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Veronika [31]
3 years ago
7

Write an algebraic expression for the word expression: 15 divided by the sum of "d" and 3

Mathematics
1 answer:
Yuki888 [10]3 years ago
8 0

the answer is

15/(3+d)

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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.

3 0
3 years ago
I can’t figure this out
patriot [66]

Answer:

m \leq 4.3

Step-by-step explanation:

We need to get m on one side all by itself. To achieve this, let's subtract both sides by 1.2 to get m \leq 5.5-1.2 \implies m \leq 4.3.

7 0
3 years ago
The measure of RST can be represented by the expression (10x+18). What is m RST rounded to the nearest hundredth?
NeX [460]

Answer: 90.86

i got this questions

8 0
1 year ago
What’s the answer ?
xxMikexx [17]

B 5x+20 hope this helps!!

8 0
3 years ago
What is the measure of the radius of the cone in the diagram below?
Anastasy [175]

Answer:

4cm

Step-by-step explanation:

the diameter is labelled as 8cm

radius is half of the diameter

3 0
3 years ago
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