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2 years ago

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HELPPP PLS show work

1 answer:

hram777 [196]2 years ago

4 0

So in this question, we’re gonna use the sine trigonometric ratio, which equals opposite/hypotenuse.

sin32° = x (the opposite angle)/ 10 (the hypotenuse)

Then rearrange the equation to solve for x:
(10)(sin32°) = x

[Solve for sine using a calculator!]

(10)(0.529919264) = x

[Multiply]

5.299192642 = x

[Round to the nearest tenth]

x ≈ 5.3

I hope this helped!

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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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2 years ago

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3 years ago

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