3 years ago

Select the correct answer.

Mathematics

1 answer:

san4es73 [151]3 years ago

6 0

Answer:

Step-by-step explanation:

Is the answer

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Find the average value of the function over the given interval. (Round your answer to three decimal places.) f(x) = −sin x, [0,

deff fn [24]

Answer with Step-by-step explanation:

We are given that

$f(x)=-sin x$

$[0,\infty]$ ]

Average value of the function is given gy

$f_{avg}=\frac{1}{b-a}\int_{a}^{b}f(x)dx=\frac{1}{\pi-0}\int_{0}^{\pi}-sinx dx$

$f_{avg}=\frac{1}{\pi}[cosx]^{\pi}_{0}$

Using the formula

$\int sin xdx=-cos x$

$f_{avg}=\frac{1}{\pi}(cos\pi-cos0)$

$f_{avg}=\frac{1}{\pi}(-1-1)=-\frac{2}{\pi}$

$f(x)=f_{avg}$

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3 years ago

What equation represents the parabola with focus (-1,4) and directrix y= -2

Llana [10]

Answer:

Hello

y=(x+1)/12 +1

Step-by-step explanation:

$\text{As the directrice is horizontal:}\\\\\\y=-2 ==> k=-2\\\\Focus=(a,b)=(-1,4)\\\\\boxed{y=\dfrac{x-a}{2(b-k)} +\dfrac{b+k}{2} }\\\\\\y=\dfrac{x+1}{2(4+2)} +\dfrac{4-2}{2} }\\\\\boxed{y=\dfrac{x+1}{12} +1}\\$

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