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3 years ago

You go out to the grocery store to buy milk and are trying to decide wether to buy the

Mathematics

1 answer:

madam [21]3 years ago

5 0

The 4L is better. Because if you bought 2 of the 2L then your total would be 5.80.

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Sonbull [250]

Answer:

56 feet, I think.

Step-by-step explanation:

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2 years ago

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oksano4ka [1.4K]

Answer:

Five more than a number

Step-by-step explanation:

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3 years ago

a helicopter is flying at 150mph on a course with a bearing of 130°. If the helicopter experiences a crosswind blowing southeast

romanna [79]

150-25=125mph

130-25=105

This means it was going 125mph and that it dropped an altitude of 25 degrees because of the wind and the slow down of the helicopter

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3 years ago

If you are offered one slice from a round pizza (in other words, a sector of a circle) and the slice must have a perimeter of 24

VARVARA [1.3K]

Answer:

A 12 in diameter will reward you with the largest slice of pizza.

Step-by-step explanation:

Let $r$ be the radius and $\theta$ be the angle of a circle.

According with the graph, the area of the sector is given by

$A=\frac{1}{2}r^2\theta$

The arc lenght of a circle with radius $r$ and angle $\theta$ is $r \theta$

The perimeter of the pizza slice is composed of two straight pieces, each of length r inches, and an arc of the circle which you know has length s = rθ inches. Thus the perimeter has length

$2r+r\theta=24 \:in$

We need to express the area as a function of one variable, to do this we use the above equation and we solve for $\theta$

$2r+r\theta=24\\r\theta=24-2r\\\theta=\frac{24-2r}{r}$

Next, we substitute this equation into the area equation

$A=\frac{1}{2}r^2(\frac{24-2r}{r})\\A=\frac{1}{2}r(24-2r)\\A=12r-r^2$

The domain of the area is

$0$

To find the diameter of pizza that will reward you with the largest slice you need to find the derivative of the area and set it equal to zero to find the critical points.

$\frac{d}{dr} A=\frac{d}{dr}(12r-r^2)\\A'(r)=\frac{d}{dr}(12r)-\frac{d}{dr}(r^2)\\A'(r)=12-2r$