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Dennis_Churaev [7]

3 years ago

9

List all the odd composite numbers less than 20 in numerical order

1 answer:

vlada-n [284]3 years ago

5 0

9, 15 9*1=9, 3*3=9 1*15=15, 3*5=15

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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

The probability of drawing a yellow or green marble out of a bag containing 3 blue, 2 green , 8 yellow , 4 red , and 3 orange ma

WINSTONCH [101]

Answer:

$\frac{10}{23}$

Step-by-step explanation:

add green and yellow which is 10 over the whole thing which is 23

5 0

3 years ago

Which description best fits the graph

Masteriza [31]

Decreasing then increasing, y goes down then y goes back up

7 0

3 years ago

Read 2 more answers

The table below shows two equations: Equation 1 |2x − 3| + 5 = 4 Equation 2 |5x + 3| − 10 = 3 Which statement is true about the

earnstyle [38]

Answer:

Equation 1 has no solution. Equation 2 does. The correct answer would be D.

8 0

4 years ago

Solve by any method (graphing, substitution, linear combination) <br> y=x−7 <br> 5x+2y=7

Virty [35]

Answer:

(x, y) = (3, -4)

Step-by-step explanation:

See the attached for a graph.

3 0

3 years ago