa and bb are real. Find the values of aa and bb such that AB=BA\mathbf{A B}=\mathbf{B A}. [6 marks] (b) If P=(3243)\mathbf{P}=\left(\begin{array}{ll}3 & -2 \\ 4 & -3\end{array}\right), show that the inverse matrix of P\mathbf{P} is also P\mathbf{P}. [4 marks]
Question 5 (a) Given the parametric equations x=t3tx=t^{3}-t and y=t2+ty=t^{2}+t where t>0t>0.
Find dydx\frac{d y}{d x} in terms of tt. [5 marks] (b) Evaluate xx25dx\int x \sqrt{x^{2}-5} d x by using the substitution u=x25u=x^{2}-5. [5 marks]

See Solution

Problem 10143

Evaluate the integral. (Use C for the constant of integration.) ln(x)x2dx\int \frac{\ln (x)}{x^{2}} d x

See Solution

Problem 10144

Question Watch Video Show Examples
Bilquis accepted a new job at a company with a contract guaranteeing annual raises. Bilquis will get a raise of $2000\$ 2000 every year and had a starting salary of $35000\$ 35000. Make a table of values and then write an equation for SS, in terms of nn, representing Bilquis' salary after working nn years for the company. \begin{tabular}{|c|c|} \hline Number of Years at the Company & Bilquis' Salary (Dollars) \\ \hline 0 & \\ \hline 1 & \\ \hline 2 & \\ \hline 3 & \\ \hline \end{tabular}

See Solution

Problem 10145

Determine whether the function is even, odd, or neither. f(x)=5x7+2x5f(x)=5 x^{7}+2 x^{5}
Which term describes the function? Choose the correct answer below. A. neither B. odd C. even

See Solution

Problem 10146

um erro inferior a 10210^{-2}
4. Usando o método de ponto fixo, determinar o valor aproximado de 75\sqrt[5]{-7} com erro inferior a 10210^{-2}. 3.5

See Solution

Problem 10147

Marc left his house to drive to work. As he heads down his street, his speed increases steadily until he sees the stop sign at the end of the street. Then his speed decreases steadily until he comes to a complete stop at the stop sign. After waiting at the stop sign for his turn to go, Marc's speed steadily increases until he reaches the speed limit. Marc then drives at this constant speed until he approaches his office. He slows down steadily and comes to a complete stop in front of his office.
Which graph represents Marc's drive to work?
Marc's Drive to Work Δy\Delta y
Marc's Drive to Work

See Solution

Problem 10148

9) Знайти: 0xsht3t3dt.\int_{0}^{x} \frac{\operatorname{sh} t^{3}}{t^{3}} d t .

See Solution

Problem 10149

point)
Evaluate 032xx2+16dx\int_{0}^{3} 2 x \sqrt{x^{2}+16} d x
Answer: \square Preview My Answers Submit Answers

See Solution

Problem 10150

1 - Derivatives of Polynomials and Exponential Functions: point)
At a time tt seconds after it is thrown up in the air, a tomato is at a height (in meters) of f(t)=4.9t2+60t+4 mf(t)=-4.9 t^{2}+60 t+4 \mathrm{~m}. A. What is the average velocity of the tomato during the first 5 seconds? (Include help (units) .) \square B. Find (exactly) the instantaneous velocity of the tomato at t=5t=5. (Include help (units) .) \square C. What is the acceleration at t=5t=5 ? (Include help (units).) \square D. How high does the tomato go? (Include help (units).) \square E. How long is the tomato in the air? (Include help (units).) ote: You can earn partial credit on this problem.
Preview My Answers Submit Answers ou have attempted this problem 0 times. ou have unlimited attempts remaining.

