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4 years ago

A cake has a circumference of 25 1/7 inches. What is the area of the cake? Use 22/7 to approximate pi

1 answer:

7 0

To calculate for area given the circumference we proceed as follows:
C=2πr
where:
r=radius
thus given that C=25 1/7 in=176/7
thus plugging in our formula to solve for r we get:
176/7=2πr
thus
r=4.002~4.00 in
hence the area will be:
A=πr²
A=π×(4²)
A=50 2/7 in²

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The length of a rectangle is the width minus 8 units. The area of the rectangle is 9 units. What is the length, in units, of the

frez [133]

Length of rectangle is 1 unit

<u>Solution: </u>

Given that

Length of a rectangle is width minus 8 units.

Area of rectangle = 9 square units

Need to calculate the length of rectangle.

Let us assume width of rectangle = x

As Length is width minus 8,

Length of the rectangle = x – 8

$\text{ Area of rectangle }=\text{ width of rectangle }\times \text{ Length of the rectangle }$

$\text{ Area of rectangle }= x\times (x-8)$

$\text { Area of rectangle }=\left(x^{2}-8 x\right)$

As given that area of rectangle = 9 square units

$\begin{array}{l}{\Rightarrow x^{2}-8 x=9} \\\\ {\Rightarrow x^{2}-8 x-9=0}\end{array}$

On solving above quadratic equation for x, we get

$\begin{array}{l}{\Rightarrow x^{2}-9 x+x-9=0} \\\\ {\Rightarrow x(x-9)+1(x-9)=0} \\\\ {\Rightarrow (x-9)(x+1)=0}\end{array}$

When $x-9 =9, x = 9$

When $x + 1 = 0, x = -1$

As width cannot be negative, so considering x = 9

$\text{ Length of rectangle }= x-8 = 9-8 = 1 \text{ unit }$

Hence, Length of rectangle is 1 unit.

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3 years ago

A community swimming pool is a rectangular prism that is 30 feet long, 12 feet wide, and 5 feet deep. The wading pool is half as

topjm [15]

Answer:

The volume of the community swimming pool is 4 times greaters than the volume of the wading pool.

Step-by-step explanation:

By definition of rectangular prism, we get the respective formulas for the volumes of the community swimming pool and the wadling pool, respectively:

Community swimming pool

$V_{c} = l\cdot w\cdot h (1)$

Wading pool

$V_{w} = \left(\frac{1}{2}\cdot l \right)\cdot \left(\frac{1}{2}\cdot h\right)\cdot w (2)$

Where:

l – Length of the swimming pool, measured in feet.

h – Depth of the swimming pool, measured in feet.

w – Width of the swimming pool, measured in feet.

$V_{c}$ – Volume of the community swimming pool, measured in cubic feet.

$V_{w}$ – Volume of the wading swimming pool, measured in cubic feet.

The ratio of the volume of the community swimming pool to the volume of the wadling pool is:

$\frac{V_{c}}{V_{w}} = \frac{l\cdot w \cdot h}{\left(\frac{1}{2}\cdot l \right)\cdot \left(\frac{1}{2}\cdot h\right)\cdot w} (3)$

$\frac{V_{c}}{V_{w}} = \frac{1}{\frac{1}{4} }$

$\frac{V_{c}}{V_{w}} = 4$

The volume of the community swimming pool is 4 times greaters than the volume of the wading pool.

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2 years ago

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The unit numbers can be 2,4,6.Suppose 2 as the unit number we can form 20 numbers the same way for 4 and 6 so totally 60 numbers.

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3 years ago

The Neolithic Revolution

Amanda [17]

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<u>Explanation:</u>

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