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3 years ago

How much trail mix will each person get if 5 people share 1/2 pound trail mix

1 answer:

7 0

Assume that each person gets an equal share.
Then the portion a person gets is
$\frac{1/2 \, pound}{5 \, persons} = ( \frac{1}{2} \times \frac{1}{5} ) \, \frac{pounds}{person} = \frac{1}{10} \, pounds/person$

Answer: 1/10 pounds per person

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Problem 1: Use the Laplace Transforms to solve:

Leokris [45]

Transforming the ODE yields

$L\left\{y'' - y'\right\} = L\left\{e^{-3t}\right\}$

$(s^2 Y(s) - sy(0) - y'(0)) - (s Y(s) - y(0)) = \dfrac1{s+3}$

$(s^2 - s) Y(s) = \dfrac1{s+3}$

$Y(s) = \dfrac1{(s^2 - s)(s+3)} = \dfrac1{s(s-1)(s+3)}$

Partial fractions:

$Y(s) = \dfrac as + \dfrac b{s-1} + \dfrac c{s+3}$

$\implies 1 = a(s-1)(s+3) + b s(s+3) + c s(s - 1)$

$\implies 1 = -3 a + (2 a + 3 b - c) s + (a + b + c) s^2$

$\implies \begin{cases}-3a=1 \\ 2a+3b-c=0 \\ a+b+c=0\end{cases} \implies a=-\dfrac13, b=\dfrac14, c=\dfrac1{12}$

$\implies Y(s) = -\dfrac13 \times \dfrac1s + \dfrac14 \times \dfrac1{s-1} + \dfrac1{12} \times \dfrac1{s+3}$

Take the inverse transform:

$\boxed{y(t) = -\dfrac13 + \dfrac{e^t}4 + \dfrac{e^{-3t}}{12}}$

3 0

2 years ago

Bella bought packs of stickers to give to her friends. Each pack cost $4. She spent a total of $12 on stickers. How many packs d

boyakko [2]

Given:

Bella bought packs of stickers to give to her friends.

Cost of each pack of stickers = $4

Total amount spent on packs of stickers = $12

To find:

The equation for the given statement.

Solution:

Let s be the number of packs of stickers.

Cost of one pack of stickers = $4

Cost of s packs of stickers = $4s

Total amount spent on packs of stickers is $12. So,

$4s=12$

Therefore, the correct option is B.

6 0

2 years ago

Please help!! +20 and brainlest if you answer all THREE correctly

devlian [24]

Answer:The FIrst 1 For Find The Volume Is 64.13

Step-by-step explanation: U Use The Fromula W x H x L

8 0

2 years ago

Read 2 more answers

This handy application of LCMs is used by astronomers. All the planets in our solar system revolve around the sun. The planets o

TiliK225 [7]

To find number of years we take LCM of planets revolution times.

Planet's revolution times are given in the chart

Solar System Planet Revolution Time

Earth 1 year

Mars 2 years

Jupiter 12 years

Saturn 30 years

Uranus 84 years

Neptune 165 years

We take LCM of 1,2,12,30,84 and 165

Prime factorization of 2 = 2

Prime factorization of 12 = 2^2 * 3

Prime factorization of 30 = 2 * 3* 5

Prime factorization of 84 = 2^2 * 3 * 7

Prime factorization of 165 = 3*5*11

We take set of prime factors that has highest exponent,

So LCM = 2^2 * 3 * 5 * 7 * 11 = 4620

Therefore it will take 4620 years.

8 0

3 years ago

What percent of 9 is 1 <br><br> Whole number,fraction,or mixed number

DaniilM [7]

9514 1404 393

Answer:

11 1/9%

Step-by-step explanation:

1/9 × 100% = (100/9)% = (11 1/9)%

6 0

3 years ago