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3 years ago

Hal records the number of winners of

Mathematics

1 answer:

aliya0001 [1]3 years ago

5 0

Answer:

He should expect to find about 630 winners

Step-by-step explanation:

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You are to manufacture a rectangular box with 3 dimensions x, y and z, and volume v=8000. Find the dimensions which minimize the

Inga [223]

Answer:

20 by 20 by 20

Step-by-step explanation:

Let the total surface of the rectangular box be expressed as S = 2xy + 2yz + 2xz

x is the length of the box

y is the width and

z is the height of the box.

S = 2xy + 2yz + 2xz ... 1

Given the volume V = xyz = 8000 ... 2

From equation 2;

z = 8000/xy

Substituting into equation 1;

S = 2xy + 2y(8000/xy)+ 2x(8000/xy)

S = 2xy+16000/x+16000/y

Differentiating the resulting equation with respect to x and y will give;

dS/dx = 2y + (-16000x⁻²)

dS/dx = 2y - 16000/x²

Similarly,

dS/dy = 2x + (-160000y⁻²)

dS/dy = 2x - 16000/y²

Note that at the turning point, ds/dx = 0 and ds/dy = 0, hence;

2y - 16000/x² = 0 and 2x - 16000/y² = 0

2y = 16000/x² and 2x = 16000/y²

2y = 16000/(8000/y²)²

2y = 16000×y⁴/64,000,000

2y = y⁴/4000

y³ = 8000

y =³√8000

y = 20

Given 2x = 16000/y²

2x = 16000/20²

2x = 16000/400

2x = 40

x = 20

Since Volume of the box is V = xyz

8000 = 20(20)z

8000 = 400z

z = 8000/400

z = 20

Hence, the dimensions which minimize the surface area of this box is 20 by 20 by 20.

3 0

3 years ago

Answer fast!! With explanation pls

Zepler [3.9K]

D is equivalent because brackets don’t change anything here

4 0

2 years ago

Read 2 more answers

triangle MNO is an equilateral triangle with sides measuring 16 units What is the height of the triangle?

fiasKO [112]

see the attached figure to better understand the problem

we know that

The equilateral triangle has three equal sides

in the equilateral triangle ABC

$AB=BC=AC=16 units$

the height of the triangle is the segment BD

in the right triangle BCD

Applying the Pythagorean Theorem

$BC^{2} =BD^{2}+DC^{2}$

solve for BD

$BD^{2}=BC^{2}-DC^{2}$

substitute the values

$BD^{2}=16^{2}-8^{2}$

$BD^{2}=192$

$BD=\sqrt{192}\ units$

therefore

<u>the answer is</u>

the height of the triangle is $\sqrt{192}\ units$

7 0

3 years ago

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What is the answer for 5-2+7x6-2?

sergiy2304 [10]

Answer: 43

Step-by-step explanation:

5-2+7x6-2

3+42-2

45-2

8 0

2 years ago

You use 4 gallons of water on 30 plants. At that rate how much water will you need for 45 plants?

Alja [10]

You would use 6 gallons of water to water 45 plants
4=30
$\frac{45}{30}$ = $\frac{3}{2}$
$\frac{3}{2}$ of 4 gallons = 6 gallons

8 0

3 years ago

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