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3 years ago

Simplify -3x³y²(-4x²y•y•y•y•y)²

Mathematics

2 answers:

Luba_88 [7]3 years ago

7 0

It is 12x^5 y^6 hope it helps

AnnZ [28]3 years ago

3 0

$-3x^3y^2(-4x^2 \underbrace{y\cdot y\cdot y\cdot y}_{y^4})^2\\\\=(-3)(-4)(x^3x^2)(y^2y^4)\\\\=12x^{3+2}y^{2+4}\\\\=\boxed{12x^5y^6}\\\\Used:\\\\a^n\cdot a^m=a^{n+m}$

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Solve 5y'' + 3y' – 2y = 0, y(0) = 0, y'(0) = 2.8 y(t) = 0 Preview

mario62 [17]

Answer: The required solution is

$y(t)=-\dfrac{7}{3}e^{-t}+\dfrac{7}{3}e^{\frac{1}{5}t}.$

Step-by-step explanation: We are given to solve the following differential equation :

$5y^{\prime\prime}+3y^\prime-2y=0,~~~~~~~y(0)=0,~~y^\prime(0)=2.8~~~~~~~~~~~~~~~~~~~~~~~~(i)$

Let us consider that

$y=e^{mt}$ be an auxiliary solution of equation (i).

Then, we have

$y^prime=me^{mt},~~~~~y^{\prime\prime}=m^2e^{mt}.$

Substituting these values in equation (i), we get

$5m^2e^{mt}+3me^{mt}-2e^{mt}=0\\\\\Rightarrow (5m^2+3y-2)e^{mt}=0\\\\\Rightarrow 5m^2+3m-2=0~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~[\textup{since }e^{mt}\neq0]\\\\\Rightarrow 5m^2+5m-2m-2=0\\\\\Rightarrow 5m(m+1)-2(m+1)=0\\\\\Rightarrow (m+1)(5m-1)=0\\\\\Rightarrow m+1=0,~~~~~5m-1=0\\\\\Rightarrow m=-1,~\dfrac{1}{5}.$

So, the general solution of the given equation is

$y(t)=Ae^{-t}+Be^{\frac{1}{5}t}.$

Differentiating with respect to t, we get

$y^\prime(t)=-Ae^{-t}+\dfrac{B}{5}e^{\frac{1}{5}t}.$

According to the given conditions, we have

$y(0)=0\\\\\Rightarrow A+B=0\\\\\Rightarrow B=-A~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(ii)$

and

$y^\prime(0)=2.8\\\\\Rightarrow -A+\dfrac{B}{5}=2.8\\\\\Rightarrow -5A+B=14\\\\\Rightarrow -5A-A=14~~~~~~~~~~~~~~~~~~~~~~~~~~~[\textup{Uisng equation (ii)}]\\\\\Rightarrow -6A=14\\\\\Rightarrow A=-\dfrac{14}{6}\\\\\Rightarrow A=-\dfrac{7}{3}.$

From equation (ii), we get

$B=\dfrac{7}{3}.$

Thus, the required solution is

$y(t)=-\dfrac{7}{3}e^{-t}+\dfrac{7}{3}e^{\frac{1}{5}t}.$

7 0

3 years ago

How do you divide (n^2-n-29)/(n-6) ??

Orlov [11]

9514 1404 393

Answer:

see attached

Step-by-step explanation:

Polynomial long division is done the way any long division is done. Find a "partial quotient", subtract from the dividend the product of that partial quotient and the divisor. The result is a new dividend. Repeat until the degree of the dividend is less than that of the divisor.

In the attached, the "Hints" show you how the partial quotient is found, and they show you how the product of the partial quotient and divisor is found.

The partial quotient term is simply the ratio of the highest degree terms of dividend and divisor. (Unlike numerical long division, there is no guessing.)

The remainder is the dividend of lower degree than the divisor. As in numerical long division, the full quotient expresses the remainder over the divisor.

For example, 5 ÷ 3 = 1 r 2 = 1 + 2/3.

Your full quotient is (n+5) +1/(n-6).

5 0

3 years ago

What is the average rate of change from x = −4 to x = 1?

kati45 [8]

Answer:

What is the average rate of change from x = −4 to x = 1? x= -4 x + 5

5 0

3 years ago

When seven is subtracted from half of a number, the result is negative three. Find the number

Harlamova29_29 [7]

Answer:

Step-by-step explanation:

0.5x-7=3

add 7 to both sides

0.5x=4

multiply both sides by 2

x=8

5 0

3 years ago

Which equations could you use to solve the following problem? Fifty-six is 85% of what number? 56 = (0.85)w = = p = (0.85)56

Sidana [21]

Answer:

56 = (0.85)w

Step-by-step explanation:

"is" translates to "=".

"of" translates to "×".

We can let "what number" translate to "w".

Then ...

56 is 85% of what number . . . . translates to ...

56 = 0.85×w

_____

Of course, you know that 85% = 85/100 = 0.85.

6 0

4 years ago