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3 years ago

A circular plate has circumference 24.5 inches. what is the area of this plate? use 3.14 for pi.

Mathematics

2 answers:

lbvjy [14]3 years ago

5 0

Answer:

The area of the plate is 47.78

Step-by-step explanation:

Alex3 years ago

4 0

Given:

Circumference of a circular plate = 24.5 inches.

To FInd:

Area of the circular plate

Solution:

By the formula of circumference

Circumference of a circular plate = 2πr

Where 'r' = radius of the plate

24.5 = 2 $\pi r$

r = $\frac{24.5}{3.14 * 2}$ [Since π = 3.14]

r = 3.90 inches

We know the formula of a circular plate is,

Area = πr²

Therefore, A = (3.14)(3.90)²

A = 47.79 square inches

Therefore, area of the circular plate is 47.79 inches.

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The area of a rectangle is represented by (x^2-14x-32) square units . If the width of the rectangle is represented by (x+2) unit

Flura [38]

The expression for length of rectangle is (x - 16) units

<h3><u>Solution:</u></h3>

Given that area of a rectangle is represented by $x^2-14x-32$ square units

width of the rectangle is represented by (x+2) units

To find: length of the rectangle

<em><u>The area of rectangle is given as:</u></em>

$\text { area of rectangle }=\text { length } \times \text { width }$

Substituting the values in formula, we get

$x^{2}-14x-32=\text{length} \times(x+2)$ ---- eqn 1

Let us first factorise the L.H.S of eqn 1

$x^{2}-14x-32$

Break the expression into groups

$=\left(x^2+2x\right)+\left(-16x-32\right)$

$\mathrm{Factor\:out\:}x\mathrm{\:from\:}x^2+2x\mathrm{:\quad }x\left(x+2\right)$

$\mathrm{Factor\:out\:}-16\mathrm{\:from\:}-16x-32\mathrm{:\quad }-16\left(x+2\right)$

$=x\left(x+2\right)-16\left(x+2\right)$

$\mathrm{Factor\:out\:common\:term\:}x+2$

$=\left(x+2\right)\left(x-16\right)$

Now substitute the above value in eqn 1

$(x + 2)(x - 16) = length \times (x + 2)$

$length = \frac{(x + 2)(x - 16)}{x + 2}$

Length = x - 16

Thus the expression for length of rectangle is (x - 16) units

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3 years ago