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Rasek [7]
2 years ago
10

Sam confirmed there will be 192 guests at his party. He thinks each guest will eat

Mathematics
1 answer:
vitfil [10]2 years ago
7 0

Answer:

Sam used estimation. He rounded the amount of guests (192) to the nearest hundred (200).

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The approximate middle value
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Question 6 (10 points)
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22

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The ratio tells us 2/5 of the swimmers are indoor swimmers.

55(2/5)=22

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Ming's team cleans 3 animals per hour after an oil
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Answer: 2 hours

Step-by-step explanation:

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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
3(x-1) - 8 = 4(1+x) +5
ryzh [129]

For this case we must simplify the following expression and find the value of the variable "x":

3 (x-1) -8 = 4 (1 + x) +5

We apply distributive property to the terms of parentheses:

3x-3-8 = 4 + 4x + 5

We add similar terms:

3x-11 = 9 + 4x

We subtract 4x on both sides:

3x-4x-11 = 9\\-x-11 = 9

We add 11 to both sides:

-x = 11 + 9\\-x = 20\\x = -20

Answer:

x = -20

8 0
4 years ago
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