All categories

3 years ago

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

You might be interested in

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