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nordsb [41]
2 years ago
11

A family is having a pool built in their backyard. If their yard is rectangular and measures 10x by 10x and the pool is circular

with a radius of 2x how much of the yard will be left over after the pool is built
Mathematics
1 answer:
Igoryamba2 years ago
7 0

Answer:

100x^2-4\pi x^2

Also can be said as:

4x^2(25-\pi )

Step-by-step explanation:

<h3>The scenario:</h3>

The question is asking you, "how much is left over."

In this scenario, you're going to have to subtract the area of the pool (P) from the total area of the backyard (B), which will leave you with the remaining area of the backyard (x).

This means your equation to solve this question is:

x=B-P

<h3>Step 1:</h3>

The value of B is the area of the backyard.

We are told that the backyard is a rectangular shape. So, we can use the formula of finding the area of a rectangle.

The formula is B=L*W, where L is the length and W is the width.

Both the length and width are 10x, so we must plug that into this equation.

We end up getting:

B=10x*10x

Which can be simplified to:

B=100x^2

<h3>Step 2:</h3>

The value of P is the area of the pool.

The pool is a circular shape. So, to get the area of it, we must use the formula of finding the area of a circle.

The formula is P=\pi r^2, where r is the radius.

Plugging in the radius of 2x, we get:

P=\pi (2x)^2

By solving this out, we end up with:

P=4\pi x^2

<h3>Step 3:</h3>

From the scenario, we have the equation:
x=B-P

And from steps 1 and 2, we have the values:

B=100x^2 and P=4\pi x^2

Now we just plug those values in to get:

x=100x^2-4\pi x^2

And finally, the amount of the backyard remaining is:

100x^2-4\pi x^2

<h3>Different format:</h3>

This answer may be simplified to:

4x^2(25-\pi )

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Vector V is in standard position and makes an angle of 50° with the positive x-axis. Its magnitude is 18. Write V in component f
Umnica [9.8K]

Answer:

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Step-by-step explanation:

V = 18 units at an angle of 50° to the positive x-axis

In component Form, this is how each component is calculated

a = 18cos50° = 11.57 units east

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check if your answer is correct

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In vector component form ai + bj = 11.57i + 13.79j

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Oduvanchick [21]
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Question 1 
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\frac{a}{x^n}
Where a is constant, x is a variable and n is a positive integer.
Here is an example of a polynomial:
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x would be is a variable, please keep in mind that you can have polynomials with more than one variable. Numbers before variables are called constants.
Here are some example of constants:
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Question 2
We can name polynomials based on their degree and number of terms.
A degree is largest exponent. Examples:
x^3+2x+3; degree=3\\ x^2+2; degree=2\\ 21;degree=0
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Here is a chart showing you special names for polynomials based on their degree:
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Question 3
When adding or subtracting polynomials we simply subtract/add like terms.
Like terms are those that have the same exponent. Here is an example:
4x^3+2x^2+x+5\\ x^4 -x^3+3x^2\\
Let us add these two polynomials:
4x^3+2x^2+x+5\\ x^4 -x^3+3x^2\\ x^4+(4x^3-x^3)+(2x^2+3x^2)+x+5=x^4+3x^3+5x^2+x+5
Question 4
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Foil can be used only to multiply two binomials( polynomials that have 2 terms). 
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Question 5
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Question 6
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(x-3)(x+3)=x^2-9=x^2-(3)^2; Using formula\\&#10;(x-3)(x+3)=x^2+3x-3x-9=x^2-9=x^2-(3)^2
You can see that we get the same result, so when you have these special cases you can use formulas as a schortcut.

8 0
3 years ago
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