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3 years ago

A line has a slope of 0 and passes through the point (9,9) what is its equation in slope-intercept form?

Mathematics

1 answer:

andreyandreev [35.5K]3 years ago

4 0

Step-by-step explanation:

The equation of the line with a slope of 0 is y=c, where c is a constant.

As the line passesvthrough a pt with a y coordinate of 9, the equation is y=9.

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Y = 4x + 2<br> on a graph

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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.

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3 years ago

Identify the solution of the inequality |4x − 2| > 14 and the graph that represents it.

kodGreya [7K]

The solution to the inequality |4x − 2| > 14 is x > 4 and x < -3

<h3>What is an inequality?</h3>

An inequality is an expression that shows the non equal comparison of two or more numbers and variables.

Given the inequality:

|4x − 2| > 14

Hence:

4x - 2 > 14 or -(4x - 2) > 14

x > 4 or x < -3

The solution to the inequality |4x − 2| > 14 is x > 4 and x < -3

Find out more on inequality at: brainly.com/question/24372553

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Vera_Pavlovna [14]

Answer:

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