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3 years ago

Can I please have help?

Mathematics

2 answers:

Anni [7]3 years ago

5 0

The answer is C

There are 200+115=315 pieces in total.

315/4 = 78.75. This means, 78 remainder 3.

To make the most even division, the remainder needs to be as small as possible.
78 remainder 3 = 79 remainder -1
So, three people get 79, and one person gets 78. That is the fairest division.

79*3 + 78 = 315

Law Incorporation [45]3 years ago

4 0

Answer:

Step-by-step explanation:

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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.

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

$12-2r=0\\-2r=-12\\\frac{-2r}{-2}=\frac{-12}{-2}\\r=6$

To check if $r=6$ is a maximum we use the Second Derivative test

if $f'(c)=0$ and $f''(c)$ , then f(x) has a local maximum at x = c.

The second derivative is

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

Because $A''(r)=-2$ the largest slice is when r = 6 in.

The diameter of the pizza is given by

$D=2r=2\cdot 6=12 \:in$

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

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3 years ago

Point M is the midpoint of AB. The coordinates of point A are (-8, 3) and the coordinates of M are (-2, 1). What are the coordin

ch4aika [34]

Answer:

the coordinates of point B are (-5, 2)

Step-by-step explanation:

1. use midpoint formula to find the midpoint (equation attached below)

2. plug in the numbers

$(\frac{-8+(-2)}{2},\frac{3+1}{2})$

3. solve

$(\frac{-8-2)}{2},\frac{3+1}{2})$

$(\frac{-10}{2},\frac{4}{2})$

$(-5,2})$

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1 employee
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3 years ago

Read 2 more answers

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Solnce55 [7]

Answer:

tn=a+(n-1)d

tn=22+(n-1)4

tn=22+4n-4

tn=4n+18

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3 years ago