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2 years ago

Express the quotient in simplest form. x^2 - 4/ x^3 + 7x^2 divided by x^3 - x^2 - 6x/x^2 + 4x - 21

Mathematics

1 answer:

amm18122 years ago

8 0

You must first transform into a multiplication and then factor to see what you can eliminate.

Explanation:

To transform a fractional division into a multiplication, you have to inverse the numerator and the denominator of the second fraction.

x2−4x3+7x2×x2+4x−21x3−x2−6x

(x+2)(x−2)x2(x+7)×(x+7)(x−3)x(x−3)(x+2)

Since aa=1,a= all real numbers, we can proceed by eliminating factors that appear in the numerator and the denominator.

We are left with x−2/x^3

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Que is on pic.i can't able to type in text.

ad-work [718]

It's not difficult to compute the values of $A$ and $B$ directly:

$A=\displaystyle\int_1^{\sin\theta}\frac{\mathrm dt}{1+t^2}=\tan^{-1}t\bigg|_{t=1}^{t=\sin\theta}$
$A=\tan^{-1}(\sin\theta)-\dfrac\pi4$

$B=\displaystyle\int_1^{\csc\theta}\frac{\mathrm dt}{t(1+t^2)}=\int_1^{\csc\theta}\left(\frac1t-\frac t{1+t^2}\right)\,\mathrm dt$
$B=\left(\ln|t|-\dfrac12\ln|1+t^2|\right)\bigg|_{t=1}^{t=\csc\theta}$
$B=\ln\left|\dfrac{\csc\theta}{\sqrt{1+\csc^2\theta}}\right|+\dfrac12\ln2$

Let's assume $0$ , so that $|\csc\theta|=\csc\theta$ .

Now,

$\Delta=\begin{vmatrix}A&A^2&B\\e^{A+B}&B^2&-1\\1&A^2+B^2&-1\end{vmatrix}$
$\Delta=A\begin{vmatrix}B^2&-1\\A^2+B^2&-1\end{vmatrix}-e^{A+B}\begin{vmatrix}A^2&B\\A^2+B^2&-1\end{vmatrix}+\begin{vmatrix}A^2&B\\B^2&-1\end{vmatrix}$
$\Delta=A(-B^2+A^2+B^2)-e^{A+B}(-A^2-A^2B-B^3)+(-A^2-B^3)$
$\Delta=A^3-A^2-B^3+e^{A+B}(A^2+A^2B+B^3)$

There doesn't seem to be anything interesting about this result... But all that's left to do is plug in $A$ and $B$ .

3 0

2 years ago

Is 15,36,39 a right triangle

NeTakaya

Answer:

Yes, is a right triangle

Step-by-step explanation:

To know if you can build a right triangle with those sides we have to make the following equality

h² = l1² + l2²

The hypotenuse is always the longest side so it should be 39

we check the equality of the equation

39² = 15² + 36²

1521 = 225 + 1296

1521 = 1521

Equality was fulfilled so it is a right triangle

7 0

2 years ago

Cheryl is planning a garden that will be

GaryK [48]

Hello There!

Great Question!

To calculate the area of a rectangular prism, you would multiply the length, the width, and the depth. As we want to measure this in cubic feet, we should convert all of the measurements to feet to begin with.

How wide is the garden? (either 7 or 8 feet)

How long is the garden? (Whichever of 7 or 8 wasn’t used)

How deep is this garden? 6 inches.

Well, that’s not feet, right?

How many inches are in a foot? 12.

Divide 6 by 12, what is the answer? .5.

5 0

2 years ago

If 1/2x+1/3=4 What is the value of 3x+2y

ivolga24 [154]

Answer:

x=3/22 ; y=-9/44

Step-by-step explanation:

1/2x+1/3=4

=>1/2x=4-1/3

=>1/2x=(12-1)/3

=>1/2x=11/3

=>22x=3

=>x=3/22....(1)

then,

3x+2y

2y=-3 . (3/22)

y=-9/44

6 0

3 years ago

Read 2 more answers

What is the slope of the line that passes through (9,3) and (2,1)

Aneli [31]

Answer:

2/7

Step-by-step explanation:

$slope = \frac{1 - 3}{2 - 9} \\ = \frac{ - 2}{ - 7} \\ = \frac{2}{7}$

3 0

1 year ago