See Solution

Problem 10151

(1 point)
Use the Fundamental Theorem of Calculus to find 116sin(x4)x34dx=\int_{1}^{16} \frac{\sin (\sqrt[4]{x})}{\sqrt[4]{x^{3}}} d x= \square

See Solution

Problem 10152

Let f(x)={0 if x<32 if 3x<15 if 1x<50 if x5f(x)=\left\{\begin{array}{ll} 0 & \text { if } x<-3 \\ 2 & \text { if }-3 \leq x<-1 \\ -5 & \text { if }-1 \leq x<5 \\ 0 & \text { if } x \geq 5 \end{array}\right. and g(x)=3xf(t)dtg(x)=\int_{-3}^{x} f(t) d t
Determine the value of each of the following: (a) g(5)=g(-5)= \square (b) g(2)=g(-2)= \square (c) g(0)=g(0)= \square (d) g(6)=g(6)= \square (e) The absolute maximum of g(x)g(x) occurs when x=x= \square and is the value \square It may be helpful to make a graph of f(x)f(x) when answering these questions.
Note: You can earn partial credit on this problem.

See Solution

Problem 10153

5.3 - ine Fundamental ineorem ot (1 point)
Suppose that F(x)=1xf(t)dtF(x)=\int_{1}^{x} f(t) d t, where f(t)=1t46+u4uduf(t)=\int_{1}^{t^{4}} \frac{\sqrt{6+u^{4}}}{u} d u
Find F(2)F^{\prime \prime}(2). F(2)=F^{\prime \prime}(2)= \square Preview My Answers Submit Answers

See Solution

Problem 10154

Problems (1 point)
Let f(x)=1xt8dtf(x)=\int_{1}^{x} t^{8} d t. Evaluate the following. f(x)=f(4)=\begin{array}{l} f^{\prime}(x)=\square \\ f^{\prime}(-4)=\square \end{array}
Note: You can earn partial credit on this problem.

See Solution

Problem 10155

oblem 11 \vee oblem 22 \checkmark oblem 33 \checkmark oblem 4 blem 5 blem 66 \checkmark blem 77 \checkmark blem 8 lem 9

See Solution

Problem 10156

(1 point) \qquad Evaluate ππsin4xcos3xdx\int_{\pi}^{\pi} \sin ^{4} x \cos ^{3} x d x Answer: \square
Preview My Answers Submit Answers
You have attempted this problem 0 times. You have unlimited attempts remaining.

See Solution

Problem 10157

5.2 - The Definite Integral: Problem 2 (1 point)
The limit limni=1n2xi+(xi)2Δx\lim _{n \rightarrow \infty} \sum_{i=1}^{n} \sqrt{2 x_{i}^{*}+\left(x_{i}^{*}\right)^{2}} \Delta x can be expressed as a definite integral on the interval [1,8][1,8] of the form abf(x)dx\int_{a}^{b} f(x) d x
Determine a,ba, b, and f(x)f(x). a=b=\begin{array}{l} a=\square \\ b=\square \end{array} f(x)=f(x)= \square

See Solution

Problem 10158

Definition: The AREA A of the region SS that lies under the graph of the continuous function ff is the limit of the sum of the areas of approximating rectangles A=limnRn=limn[f(x1)Δx+f(x2)Δx++f(xn)Δx]A=\lim _{n \rightarrow \infty} R_{n}=\lim _{n \rightarrow \infty}\left[f\left(x_{1}\right) \Delta x+f\left(x_{2}\right) \Delta x+\ldots+f\left(x_{n}\right) \Delta x\right]
Consider the function f(x)=ln(x)x,3x10f(x)=\frac{\ln (x)}{x}, 3 \leq x \leq 10. Using the above definition, determine which of the following expressions represents the area under the graph of ff as a limit. A. limni=1n7nln(3+7in)3+7in\lim _{n \rightarrow \infty} \sum_{i=1}^{n} \frac{7}{n} \frac{\ln \left(3+\frac{7 i}{n}\right)}{3+\frac{7 i}{n}} B. limni=1n7nln(7in)7in\lim _{n \rightarrow \infty} \sum_{i=1}^{n} \frac{7}{n} \frac{\ln \left(\frac{7 i}{n}\right)}{\frac{7 i}{n}} C. limni=1n10nln(10in)10in\lim _{n \rightarrow \infty} \sum_{i=1}^{n} \frac{10}{n} \frac{\ln \left(\frac{10 i}{n}\right)}{\frac{10 i}{n}} D. limni=1nln(3+7in)3+7in\lim _{n \rightarrow \infty} \sum_{i=1}^{n} \frac{\ln \left(3+\frac{7 i}{n}\right)}{3+\frac{7 i}{n}} E. limni=1n10nln(3+10in)3+10in\lim _{n \rightarrow \infty} \sum_{i=1}^{n} \frac{10}{n} \frac{\ln \left(3+\frac{10 i}{n}\right)}{3+\frac{10 i}{n}} Preview My Answers Submit Answers

