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denpristay [2]
3 years ago
13

A can in the shape of a right circular cylinder is required to have a volume of 500 cubic centimeters. The top and bottom are ma

de of a material that costs 11 cents per square​ centimeter, while the sides are made of a material that costs 8 cents per square centimeter. Express the total cost C of the material as a function of the radius r of the cylinder.
Mathematics
1 answer:
borishaifa [10]3 years ago
3 0

Answer:

The answer to the question is

The total cost C of the material as a function of the radius r of the cylinder is

0.6912·r² + 800/r Dollars.

Step-by-step explanation:

To solve the question, we note that

The area of the top and bottom combined  = 2·π·r²

The area of the sides = 2·π·r·h

and the volume = πr²h = 500 cm²

Therefore height = 500/(πr²)

Substituting the value of h into the area of the side we have

Area of the side = 2πr·500/(πr²) = 1000/r

Therefore total area of can = Area of top + Area of bottom + Area of side

Whereby the cost of the can = 0.11×Area of top +0.11×Area of bottom +0.8×Area of side

Which is equal to

0.11×2×π×r²+ 0.8×1000/r = 0.6912·r² + 800/r

The cost of the can is $(0.6912·r² + 800/r)

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Answer:

C) 9,40,41

Step-by-step explanation:

Pythagorean triple is when a²+b²=c²

A) 1,3,10

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B) 4,5,9

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C) 9,40,41

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3 years ago
The base of a rectangular prism has an area of 8 square meters. The height of the rectangular prism is 5 meters.
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<h3>Answer:   14x - 8</h3>

=======================================================

Explanation:

I'll use the quadratic formula to find the roots or x intercepts. This slight detour allows us to factor without having to use guess-and-check methods.

The equation is of the form ax^2+bx+c = 0

  • a = 12
  • b = -11
  • c = -5

This leads to...

x = \frac{-b\pm\sqrt{b^2-4ac}}{2a}\\\\x = \frac{-(-11)\pm\sqrt{(-11)^2-4(12)(-5)}}{2(12)}\\\\x = \frac{11\pm\sqrt{361}}{24}\\\\x = \frac{11\pm19}{24}\\\\x = \frac{11+19}{24} \ \text{ or } \ x = \frac{11-19}{24}\\\\x = \frac{30}{24} \ \text{ or } \ x = \frac{-8}{24}\\\\x = \frac{5}{4} \ \text{ or } \ x = -\frac{1}{3}

Now use those roots to form these steps

x = \frac{5}{4} \ \text{ or } \ x = -\frac{1}{3}\\\\4x = 5 \ \text{ or } \ 3x = -1\\\\4x - 5 =0 \ \text{ or } \ 3x+1 = 0\\\\(4x-5)(3x+1) = 0

Refer to the zero product property for more info.

Therefore, the original expression factors fully to (4x-5)(3x+1)

Use the FOIL rule to expand it out and you should get 12x^2-11x-5 again.

----------------------------------------------

We did that factoring so we could find the side lengths of the rectangle.

I'm using the fact that area = length*width

  • L = length = 4x-5
  • W = width = 3x+1

The order of length and width doesn't matter.

From here, we can then compute the perimeter of the rectangle

P = 2(L+W)

P = 2(4x-5+3x+1)

P = 2(7x-4)

P = 14x - 8

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Answer:

arah is at a miniature exhibit. There is a model of a skyscraper. Underneath the model was a ratio. It said:

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If the model is 38 inches tall, how Sarah use this information to find the actual height of the skyscraper?

In this concept, you will learn how proportions are used to find actual and scale dimensions using a scale ratio.

Using Proportions to Find Dimensions

A scale is a ratio that shows the relationship between the representation of an object and the real measurement of an object. Toy makers use scale ratios to make models of cars and airplanes that are proportional to the real thing. Architects use scale drawings to plan the design of buildings.

A scale drawing is a drawing that is used to represent and object that is too large to be drawn in its actual dimensions. If a drawing is to scale, you can use proportions to determine the actual dimensions of the scale drawing.

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Then, cross multiply and simplify the equation to find the value of x.

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