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3 years ago

13

A community park is shaped like a trapezoid with a height of 30 yd, a top base of 25yd,and a bottom base of 33yd. The park has a

circular fountain whose radius is 4yd. What is the area of the park without the fountain?

1 answer:

Likurg_2 [28]3 years ago

6 0

Answer: 819.73 yd²

<u>Step-by-step explanation:</u>

$A_{trapezoid} = \frac{b_{1}+b_{2}}{2}*h$

= $\frac{25+33}{2}*30$

= $\frac{58}{2}*30$

= 29 * 30

= 870

$A_{circle} = \pi r^{2}$

= π(4)²

= 16π

≈ 50.27

Area of the park = $A_{trapezoid} - A_{circle}$

= 870 - 50.27

= 819.73

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3 years ago

A cardboard box without a lid is to be made with a volume of 4 ft 3 . Find the dimensions of the box that requires the least amo

Blababa [14]

Answer:

<h2><em>2ft by 2ft by 1 ft</em></h2>

Step-by-step explanation:

Total surface of the cardboard box is expressed as S = 2LW + 2WH + 2LH where L is the length of the box, W is the width and H is the height of the box. Since the cardboard box is without a lid, then the total surface area will be expressed as;

S = lw+2wh+2lh ... 1

Given the volume V = lwh = 4ft³ ... 2

From equation 2;

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Substituting into r[equation 1;

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Differentiating the resulting equation with respect to w and l will give;

dS/dw = l + (-8w⁻²)

dS/dw = l - 8/w²

Similarly,

dS/dl = w + (-8l⁻²)

dS/dw = w - 8/l²

At turning point, ds/dw = 0 and ds/dl = 0

l - 8/w² = 0 and w - 8/l² = 0

l = 8/w² and w =8/l²

l = 8/(8/l² )²

l = 8/(64/I⁴)

l = 8*l⁴/64

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l = 2

Hence the length of the box is 2 feet

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2 = 8/w²

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w² = 4

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<em>The dimensions of the box that requires the least amount of cardboard is 2ft by 2ft by 1 ft</em>

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3 years ago

1. Ellie has 2/8 pound of cheese. She used 1/2 of the cheese to make tacos. Since there are 16 ounces in one pound, how many oun

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2 years ago

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pashok25 [27]

Answer:

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3 years ago

A sphere of radius 2x m has an area of 152.4 m2 and a volume of 360.9 m3. How much will the area and volume of another sphere

VladimirAG [237]

Answer:

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Step-by-step explanation:

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$\sqrt{12.128} = x$ *Solve*

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Now take the same equation but replace 2x with 3x

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$A = 342.9m^{2\\}$

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Now replace x with 2.208 and solve for volume.

$V = 1218.0375m^{3}$

4 0

3 years ago