See Solution

Problem 10159

Find the most general antiderivative of the function g(x)=x67+x76g(x)=\sqrt[7]{x^{6}}+\sqrt[6]{x^{7}}
Answer: G(x)=G(x)= \square (i) Preview My Answers Submit Answers

See Solution

Problem 10160

(1 point)
Find ff if f(x)=sin(x)+cos(x),f(0)=7,f(0)=1f^{\prime \prime}(x)=\sin (x)+\cos (x), f(0)=-7, f^{\prime}(0)=1. f(x)=f(x)= \square Preview Mv Answers Submit Answers

See Solution

Problem 10161

(1 point)
Find the function with derivative f(x)=e9xf^{\prime}(x)=e^{9 x} that passes through the point P=(0,2/9)P=(0,2 / 9). f(x)=f(x)= \square Preview My Answers Submit Answers
You have attempted this problem 0 times. You have unlimited attempts remaining.

See Solution

Problem 10162

Let f(x)=191x2f(x)=\frac{19}{\sqrt{1-x^{2}}}. Enter an antiderivative of f(x)f(x). \square

See Solution

Problem 10163

Find an antiderivative of q(t)=(t+4)2q(t)=(t+4)^{2} Q(t)=Q(t)= \square Preview My Answers Submit Answers

See Solution

Problem 10164

Evaluate the limit using L'Hospital's rule if necessary. limx0+x9sin(x)\lim _{x \rightarrow 0^{+}} x^{9 \sin (x)}
Answer: \square

See Solution

Problem 10165

(1 point)
Evaluate the following limits, using L'Hopital's rule if appropriate. limx0+x4ln(x)=\lim _{x \rightarrow 0^{+}} \sqrt[4]{x} \ln (x)= \square Preview My Answers Submit Answers

See Solution

Problem 10166

At Sunrise Mountain Resort, skiers and snowboarders use a chairlift to get to the top of a hill. The graph shows the relationship between the number of full chairs, cc, that arrive at the top of the hill and the total number of people transported, pp.

See Solution

Problem 10167

Period: The formula for the amount of money in an account paying compound interest is: A=P(1+rn)ntA=P\left(1+\frac{r}{n}\right)^{n t}
13. Write an equation that models the amount of money in an account that pays 2.5%2.5 \% annual interest, compounded quarterly, with an initial investment of \1,000.1,000. A= \qquad$

Graph each function.
14. f(x)=2+log2(x+1)f(x)=-2+\log _{2}(x+1)
15. f(x)=(x+2)34f(x)=(x+2)^{3}-4

See Solution

Problem 10168

For the following equation, what is the instantaneous rate of change at x=1?x=-1 ? f(x)=2x3x2f(x)=-2 x^{3}-x^{2}

See Solution

Problem 10169

\begin{tabular}{|r|r|} \hlinexx & yy \\ \hline-2 & -4 \\ \hline-1 & -3 \\ \hline 0 & -2 \\ \hline 1 & -1 \\ \hline 2 & 0 \\ \hline \end{tabular}
Function 3 Function 4 y=2x4y=-2 x-4 The slope is 3 and the yy-intercept is 5 .
Answer the following questions. (a) Which function has the graph with a yy-intercept closest to 0 ? Function 1 Function 2 Function 3 Function 4 (b) Which functions have graphs with slopes less than 2? (Check all that apply.) Function 1 Function 2 Function 3 Function 4 (c) Which function has the graph with the greatest yy-intercept? Function 1 Function 2 Function 3 Function 4

