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1 year ago

7

I WILL GIVE BRAINLIEST TO WHOEVER ANSWERS FIRST! A circle has a diameter AB, and its center is at (-3, 3). Point A is at (1/2,6)

. ). Where is point B located
ANSWER CHOICES:
(0, -6.5)
(-1.25, 4.5)
(6.5, 0)
(-6.5, 0)

1 answer:

kow [346]1 year ago

3 0

Using the mid-point concept, it is found that point B is located at coordinates (-6.5, 0).

<h3>What is the midpoint concept?</h3>

The midpoint between two points is the halfway point between them, and is found using the mean of the coordinates.

The center is the midpoint of the two coordinates of the diameter, hence:

$C = \frac{B + A}{2}$

For the x-coordinate:

$-3 = \frac{x + 0.5}{2}$

x + 0.5 = -6

x = -6.5

For the y-coordinate:

$3 = \frac{y + 6}{2}$

y + 6 = 6

y = 0

More can be learned about the mid-point concept at brainly.com/question/10956693

#SPJ1

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Aleksandr-060686 [28]

Answer:

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$h\approx 1.084\ feet$

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Step-by-step explanation:

<u>Optimizing With Derivatives </u>

The procedure to optimize a function (find its maximum or minimum) consists in :

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We know a cylinder has a volume of 4 $ft^3$ . The volume of a cylinder is given by

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Equating it to 4

$\displaystyle \pi r^2h=4$

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$\displaystyle h=\frac{4}{\pi r^2}$

A cylinder with an open-top has only one circle as the shape of the lid and has a lateral area computed as a rectangle of height h and base equal to the length of a circle. Thus, the total area of the material to make the cylinder is

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$\displaystyle A=\pi r^2+2\pi r \left (\frac{4}{\pi r^2}\right )$

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Rearranging

$\displaystyle 2\pi r=\frac{8}{r^2}$

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$\displaystyle r^3=\frac{4}{\pi }$

$\displaystyle r=\sqrt[3]{\frac{4}{\pi }}\approx 1.084\ feet$

Computing h

$\displaystyle h=\frac{4}{\pi \ r^2}\approx 1.084\ feet$

We can see the height and the radius are of the same size. We check if the critical point is a maximum or a minimum by computing the second derivative

$\displaystyle A''=2\pi+\frac{16}{r^3}$

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The minimum area is

$\displaystyle A=\pi(1.084)^2+\frac{8}{1.084}$

$\boxed{ A=11.07\ ft^2}$

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