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3 years ago

6

rhada has a 5-pound bag of clay. her craft project requries 5 ounces of clay for each batch of 6 ornaments . if she use all of t

he clay how many ornaments can rhada make

2 answers:

frutty [35]3 years ago

7 0

96 ornaments can be created

butalik [34]3 years ago

5 0

66, and then she will have some clay left over

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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 mass of mars is approximately 100000000000000000000000 kilograms and that of neptune is about 100000000000000000000000000 ki

rusak2 [61]

Mars-10^23
Neptune-10^26

4 0

3 years ago

La factorización de la expresión 33x^2-34x+8 es (3x-2)(11x-4)

USPshnik [31]

Answer:

B i think

Step-by-step explanation:

8 0

3 years ago

What are the values of a and b?

ivann1987 [24]

Answer:

<h2>a = 400/21, b = 580/21</h2>

Step-by-step explanation:

Small triangles are similar. Therefore, the sides are proportional

$\dfrac{a}{20}=\dfrac{20}{21}$ <em>cross multiply</em>

$21a=(20)(20)$ <em>divide both sides by 21</em>

$a=\dfrac{400}{21}$

For b, we can use the Pythagorean theorem:

$b^2=\left(\dfrac{400}{21}\right)^2+20^2\\\\b^2=\dfrac{160000}{441}+400\\\\b^2=\dfrac{160000}{441}+\dfrac{176400}{441}\\\\b^2=\dfrac{336400}{441}\to b=\sqrt{\dfrac{336400}{441}}\\\\b=\dfrac{\sqrt{336400}}{\sqrt{441}}\\\\b=\dfrac{580}{21}$

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3 years ago

What is the slope of this non vertical line

bija089 [108]

The slope is 3/1. (Rise over run, rise 3 run 1)

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3 years ago

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