See Solution

Problem 10170

Name: \qquad Part 1. Multiple Choice Graphing Calculator Permitted. Select the correct answer for each problem. Be sure to fill out the answer sheet on the back of the test. (a) 92-\frac{9}{2} (b) -4 (c) 4 (d) 92\frac{9}{2}

See Solution

Problem 10171

Détermine if the two functions are inverses of each othe f(x)=3x3g(x)=x33\begin{array}{l} f(x)=\sqrt[3]{3-x} \\ g(x)=x^{3}-3 \end{array} No because f(g(x))=x3+63f(g(x))=\sqrt[3]{-x^{3}+6} and g(f(x))=xg(f(x))=-x No because f(g(x))=xf(g(x))=-x and g(f(x))=xg(f(x))=-x Yes because f(g(x))=xf(g(x))=-x and g(f(x))=xg(f(x))=-x Yes because f(g(x))=x3+63f(g(x))=\sqrt[3]{-x^{3}+6} and g(f(x))=xg(f(x))=-x

See Solution

Problem 10172

Name \qquad Date \qquad
1. Jacob lives on a street that runs east and west. The grocery store is to the east and the post office is to the west of his house. Both are on the same street as his house. Answer the questions below about the following story:

At 1:00 p.m., Jacob hops in his car and drives at a constant speed of 25 mph for 6 minutes to the post office. After 10 minutes at the post office, he realizes he is late and drives at a constant speed of 30 mpl to the grocery store, arriving at 1:28 p.m. He then spends 20 minutes buying groceries. a. Draw a graph that shows the distance Jacob's car is from his house with respect to time. Remember to label your axes with the units you chose and any important points (home, post office, grocery store).

See Solution

Problem 10173

1. Below is a table of a partial set of values of the linear function h(x)h(x). \begin{tabular}{|c|c|} \hlinexx & h(x)h(x) \\ \hline-4 & -1 \\ \hline 0 & 1 \\ \hline 2 & 2 \\ \hline 8 & 5 \\ \hline 10 & 6 \\ \hline \end{tabular}
If the function is of the form h(x)=mx+bh(x)=m x+b, what is the value of the parameter mm ? A. 1 B. -2 C. 0 D. 12\frac{1}{2} A B C D

See Solution

Problem 10174

(1) 3x2dx\int^{3} x^{2} d x

See Solution

Problem 10175

Find dy/dxd y / d x if (1) y=e4x2+2x2x+1y=\frac{e^{4 x^{2}+2 x}}{2 x+1}

See Solution

Problem 10176

(11) y=1(x2+5x+3)y=1\left(x^{2}+5 x+3\right)

See Solution

Problem 10177

(2) Find the points of discontinuity of the function x23x4x32x25x+6\frac{x^{2}-3 x-4}{x^{3}-2 x^{2}-5 x+6}

See Solution

Problem 10178

Complete the equation using the distributive property: 2(x+y+7)=2(x+y+7)=

See Solution

Problem 10179

Complete the equation to show the distributive property: 2(x+y+7)=2(x+y+7)=

See Solution

Problem 10180

A car bought for \$38,000 is worth \$2,600 after 6 years. What was its value at the end of year 3?

See Solution

Problem 10181

Find (fg)(x)(f \circ g)(x), (gf)(x)(g \circ f)(x), and (fg)(3)(f \circ g)(3) for f(x)=2x+1f(x)=2x+1 and g(x)=x+34+xg(x)=\frac{x+3}{4+x}.

See Solution

Problem 10182

Find a matrix for the linear transformation T(x1,x2,x3)=(x18x2+5x3,x27x3)T(x_{1}, x_{2}, x_{3})=\left(x_{1}-8 x_{2}+5 x_{3}, x_{2}-7 x_{3}\right). A=A=

See Solution

Problem 10183

Find the equation of the line with a yy-intercept of -7 and a slope of 13-\frac{1}{3}.

