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wlad13 [49]
1 year ago
7

Please please help Given the function f(x)=1/3x*2-3x+5 determine the inverse relation

Mathematics
1 answer:
yuradex [85]1 year ago
5 0

The inverse relation of the function f(x)=1/3x*2-3x+5 is f-1(x) = 9/2 + √(3x + 21/4)

<h3>How to determine the inverse relation?</h3>

The function is given as

f(x)=1/3x^2-3x+5

Start by rewriting the function in vertex form

f(x) = 1/3(x - 9/2)^2 -7/4

Rewrite the function as

y = 1/3(x - 9/2)^2 -7/4

Swap x and y

x = 1/3(y - 9/2)^2 -7/4

Add 7/4 to both sides

x + 7/4= 1/3(y - 9/2)^2

Multiply by 3

3x + 21/4= (y - 9/2)^2

Take the square roots

y - 9/2 = √(3x + 21/4)

This gives

y = 9/2 + √(3x + 21/4)

Hence, the inverse relation of the function f(x)=1/3x*2-3x+5 is f-1(x) = 9/2 + √(3x + 21/4)

Read more about inverse functions at:

brainly.com/question/14391067

#SPJ1

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melisa1 [442]

Answer:

Answer:

a) The base of the rectangular pyramid shown has an area of

60 square inches

b) A triangular face with a base of 10 inches has an area of 28 square inches.

c) A triangular face with a base of 5 inches has an area of 17.75 square inches.

d) The total surface area of the pyramid is 151.5 square inches.

Step-by-step explanation:

a) Solving for question a, we were given the following parameters

A rectangular pyramid. The rectangular base has a length of 10 inches and a width of 6 inches

The formula used to calculate the rectangular base of a rectangular pyramid =

Length × Width

Where :

Length = 10 inches

Width = 6 inches

Rectangular base = 10 inches × 6 inches

= 60 inches²

Hence, the base of the rectangular pyramid shown has an area of 60 square inches

b) Solving for question b, we have the following values given:

2 triangular sides have a base of 10 inches and height of 5.6 inches.

First step would be to solve for one triangular side first.

The area of the one triangular side = (Base × Height) ÷ 2

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= 56inches² ÷ 2

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Therefore, for the 2 triangular sides, since they have the same base and height, the other side as well would be 28 inches².

A triangular face with a base of 10 inches has an area of 28 square inches.

c) Solving for question c, the following parameters are given:

2 triangular sides have a base of 5 inches and height of 7.1 inches.

We would be to solving for one triangular side first.

The area of the one triangular side = (Base × Height) ÷ 2

= (5 inches × 7.1 inches) ÷ 2

= 35.5 inches² ÷ 2

= 17.75 inches²

Therefore, for the 2 triangular sides, since they have the same base and height, the other side as well would be 17.75 inches².

A triangular face with a base of 5 inches has an area of 17.75 square inches.

d) Solving for d, it is important to note that, a rectangular pyramid has 5 faces and they are: The rectangular base and 4 triangular faces

The formula for the total surface area of the rectangular pyramid is given as

Total Surface Area of the rectangular pyramid = Rectangular Base + Area of Triangular Side A + Area of Triangular Side B + Area of Triangular Side C + Area of Triangular Side D + Area of Triangular Side E

Total Surface Area of the Rectangular Pyramid = 60 inches² + 28 inches² + 28 inches² + 17.75 inches² + 17.75 inches²

Total surface Area of the Rectangular pyramid = 151.5 inches²

The total surface area of the pyramid is 151.5 square inches.

Step-by-step explanation:

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