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maria [59]
2 years ago
8

Simplify this expression.

Mathematics
2 answers:
olchik [2.2K]2 years ago
7 0

Answer:

(y^2+3y-28)/(4y^2-15y-4)

Step-by-step explanation:

(4y-1)(y-3)(2y+3)(y+3)(y+7)(y-3)/(2y+3)(y-4)(4y+1)(4y-1)(y-3)(y+3)

= (y+7)(y-3)/(y-4)(4y+1)

= (y^2+3y-28)/(4y^2-15y-4)

ANEK [815]2 years ago
6 0

Answer:

(y+7)/(4y+1).

Step-by-step explanation:

If we factor  all the polynomials we get:

(4y-1)(y-3) .  (2y+3)(y+3) . (y-4)(y+7)

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

(2y+3)(y-4)    (4y-1)(4y+1)   (y-3)(y+3)

we see that  (4y-1), (y -3), (2y+3), (y+3) and (y - 4)  are in the numerators and denominators so we can cancel them out.

This leaves us with:

(y + 7)

--------

(4y + 1)

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In order to be differentiable everywhere, f must first be continuous everywhere, which means the limits from either side as x\to2 must be the same and equal to f(2). By definition, f(2)=2^2=4, and

\displaystyle\lim_{x\to2^-}f(x)=\lim_{x\to2}x^2=4

\displaystyle\lim_{x\to2^+}f(x)=\lim_{x\to2}(mx+b)=2m+b

so we need to have 4m+b=4.

For f to be differentiable at x=2, the derivative needs to be continuous at x=2, i.e.

\displaystyle\lim_{x\to2^-}f'(x)=\lim_{x\to2^+}f'(x)

We then need to have

\displaystyle\lim_{x\to2}2x=\lim_{x\to2}m\implies\boxed{m=4}

Then

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7 0
3 years ago
What is the volume of this sphere?
photoshop1234 [79]

Answer:

3052.08

Step-by-step explanation:

We use the volume formula for spheres

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2 years ago
Which symbol creates a true sentence when x equals 3?
Marta_Voda [28]
Hi <span>Tysona90!
Let's write it with the X as a 3
8*3-4*3_7(10-3) Now let's solve it 8*3 is 24 and 4*3 is 12 so then we do 24-12 which is 12. So now we have 12_7(10-3) so let's solve the other half which is 10-3 is 7 times 7 (since parenthesis can also mean multiplication) which is 49 so we now have 12_49 which means the answer is A.
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3 years ago
I have a flower vase with a 6 " diameter and is 12 " tall I want to fill it 2/3 of the way full how many cubic inches will I fil
RSB [31]

Answer:

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Step-by-step explanation:

step 1

<em>Calculate the volume of the cylinder (flower vase)</em>

The volume is equal to

V=\pi r^{2}h

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r=6/2=3\ in -----> the radius is half the diameter

h=12\ in

substitute the values

V=\pi (3)^{2}(12)=108\pi\ in^{3} ------> exact value

step 2

Calculate  2/3 of the volume

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Me hill will get 1.76 in change
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