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katen-ka-za [31]
1 year ago
11

The table below represents the function f, and the following graph represents the function g. x -6 -5 -4 -3 -2 -1 0 1 f(x) 8 -2

-8 -10 -8 -2 8 22 Complete the following statements. The functions f and g have . The y-intercept of f is the y-intercept of g. Over the interval [-6, -3], the average rate of change of f is the average rate of change of g
Mathematics
1 answer:
BigorU [14]1 year ago
7 0

Answer:

Complete the following statements.

The functions f and g have the same axis of symmetry.

The y-intercept of f is greater than the y-intercept of g.

Over the interval [-6, -3], the average rate of change of f is less than the average rate of change of g.

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Given f(x) = (lnx)^3 find the line tangent to f at x = 3
kirill [66]
Explanation

We must the tangent line at x = 3 of the function:

f(x)=(\ln x)^3.

The tangent line is given by:

y=m*(x-h)+k.

Where:

• m is the slope of the tangent line of f(x) at x = h,

,

• k = f(h) is the value of the function at x = h.

In this case, we have h = 3.

1) First, we compute the derivative of f(x):

f^{\prime}(x)=\frac{d}{dx}((\ln x)^3)=3*(\ln x)^2*\frac{d}{dx}(\ln x)=3*(\ln x)^2*\frac{1}{x}=\frac{3(\ln x)^2}{x}.

2) By evaluating the result of f'(x) at x = h = 3, we get:

m=f^{\prime}(3)=\frac{3}{3}*(\ln3)^2=(\ln3)^2.

3) The value of k is:

k=f(3)=(\ln3)^3

4) Replacing the values of m, h and k in the general equation of the tangent line, we get:

y=(\ln3)^2*(x-3)+(\ln3)^3.

Plotting the function f(x) and the tangent line we verify that our result is correct:

Answer

The equation of the tangent line to f(x) and x = 3 is:

y=(\ln3)^2*(x-3)+(\ln3)^3

6 0
1 year ago
The area of a square quilt is 289 square inches. There is a smaller square patch on the quilt with an area of 121 square inches.
alisha [4.7K]
Area of a square quilt = 289 square inches
Area of a smaller square quilt = 121 square inches

Area of a square = a²

Side length of big square quilt = √289 in² = 17 inches
side length of small square quilt = √121 in² = 11 inches

Perimeter of big square = 17 inches * 4 = 68 inches
perimeter of small square = 11 inches * 4 = 44 inches

difference = 68 inches - 44 inches = 24 inches.
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3 years ago
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Weight of man and paint = 160 + 5 = 165 total pounds.

Gravitational force is independent of the path taken so we can ignore the radius of the silo.

Work done = total weight x height

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Work = 165 lbs x 90 ft = 14,850 ft-lbs

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Pls hurry I need help
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Answer:

-403.2

Step-by-step explanation:

multiply the numbers together.  a negative x a postive is a neg

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Translate to English and I can help u, if I were to give u a answer it would be -8.5 based on the stuff given
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