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Julli [10]
3 years ago
8

Which expression is equivalent to 'the third power of (7 + 4) I neeeed help

Mathematics
1 answer:
lara31 [8.8K]3 years ago
4 0

Answer:

1331

Step-by-step explanation:

7 +4 = 11

11^3 = 1331

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Kareem took 4 2/5 hours to clean the bathroom. Then he took 2 1/4 hours to clean the den. How much total time did Kareem take to
nika2105 [10]

Answer:

  6 13/20 hours

Step-by-step explanation:

Addition of fractions requires they be expressed using a common denominator. Here, that will be 5·4 = 20, and the two fractions can be written as ...

  2/5 = 8/20

  1/4 = 5/20

Then the sum of the mixed numbers is ...

  (4 2/5) +(2 1/4) = (4 +2) +(2/5 +1/4) = 6 +(8/20 +5/20)

  = 6 13/20

It took Kareem 6 13/20 hours to clean the two rooms.

6 0
3 years ago
Observe that x and e^x are solutions to the homogeneous equation associated with:
yanalaym [24]

To take advantage of the characteristic solutions y_1(x)=x and y_2(x)=e^x, you can try the method of variation of parameters, where we look for a solution of the form

y=y_1u_1+y_2u_2

with the condition that

{u_1}'y_1+{u_2}'y_2=0

\implies{u_1}'x+{u_2}'e^x=0 (\mathbf 1)

Then

y'={y_1}'u_1+y_1{u_1}'+{y_2}'u_2+y_2{u_2}'

\implies y'={y_1}'u_1+{y_2}'u_2

y''={y_1}''u_1+{y_1}'{u_1}'+{y_2}''u_2+{y_2}'{u_2}'

Substituting into the ODE gives

(1-x)({y_1}''u_1+{y_1}'{u_1}'+{y_2}''u_2+{y_2}'{u_2}')+x({y_1}'u_1+{y_2}'u_2)-y_1u_1+y_2u_2=2(x-1)^2e^{-x}

Since

y_1=x\implies{y_1}'=1\implies{y_1}''=0

y_2=e^x\implies{y_2}'=e^x\implies{y_2}''=e^x

the above reduces to

(1-x)({u_1}'+e^x{u_2}')=2(x-1)^2e^{-x}

{u_1}'+e^x{u_2}'=2(1-x)e^{-x} (\mathbf 2)

(\mathbf 1) and (\mathbf 2) form a linear system that we can solve for {u_1}',{u_2}' using Cramer's rule:

{u_1}'=\dfrac{W_1(x)}{W(x)},{u_2}'=\dfrac{W_2(x)}{W(x)}

where W(x) is the Wronskian determinant of the fundamental system and W_i(x) is the same determinant, but with the i-th column replaced with (0,2(x-1)^2e^{-x}).

W(x)=\begin{vmatrix}x&e^x\\1&e^x\end{vmatrix}=e^x(x-1)

W_1(x)=\begin{vmatrix}0&e^x\\2(x-1)^2e^{-x}&e^x\end{vmatrix}=-2(x-1)^2

W_2(x)=\begin{vmatrix}x&0\\e^x&2(x-1)^2e^{-x}\end{vmatrix}=2xe^{-x}(x-1)^2

So we have

{u_1}'=\dfrac{-2(x-1)^2}{e^x(x-1)}\implies u_1=2xe^{-x}

{u_2}'=\dfrac{2xe^{-x}(x-1)^2}{e^x(x-1)}\implies u_2=-x^2e^{-2x}

Then the particular solution is

y_p=2x^2e^{-x}-x^2e^{-x}=x^2e^{-x}

giving the general solution to the ODE,

\boxed{y(x)=C_1x+C_2e^x+x^2e^{-x}}

5 0
4 years ago
The sum of the measures of the interior angles of a convex polygon is 2160. how many sides does the polygon have?
horsena [70]
<span>Sum of Interior Angles = (Number of Sides -2) • 180 degrees
2,160 = (sides -2) * 180
2,160 / 180 = sides -2
12 = sides -2
sides = 14
Source:
http://www.1728.org/polygon.htm

</span>
4 0
3 years ago
Mr.Kork sold his car for $8,400. This was $200 more than two fifths of what he had paid for the car originally. How much had Mr.
Hitman42 [59]

Answer:

He paid = $20,500

Step-by-step explanation:

Let the amount he bought the car originally be X

so from the statement,

(2/5)*X + $200 = $8,400

(2/5)*X = $8,400 - $200

solving for X

X = $8200 * 5/2

X = $20,500

4 0
3 years ago
Henry bought a basketball that was on sale for $12. It was 40% off. What was the original price of the basketball? Please Help.
kodGreya [7K]

Answer:

The original price of the basketball was $16.80 hope this helps!

5 0
3 years ago
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