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Nitella [24]
3 years ago
14

Your family is going on a road trip to Disney World! On Day 1, you traveled x miles. On Day 2, you drove 58 miles more than 3 ti

mes the miles on Day 1. On Day 3, your family went 25 fewer miles than Day 1.
RESTATE: Rewrite this problem in your own words


ANSWER: 1. Write an expression that represents the miles traveled for Day 1 + Day 2 + Day 3. *


ANSWER: 2. Simplify your expression by combining like terms.


ANSWER: 3. If your family drove 100 miles on Day 1, how many total miles did your family travel from your home to Disney World? *


CITE YOUR SOURCE: What helped you solve this problem? *


EXPLAIN: How do you know you are correct? Show your thinking here... *


REFLECT: Did you like this problem? Why or why not? How would you improve this problem? *
Mathematics
1 answer:
Eva8 [605]3 years ago
8 0

Answer:i need help with this also

Step-by-step explanation:

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3 years ago
1. Write the form of the partial fraction decomposition of the rational expression. Do not solve for the constants.
german

Answer:

Step-by-step explanation:

1.

To write the form of the partial fraction decomposition of the rational expression:

We have:

\mathbf{\dfrac{8x-4}{x(x^2+1)^2}= \dfrac{A}{x}+\dfrac{Bx+C}{x^2+1}+\dfrac{Dx+E}{(x^2+1)^2}}

2.

Using partial fraction decomposition to find the definite integral of:

\dfrac{2x^3-16x^2-39x+20}{x^2-8x-20}dx

By using the long division method; we have:

x^2-8x-20 | \dfrac{2x}{2x^3-16x^2-39x+20 }

                  - 2x^3 -16x^2-40x

                 <u>                                         </u>

                                            x+ 20

So;

\dfrac{2x^3-16x^2-39x+20}{x^2-8x-20}= 2x+\dfrac{x+20}{x^2-8x-20}

By using partial fraction decomposition:

\dfrac{x+20}{(x-10)(x+2)}= \dfrac{A}{x-10}+\dfrac{B}{x+2}

                         = \dfrac{A(x+2)+B(x-10)}{(x-10)(x+2)}

x + 20 = A(x + 2) + B(x - 10)

x + 20 = (A + B)x + (2A - 10B)

Now;  we have to relate like terms on both sides; we have:

A + B = 1   ;   2A - 10 B = 20

By solvong the expressions above; we have:

A = \dfrac{5}{2}     B =  \dfrac{3}{2}

Now;

\dfrac{x+20}{(x-10)(x+2)} = \dfrac{5}{2(x-10)} + \dfrac{3}{2(x+2)}

Thus;

\dfrac{2x^3-16x^2-39x+20}{x^2-8x-20}= 2x + \dfrac{5}{2(x-10)}+ \dfrac{3}{2(x+2)}

Now; the integral is:

\int \dfrac{2x^3-16x^2-39x+20}{x^2-8x-20} \ dx =  \int \begin {bmatrix} 2x + \dfrac{5}{2(x-10)}+ \dfrac{3}{2(x+2)} \end {bmatrix} \ dx

\mathbf{\int \dfrac{2x^3-16x^2-39x+20}{x^2-8x-20} \ dx =  x^2 + \dfrac{5}{2}In | x-10|\dfrac{3}{2} In |x+2|+C}

3. Due to the fact that the maximum words this text box can contain are 5000 words, we decided to write the solution for question 3 and upload it in an image format.

Please check to the attached image below for the solution to question number 3.

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3 years ago
Solve and show your work for each question.
Harlamova29_29 [7]

Answer:

9/20

Step-by-step explanation:

You set the fraction up at first as 45/100. Then you know that 5 goes into each so you divide by 5 \frac{45}{100} /5

45/5=9

100/5=20

You get 9/20, and this is in simplest form.

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Service entrance head. Hope this helps :)

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