Consider the figure below. Find m∠ABAC.will give 20 points

Mathematics

1 answer:

lesya692 [45]3 years ago

3 0

Answer:

Step-by-step explanation:

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A church window consisting of a rectangle topped by a semicircle is to have perimeter p . find the radius of the semicircle if t

Y_Kistochka [10]

Answer:

$r=\dfrac{p}{4+\pi}$

Step-by-step explanation:

Let r be the radius of the semicircle, then 2r is the width of the rectangle. Let y be the length of the rectangle. The perimeter of the window consists of two lengths, one width and length of semicircle, then

$p=2y+2r+\pi r.$

Express y:

$y=\dfrac{p-2r-\pi r}{2}.$

The area of the window is

$A=y\cdot 2r+\dfrac{1}{2}\pi r^2.$

Substitute y into the area expression:

$A=\dfrac{p-2r-\pi r}{2}\cdot 2r+\dfrac{1}{2}\pi r^2=pr-2r^2-\pi r^2+\dfrac{1}{2}\pi r^2=pr-2r^2-\dfrac{1}{2}\pi r^2.$

Find the derivative A':

$A'=p-4r-\pi r.$

Equate A' to 0:

$p-4r-\pi r=0\Rightarrow r=\dfrac{p}{4+\pi}.$

When $r$ then $A'>0$ and the function A is increasing, when $r>\dfrac{p}{4+\pi},$ then $A'$ and the function A is decreasing. This means that at point $r=\dfrac{p}{4+\pi}$ the function A takes it maximal value (the area is maximal).

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Joel wants to find the best model for a bivariate data set that he is working with. He used a calculator to create a linear mode

laiz [17]

Answer:

exponential

Step-by-step explanation:

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3 years ago

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Look at the multiples of 4 that have an odd number in the tens place what values do they have

VladimirAG [237]

Answer: The values in the ones place are always a 2 or a 6

<u>Step-by-step explanation:</u>

$04\\08\\ \rightarrow 12 \leftarrow \\ \rightarrow 16\leftarrow \\20\\24\\28\\ \rightarrow 32 \leftarrow \\ \rightarrow 36\leftarrow \\40\\44\\48\\ \rightarrow 52\leftarrow \\ \rightarrow 56\leftarrow \\60\\64\\68\\ \rightarrow 72\leftarrow \\ \rightarrow 76\leftarrow \\80\\84\\88\\ \rightarrow 92\leftarrow \\ \rightarrow 96\leftarrow \\100$