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3 years ago

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Bonnie buys a used car for $2500. She calculates her average monthly expenses for gas, insurance, and maintenance at $150 per mo

nth. The function f(x) = 150x + 2500 represents her total cost of owning the car for x number of months.

1 answer:

zhannawk [14.2K]3 years ago

6 0

F(x) = 150x + 2500

The range is f(x) ≥ 2500

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Let g be the function given by g(x)=limh→0sin(x h)−sinxh. What is the instantaneous rate of change of g with respect to x at x=π

lorasvet [3.4K]

The <em>instantaneous</em> rate of change of <em>g</em> with respect to <em>x</em> at <em>x = π/3</em> is <em>1/2</em>.

<h3>How to determine the instantaneous rate of change of a given function</h3>

The <em>instantaneous</em> rate of change at a given value of $x$ can be found by concept of derivative, which is described below:

$g(x) = \lim_{h \to 0} \frac{f(x+h)-f(x)}{h}$

Where $h$ is the <em>difference</em> rate.

In this question we must find an expression for the <em>instantaneous</em> rate of change of $g$ if $f(x) = \sin x$ and evaluate the resulting expression for $x = \frac{\pi}{3}$ . Then, we have the following procedure below:

$g(x) = \lim_{h \to 0} \frac{\sin (x+h)-\sin x}{h}$

$g(x) = \lim_{h \to 0} \frac{\sin x\cdot \cos h +\sin h\cdot \cos x -\sin x}{h}$

$g(x) = \lim_{h \to 0} \frac{\sin h}{h}\cdot \lim_{h \to 0} \cos x$

$g(x) = \cos x$

Now we evaluate $g(x)$ for $x = \frac{\pi}{3}$ :

$g\left(\frac{\pi}{3} \right) = \cos \frac{\pi}{3} = \frac{1}{2}$

The <em>instantaneous</em> rate of change of <em>g</em> with respect to <em>x</em> at <em>x = π/3</em> is <em>1/2</em>. $\blacksquare$

To learn more on rates of change, we kindly invite to check this verified question: brainly.com/question/11606037

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1 year ago

point P is located at (-2, 7), and point R is located at (1, 0). find the y value for the point Q that is located 2/3 the distan

natulia [17]

Answer: 7/3

Step-by-step explanation:

R-P= (3,-7). the displacement vector.

P+x(R-P) moves to x times distance between

P+(R-P) = R moves to 100% of the distance.

Q = P+2/3(R-P)

= (-2,7)+2/3(3,-7)

= (-2,7)+(2,-14/3)

= (0,7-14/3)

= (0,7/3)

= (0,2.3333...)

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2 years ago

If f(x) = 3x + –, what is f(a+ 2)?

svetlana [45]

Answer:

C

Step-by-step explanation:

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2 years ago

(-16,-4),(8,-2) in a graph NOWW!!!!

Charra [1.4K]

Answer:

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2 years ago

19. Use the unit circle to find the value of tan 315º.<br> Show work pls.

Free_Kalibri [48]

Answer: -1

Step-by-step explanation:

First change tan(315) to:

$\frac{\sin(315)}{\cos(315)}$

Then evaluate the sine and cosine function. What is the y component of 315 degrees? What is the x component of 315 degrees?

$-\frac{\sqrt{2} }{2} /\frac{\sqrt{2} }{2} =-1$

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2 years ago