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3 years ago

15

Simplify completely quantity 2 x squared plus 20 x plus 32 all over x squared minus 2 x minus 80

2 answers:

VARVARA [1.3K]3 years ago

4 0

Answer: Simplified form will be

$\frac{2(x+2)}{(x-10}$

Explanation:

Since we have given that

$\frac{2x^2+20x+32}{x^2-2x-80}$

and we need to simplify it,

First we take 2 as common factor from the numerator,

So, it becomes,

$\frac{2(x^2+10x+16)}{x^2-2x-80}$

By using splitting the middle terms, we get

$\frac{2(x^2+8x+2x+16)}{x^2-10x+8x-80}\\\\=\frac{2[(x(x+8)+2(x+8)]}{x(x-10)+8(x-10)}\frac{2(x+8)(x+2)}{(x-10)(x+8)}\\\\=\frac{2(x+2)}{(x-10}$

Hence, Simplified form will be

$\frac{2(x+2)}{(x-10}$

erastovalidia [21]3 years ago

3 0

The answer is 2(x+2)/x-10

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2 years ago

The blades of a windmill turn on an axis that is 35 feet above the ground. The blades are 10 feet long and complete two rotation

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Answer:

h = 10sin(π15t)+35

Step-by-step explanation:

The height of the blade as a function f time can be written in the following way:

h = Asin(xt) + B, where:

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alukav5142 [94]

Answer:

$y(x)=4+\frac{C}{\sqrt{x^2+10}}$

Step-by-step explanation:

We are given that a differential equation

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Compare with

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We get

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$y\cdot \sqrt{x^2+10}=\int \frac{4x}{\sqrt{x^2+10}}+C$

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3 years ago

A bridge in the shape of an arch connects two cities separated by a river. The two ends of the bridge are located at (–7, –13) a

sdas [7]

Answer:

$y=-\dfrac{13}{49}x^2$

Step-by-step explanation:

The shape of an arch corresponds to a parabola.

the general equation for a parabola is:

$y=ax^2+bx+c$

we're given three coordinates: (-7,-13),(7,-13) and (0,0)

so we can plug these values in the general equation to make 3 separate equations:

(x,y) = (-7,-13)

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so we have three equations. and we can solve them simultaneously to find the values of a,b, and c.

we've already found c = 0, let's use substitute it to other equations.

$49a-7b+c=-13\quad\Rightarrow\quad49a-7b=-13$

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we can solve these two equation using the elimination method, by simply adding the two equations

$\quad\quad49a-7b=-13\\+\quad49a+7b=-13$

------------------------------

$\quad\quad 98a=-26$

$\quad\quad a=-\dfrac{13}{49}$

Now we can plug this value of a in any of the two equations.

$49a-7b=-13$

$49\left(-\dfrac{13}{49}\right)-7b=-13$

$-13-7b=-13$

$-7b=0$

$b=0$

We have the values of a,b, and c. We can plug them in the general equation to find the equation of the arch.

$y=\left(-\dfrac{13}{49}\right)x^2+0x+0$

$y=-\dfrac{13}{49}x^2$

$49y=-13x^2$

This our equation of the arch!

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3 years ago