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Ivan
3 years ago
15

Melissa's family is driving out of state to her grandmothers house.They know it takes 20 gallons of gas to get there,and the cos

t of three gallons of gasoline is $10.50.How much should the family budget to make the one- way trip
Mathematics
1 answer:
Lady_Fox [76]3 years ago
6 0
I believe the family budget to make a one- way trip will be $140 because each gallon is $3.50. You need 20 gallons to get there which is $70. You need 20 gallons to get back which is another $70. You add both and is $140. Hope this helped.
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Indefinite integral need help pleaseeeeeee
tatiyna
Integrate indefinite integral:
I=\int\frac{dx}{e^{2x}+3e^x+2}dx

Solution:
1. use substitution u=e^x 
=>
du=e^xdx
=>
dx=\frac{du}{e^x}
=>
dx=\frac{du}{u}
=>
I=\int\frac{du}{u(u^2+3u+2)}du
=\int\frac{du}{u(u+2)(u+1)}du
2. decompose into partial fractions
\frac{1}{u(u+2)(u+1)}
=\frac{A}{u}+\frac{B}{u+2}+\frac{C}{u+1}
where A=1/2, B=1/2, C=-1
=\frac{1}{2u}+\frac{1}{2(u+2)}-\frac{1}{u+1}
3. Substitute partial fractions and continue
I=\int\frac{du}{2u}+\int\frac{du}{2(u+2)}-\int\frac{du}{u+1}
=\frac{log(u)}{2}+\frac{log(u+2)}{2}-log(u+1)}
4. back-substitute u=e^x
=\frac{log(e^x)}{2}+\frac{log(e^x+2)}{2}-log(e^x+1)}
=\frac{x}{2}+\frac{log(e^x+2)}{2}-log(e^x+1)}

Note: log(x) stands for natural log, and NOT log10(x)

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3 years ago
If<br> tan (0) = -√3<br> then one possible value of<br> 0<br> in degrees is:
barxatty [35]

One possible answer is 120°

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2 years ago
17. Factor x ^ 3 + 5x ^ 2 - 9x - 45 . A. (x - 5)(x ^ 2 + 9) b . (x - 5)(x - 3) * (x + 3) Factor By Groupin (x + 5)(x - 3) * (x +
jok3333 [9.3K]

Answer:

b

Step-by-step explanation:

Given

x³ + 5x² - 9x - 45 ( factor the first/second and third/fourth terms )

= x²(x + 5) - 9(x + 5) ← factor out (x + 5) from each term

= (x + 5)(x² - 9) ← factor as a difference of squares

= (x + 5)(x - 3)(x + 3)

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3 years ago
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olganol [36]
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Step-by-step explanation:

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