See Solution

Problem 10184

Calculate the limit: limxe(xlnxx)\lim _{x \rightarrow e}(x \ln x - x)

See Solution

Problem 10185

Given A=[130001300013]A=\left[\begin{array}{ccc}\frac{1}{3} & 0 & 0 \\ 0 & \frac{1}{3} & 0 \\ 0 & 0 & \frac{1}{3}\end{array}\right], u=[91215]u=\left[\begin{array}{r}9 \\ 12 \\ -15\end{array}\right], find T(u)T(u) and T(v)T(v) for T(x)=AxT(\mathbf{x})=A \mathbf{x}.

See Solution

Problem 10186

Find where the piecewise function f(x)f(x) is not continuous:
f(x)={sinxx<0x0x1x+21<x<2x3x2 f(x)=\left\{\begin{array}{cc} \sin x & x<0 \\ x & 0 \leq x \leq 1 \\ -x+2 & 1<x<2 \\ x-3 & x \geq 2 \end{array}\right.

See Solution

Problem 10187

Calculate the wavelength for a hydrogen atom transition from (n=2)(n=2) to (n=4)(n=4) using λ=hcΔE\lambda=\frac{h c}{\Delta E}. What color is it?

See Solution

Problem 10188

Find a matrix for the linear transformation T(x1,x2,x3)=(x14x2+7x3,x26x3)T(x_{1}, x_{2}, x_{3})=\left(x_{1}-4 x_{2}+7 x_{3}, x_{2}-6 x_{3}\right). A=A=\square

See Solution

Problem 10189

A potato is shot up with an initial speed of 34ft/s34 \mathrm{ft/s} from a 42 ft building. Find the time it stays in the air using s(t)=16t2+34t+42s(t)=-16 t^{2}+34 t+42.

See Solution

Problem 10190

A ball is thrown down at 50ft/s50 \mathrm{ft/s} from a 56 ft building. Find the time it stays in the air using s(t)=16t250t+56s(t)=-16 t^{2}-50 t+56.

See Solution

Problem 10191

Graph the function f(x)=19x2f(x)=\frac{1}{9} x^{2} and find its domain and range.

See Solution

Problem 10192

Find the velocity function v(t)v(t) for the hummingbird's position s(t)=10t3t6s(t)=-10 t^{3}-t-6 in feet.

See Solution

Problem 10193

Graph the function f(x)=19x2f(x)=\frac{1}{9} x^{2} and find its domain and range. Choose from A, B, C, or D.

See Solution

Problem 10194

Find the area of the region enclosed by the curves y=2cosxy=2 \cos x and y=2cos2xy=2 \cos 2 x for 0xπ0 \leq x \leq \pi.

See Solution

Problem 10195

Find dydx\frac{d y}{d x} of the following finctions: if y=2cos2x1y=2 \cos 2 x-1

See Solution

Problem 10196

Find dydx\frac{d y}{d x} of the following function (1) if y=x2x+1y=\frac{x^{2}}{x+1}

See Solution

Problem 10197

Defferentiate with respect to x:4x2x: 4-x^{2}

See Solution

Problem 10198

If f(x,y)=2x2yeyf(x, y)=2 x^{2}-y e^{y} and the maximum rate of change of ff at (1,0)(1,0) is aa then a2a^{2} equal
Answer: \square

See Solution

Problem 10199

If f(x,y)=2x2yeyf(x, y)=2 x^{2}-y e^{y} and the maximum rate of change of ff at (1,0)(1,0) is aa then a2a^{2} equal
Answer: \square

See Solution

Problem 10200

\begin{align*} f(-6) &= 1, \\ f(-5) &= 3, \\ f(-2) &= 0, \\ f(-1) &= -1, \\ f(0) &= 0, \\ f(4) &= 4, \\ f(6) &= 2, \\ f(8) &= 2. \end{align*} Determine if the function f(x) f(x) is even, odd, or neither based on the given values.

See Solution
banner

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

ParentsInfluencer programContactPolicyTerms
TwitterInstagramFacebookTikTokDiscord