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3 years ago

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‼️ What is the height of a right triangle with an angle that measures 60 degrees and a base of 14 adjacent to the 60 degree angl

e???

1 answer:

puteri [66]3 years ago

7 0

You'd use tangent for this.

opposite / adjacent

tan 60* = x/14

multiply both sides by 14

tan 60* = 1.73

tan 60* (1.73 x 14) = x

24.22 = x

Your answer should be 24.22

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Here we will study the function f (x) = e ^ x sin (x), where x ∈ [0, 2π]. a) Determine where the function is decreasing and incr

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To find increasing and decreasing intervals we take derivative

$f'(x) = e^xsin(x)+e^x(cosx)= e^x(sinx+cosx)$

Now we set the derivative =0 and solve for x

$e^x(sinx+cosx)=0$

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Now we pick a number between 0 to $\frac{3\pi }{4}$

Lets pick $\frac{\pi }{2}$

Plug it into the derivative

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Now we pick a number between $\frac{7\pi}{4}$ to 2pi

Lets pick $\frac{11\pi}{6}$

Plug it into the derivative

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Increasing interval is $(0,\frac{3\pi }{4}) U (\frac{7\pi }{4}, 2\pi)$

Decreasing interval is $(\frac{3\pi}{4}, \frac{7\pi}{4})$

(b)

The graph of f(x) increases and reaches a local maximum at $x=\frac{3\pi}{4}$

The graph of f(x) decreases and reaches a local minimum at $x=\frac{7\pi}{4}$

(c)

f(0) = 0

$f(2\pi)=0$

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Here global maximum at $x=\frac{3\pi}{4}$

Here global minimum at $x=\frac{7\pi}{4}$

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