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3 years ago

8

Area of rectangle 2x8/9

1 answer:

Vikki [24]3 years ago

3 0

Answer:

32/9

Step-by-step explanation:

2*(2)(8/9) = 4*8/9 = 32/9

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If (6^2)^x =1 what is the value of x

masya89 [10]

Answer:

x = 0

Step-by-step explanation:

Rewrite (6^2)^x =1 as 6^(2x) = 1.

Next, take the logarithm (common or natural) of both sides, obtaining

2x log 6 = log 1

2x log 6 = 0

Then x = 0.

Note that (6^2)^0 = 1, since any positive number raised to the prower 0 is 1.

6 0

4 years ago

Nels works 8 hours and earns $52. How many hours would he have to work to earn $130?

asambeis [7]

Answer:

20 hours

Step-by-step explanation:

52/8 = $6.5/hour

130 / 6.5 = 20

20 hours

7 0

3 years ago

We would like to use the power series method to find the general solution to the differential equation d 2y dx2 − 4x dy dx + 12y

Feliz [49]

$y=\displaystyle\sum_{n\ge0}a_nx^n$

$\dfrac{\mathrm dy}{\mathrm dx}=\displaystyle\sum_{n\ge1}na_nx^{n-1}\implies4x\dfrac{\mathrm dy}{\mathrm dx}=4\sum_{n\ge1}na_nx^n=4\sum_{n\ge0}na_nx^n$

$\dfrac{\mathrm d^2y}{\mathrm dx^2}=\displaystyle\sum_{n\ge2}n(n-1)a_nx^{n-2}=\sum_{n\ge0}(n+2)(n+1)a_{n+2}x^n$

Substituting into the ODE

$\dfrac{\mathrm d^2y}{\mathrm dx^2}-4x\dfrac{\mathrm dy}{\mathrm dx}+12y=0$

gives

$\displaystyle\sum_{n\ge0}\bigg((n+2)(n+1)a_{n+2}-4na_n+12a_n\bigg)x^n=0$

so that the coefficients of the series are given according to

$\begin{cases}a_0=y(0)\\a_1=y'(0)\\a_{n+2}=\dfrac{4(n-3)a_n}{(n+2)(n+1)}&\text{for }n\ge0\end{cases}$

We can shift the index in the recursive part of this definition to get

$a_n=\dfrac{4(n-5)a_{n-2}}{n(n-1)}$

for $n\ge2$ . There's dependency between coefficients that are 2 indices apart, so we can consider 2 cases:

If $n=2k$ , where $k\ge0$ is an integer, then

$k=0\implies n=0\implies a_0=a_0$

but since $y(0)=0$ , we have $a_0=0$ and $a_{2k}=0$ for all $k\ge0$ .

If $n=2k+1$ , then

$k=0\implies n=1\implies a_1=a_1$

$k=1\implies n=3\implies a_3=\dfrac{4(-2)a_1}{3\cdot2}=-\dfrac43a_1$

$k=2\implies n=5\implies a_5=0$

and so $a_{2k+1}=0$ for all $k\ge2$ . If $y'(0)=1$ , we then have $a_1=1$ and $a_3=-\dfrac43$ .

So the ODE has solution

$y(x)=\displaystyle\sum_{k\ge0}(a_{2k}x^{2k}+a_{2k+1}x^{2k+1})\implies\boxed{y(x)=x-\dfrac43x^3}$

8 0

3 years ago

The high school dance team has 88

nika2105 [10]

Answer:

64 members

Step-by-step explanation:

88 total members

24 are in the students council

so those in the dance team and not in the council:

88-24 = 64.

3 0

3 years ago

Read 2 more answers

Combine like terms to simplify 12x+4y-3x+2-8y²+3²

Vlad1618 [11]

Answer:
15x+60y+6
I think so

3 0

3 years ago