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nasty-shy [4]
3 years ago
13

For the function given, state the middle line: ƒ(t) = 3 cos(π t − 1).

Mathematics
1 answer:
kozerog [31]3 years ago
8 0
Cos (πt - 1) oscilates periodically between -1 and +1.

3Cos (πt - 1) oscilates periodically between -3 and +3.

The x-axis is the middle line. The equation of the x-axis is y = 0.

So the, the middle line is y=0.
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The graph of f(x) is show below.
vlada-n [284]

ANSWER

(2,2)

EXPLANATION

Since f(x) and its inverse function are symmetric about the line y=x, if (a,b) lies on the graph of f, then (b,a) must lie on f inverse.

The point (2,2) lies on f and the same time on f inverse.

The solution is a point that satisfies both equations.

Hence the correct choice is:

(2,2)

5 0
4 years ago
Read 2 more answers
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
Please help!!!!!!!!!
Andrews [41]
Since sides kl and kj are congruent that means that angles klj and kjl are congruent. if angle klj is 58 then that means kjl is also 58. so you take the total number of degrees in a triangle (180) and subtract 58 and 58 (116) which leaves you with 64 ( the degree measure of lkj) 
5 0
3 years ago
What is the size of angle c?
lesantik [10]

Answer:

55°

Step-by-step explanation:

d = 180 - 80 = 100

100 + 130 + 90 + (180 - 85) + (180 - c)

= 540

595 - c = 540

c = 595 - 540

c = 55°

6 0
3 years ago
Multiplying two digits<br>​
Vika [28.1K]

Answer:

Get a calculator

Step-by-step explanation:

Most of the time for simple math like multiplying 2 digits, it is easiest if you just get a calculator. It saves a lot of time.

If you can't get a calculator then i recommend memorizing some common equations.

For example 10*15= 150

so that if you get 12*15=?, you can easily just add two extra 15's to your answer of 150.

15+15 is 30, and 30+150(from 10*15)=180.

Therefore 12*15=180.

:) Hope that helped!

4 0
3 years ago
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