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fiasKO [112]
3 years ago
5

Find (f-g)(x). What is the domain of f/g f(x)=2x-5 g(x)=2-x

Mathematics
1 answer:
Elden [556K]3 years ago
6 0

f(x)=2x-5 , \ \ \ \ g(x)=2-x \\\\(f-g)(x)=f(x)-g(x) = 2x-5 -(2-x)=2x-5-2+x = 3x+5 \\\\\\
  domain :  \frac{f}{g}=\frac{2x-5}{2-x}\\\\2-x\neq 0 \\ \\x\neq 2 \\ \\D=R\setminus \left \{ 2 \right \}
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A rectangle with a length of L and a width of W has a diagonal of 10 inches. Express the perimeter P of the rectangle as a funct
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<h2>Answer:</h2>

The expression which represents the perimeter P of the rectangle as a function of L is:

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<h2>Step-by-step explanation:</h2>

The length and width of a rectangle are denoted by L and W respectively.

Also the diagonal of a rectangle is: 10 inches.

We know that the diagonal of a rectangle in terms of L and W are given by:

10=\sqrt{L^2+W^2}

( Since, the diagonal of a rectangle act as a hypotenuse of the right angled triangle and we use the Pythagorean Theorem )

Hence, we have:

10^2=L^2+W^2\\\\i.e.\\\\W^2=100-L^2\\\\W=\pm \sqrt{100-L^2}

But we know that width can't be negative. It has to be greater than 0.

Hence, we have:

W=\sqrt{100-L^2}

Now, we know that the Perimeter of a rectangle is given by:

Perimeter=2(L+W)

Here we have:

Perimeter=2(L+\sqrt{100-L^2})

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