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IgorLugansk [536]
3 years ago
13

Evaluating integral by net area

Mathematics
1 answer:
N76 [4]3 years ago
8 0

The graph of f(x)=2 is a horizontal line. So the area under f(x) on [0, 8] is equal to the area of a rectangle with length 8 and height 2, or 16.

The graph of g(x)=\sqrt{64-x^2} is the upper half of a circle with radius \sqrt{64}=8. It's symmetric about x=0, so on the interval [0, 8], we're considering a quarter of the circle. The area of such a sector is \frac{\pi 8^2}4=16\pi.

Then use the fact that the definite integral is distributive over sums, meaning

\displaystyle\int_0^8f(x)+g(x)\,\mathrm dx=\int_0^8f(x)\,\mathrm dx+\int_0^8g(x)\,\mathrm dx=16+16\pi

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Step-by-step explanation:

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The correct answer is B. -12
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Amy's current age is 16 years greater than Peter's age, so Amy's current age is equal to x + 16.

6 years ago, Amy's age was equal to twice that of Peter's age at that point, so her age was 2(x - 6).

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If b is the midpoint of ac, ac=cd, ab=3x+4, ac=11x-17, and ce=49, find de
IrinaK [193]

First, we draw our line.

 

|------------------------------------------------------------------------------------|

a                                                                                                            e

 

 

Next, break up this line into segments using the information.

 

|----------------------|----------------------|--------------------|------------------|

a                            b                            c                         d                      e

 

 

The entire line is 29.

 

ab + bc + cd + de = ae

ab + bc + cd + de = 29

 

You also know that

 

bd = bc + cd

 

 

Due to midpoint theorem,

 

ab = bc

cd = de

 

 

Then,

 

2ab + 2cd = 29

 

 

The equations we will use are

 

bd = bc + cd                       eq1

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3 years ago
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nikdorinn [45]

Answer:

2. -2x^{8}y^{18}  

Step-by-step explanation:  

We have been given an expression \frac{10x^{6}y^{12}}{-5x^{-2}y^{-6}} and we are asked to find equivalent expression to our given expression.

Using fraction rule \frac{a}{-b} =-\frac{a}{b} we can write our expression as: -\frac{10x^{6}y^{12}}{5x^{-2}y^{-6}}. 

Upon dividing 10 by 5 we will get,

-\frac{2x^{6}y^{12}}{x^{-2}y^{-6}}      

Upon using exponent property for quotient (\frac{a^{m}}{a^{n}} =a^{(m-n)}) we will get,  

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3 years ago
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