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snow_tiger [21]

3 years ago

6

Simplify the sum. (7u3 + 4u2 + 7) + (7u3 – 6u + 4)

1 answer:

andreyandreev [35.5K]3 years ago

7 0

Answer:

$14u^{3}+4u^{2}-6u+11$

Step-by-step explanation:

The question is to simplify $(7u^{3}+4u^{2}+7)+(7u^{3}-6u+4)$

<em>We combine like terms, as in, combine cubes with cubes, squares with squares, numbers with numbers and so on.</em>

There are 2 cubed terms, so they should be combined.
There are 2 numbers, so they should be combined.
Others, leave as is.

So we have:

$(7u^{3}+4u^{2}+7)+(7u^{3}-6u+4)\\(7u^3+7u^{3})+4u^{2}-6u+(7+4)\\14u^{3}+4u^{2}-6u+11$

This is the simplified form of the sum given.

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Solve the initial value problem

tigry1 [53]

$9(t+1)\dfrac{\mathrm dy}{\mathrm dt}-7y=14t\implies\dfrac{\mathrm dy}{\mathrm dt}-\dfrac7{9(t+1)}y=\dfrac{14t}{9(t+1)}$

Look for an integrating factor $\mu(t)$ :

$\ln\mu=\displaystyle-\frac79\int\frac{\mathrm dt}{t+1}=-\frac79\ln(t+1)\implies\mu=(t+1)^{-7/9}$

Multiply both sides by $\mu$ :

$(t+1)^{-7/9}\dfrac{\mathrm dy}{\mathrm dt}-\dfrac79(t+1)^{-16/9}y=\dfrac{14}9t(t+1)^{-16/9}$

Condense the left side as the derivative of a product:

$\dfrac{\mathrm d}{\mathrm dt}\left[(t+1)^{-7/9}y\right]=\dfrac{14}9t(t+1)^{-16/9}$

Integrate both sides:

$(t+1)^{-7/9}y=\displaystyle\frac{14}9\int t(t+1)^{-16/9}\,\mathrm dt$

For the integral on the right, substitute

$u=t+1\implies t=u-1\implies\mathrm dt=\mathrm du$

$\displaystyle\int t(t+1)^{-16/9}\,\mathrm dt=\int(u-1)u^{-16/9}\,\mathrm du$

$\displaystyle=\int\left(u^{-7/9}-u^{-16/9}\right)\,\mathrm du=\frac92u^{2/9}+\frac97u^{-7/9}+C$

$\implies(t+1)^{-7/9}y=\dfrac{14}9\left(\dfrac92(t+1)^{2/9}+\dfrac97(t+1)^{-7/9}+C\right)$

$\implies(t+1)^{-7/9}y=7(t+1)^{2/9}+2(t+1)^{-7/9}+C$

$\implies y=7(t+1)+2+C(t+1)^{7/9}=7t+9+C(t+1)^{7/9}$

Given that $y(0)=12$ , we get

$12=9+C\implies C=3$

$\implies\boxed{y(t)=7t+9+3(t+1)^{7/9}}$

6 0

3 years ago

Randy, Sandy and Todd are my cousins and their combined age is 87 years. Randy is four times as old as Sandy, but Todd is actual

NISA [10]

Answer:

Randy is 48 years old

Sandy is 12 years old

Todd is 27 years old

<em></em>

Step-by-step explanation:

Given

Represent their ages with the first letters of their names:

$R + S + T = 87$

$R = 4 * S$

$T = 15 + S$

Required

Determine their individual ages

We'll solve the above equations using substitution method of simultaneous equations

Substitute 15 + S for T and 4 * S for R in $R + S + T = 87$

This gives:

$4 * S + S + 15 + S = 87$

$4 S + S + 15 + S = 87$

Collect Like Terms

$4 S + S + S = 87 - 15$

$6S = 72$

Divide through by 6

$S = 72/6$

$S = 12$

<em>This implies that Sandy is 12 years old</em>

Substitute 12 for S in $R = 4 * S$ and $T = 15 + S$

$R = 4 * 12$

$R = 48$

$T = 15 + 12$

$T = 27$

<em>This implies that Randy is 48 years old and Todd is 27</em>

7 0

3 years ago

A study was done by a social media company to determine the rate at which users used its website. A graph of the data that was c

Sergeeva-Olga [200]

Answer:

The range represents the number of users each month for 24 months

Step-by-step explanation:

The range depends on the y axis. Looking at the y axis we see the number of users for each month. Looking at the x axis we see that it's 24 months not 20 months

8 0

3 years ago

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inysia [295]

Answer:

<u>2: 1/25</u>

<u>-1: -1/5</u>

<u>-2: -1/25th</u>

Step-by step

number 2 on the number line is: 1/25

<u>125 divided by 5 is 25</u>

-1 on the number line: -1/5

number one on the number line is 1/5th so -1 should be the opposite

-2 on the number line is: -1/25th

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3 years ago

The graphs below were created by an advertising agency for the computer store TechPlus to show its average price on laptops and

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Answer:

Step-by-step explanation:

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