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Damm [24]
3 years ago
8

Calculate the area of the shaded sector in the circle​

Mathematics
1 answer:
agasfer [191]3 years ago
6 0

Answer:

Approximately, 6.283..

Step-by-step explanation:

First calculate the area of the whole circle

We have radius(r)=4 cm

Area of circle(a)=pir^2

=pi×(4)^2

=pi×16

=Approximately,50.265......

A cirlce has a total of 360 degrees

Therefore,we can conclude 360 degrees=50.265...

or,1 degree=50.265/360

1 degree=Approximately,0.139

Now,

Area for the shaded region = Area of 45 degree

=0.139×45=Approximately,6.283.....

Therefore,the area of the shaded region is approximately,6.283....

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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

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Step-by-step explanation:

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Step-by-step explanat

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