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3 years ago

Given the diagram below find the value of x if the area is 21 aquare meters

Mathematics

1 answer:

Oksanka [162]3 years ago

5 0

Answer:

The answer is <u><em>7</em></u>!

Step-by-step explanation:

(x-4) (x) = 21, x^2 - 4x = 21, x^2 - 4x - 21 = 0, (x - 7) (x + 3) = 0, x = 7 and -3; x can't be negative so the answer is 7!

x = 7 and x - 4 (other side) = 3

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An iceberg weighs 450,000 lb. If it loses 0.2% of its weight during the day, what is its new weight at the end of the day?

JulsSmile [24]

Answer: The weight of the iceberg at the end of the day will be 449,100 lbs.

Step-by-step explanation: The question is solved by first calculating what the loss of weight is during the day. The question indicates that it will lose .2%. In order to calculate the loss you need to multiply 450,000 x .002, which equals 900. Next, we subtract the weight loss from the original weight to determine the end of day weight. 450,000 - 900 = 449,100 lbs.

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3 years ago

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denpristay [2]

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3 years ago

Yesterday's afternoon temperature was 21*F. It plunged overnight to 3*F. How many degrees did the temperature drop? I think the

Igoryamba

Answer: its D) 24

Step-by-step explanation:

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3 years ago

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

Inequality / Linear Systems Help - 30 points!

Sholpan [36]

They did not include the constraint for y ≤x+3 on the graph.

See attached picture with added constraint.

Using the 4 points that are given as the solution on the graph, replace t he x and Y in the original equation to solve and see which is the greater value.

Point (0,3) P = -0 +3(3) = 0+9 = 9

Point (1,4) P = -1 + 3(4) = -1 +12 = 11

Point (0,0) P = -0 + 3(0) = 0 + 0 = 0

Point (3,0) P = -3 + 3(0) = -3 + 0 = -3

The correct solution to maximize P is (1,4)

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2 years ago