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Fiesta28 [93]
3 years ago
13

Keisha bikes 5 miles on monday and m miles on tuesday. write two equivalent expressions for the total number of miles she bikes

on monday and tuesday.
Mathematics
1 answer:
Alex787 [66]3 years ago
8 0
5+m=T
T-m=5

Those are equivalent equations.
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Integrate this two questions ​
tankabanditka [31]

Simplify the integrands by polynomial division.

\dfrac{t^2}{1 - 3t} = -\dfrac19 \left(3t + 1 - \dfrac1{1 - 3t}\right)

\dfrac t{1 + 4t} = \dfrac14 \left(1 - \dfrac1{1 + 4t}\right)

Now computing the integrals is trivial.

5.

\displaystyle \int \frac{t^2}{1 - 3t} \, dt = -\frac19 \int \left(3t + 1 - \frac1{1-3t}\right) \, dt \\\\ = -\frac19 \left(\frac32 t^2 + t + \frac13 \ln|1 - 3t|\right) + C \\\\ = \boxed{-\frac{t^2}6 - \frac t9 - \frac{\ln|1-3t|}{27} + C}

where we use the power rule,

\displaystyle \int x^n \, dx = \frac{x^{n+1}}{n+1} + C ~~~~ (n\neq-1)

and a substitution to integrate the last term,

\displaystyle \int \frac{dt}{1-3t} = -\frac13 \int \frac{du}u \\\\ = -\frac13 \ln|u| + C \\\\ = -\frac13 \ln|1-3t| + C ~~~ (u=1-3t \text{ and } du = -3\,dt)

8.

\displaystyle \int \frac t{1+4t} \, dt = \frac14 \int \left(1 - \frac1{1+4t}\right) \, dt \\\\ = \frac14 \left(t - \frac14 \ln|1 + 4t|\right) + C \\\\ = \boxed{\frac t4 - \frac{\ln|1+4t|}{16} + C}

using the same approach as above.

5 0
2 years ago
The circumference of a
timama [110]

9514 1404 393

Answer:

  • 160,000 m²
  • 16 ha

Step-by-step explanation:

The side length of a square is 1/4 of the perimeter, so the side length of the square orchard is (1600 m)/4 = 400 m.

The area of a square is the square of the side length, so the area of the orchard is (400 m)² = 160,000 m².

A hectare is 10,000 m², so the area of the orchard in hectares is ...

  16·(10,000 m²) = 16 ha

3 0
3 years ago
Write another name for < 5​
victus00 [196]

Answer:

less than 5

x < 5

6 0
3 years ago
Read 2 more answers
Keegan had 3.25 pounds of flour. After making bread, he had 1.75 pounds of flour left over. i know its 1.5 but whats the Equatio
astraxan [27]

Answer:

3.25 - 1.75 = 1.50 pounds of flour

Step-by-step explanation:

7 0
3 years ago
A man flys out of Korea on Wednesday at 4:30pm and lands in Colorado on Wednesday at 4:15pm how does he do it
nekit [7.7K]
Well there is a time difference between Korea and Colorado. So when the man leaves Korea it is 4:30 pm but when he reaches Colorado the next day, it is 4:15 pm. I hope this helps you!
8 0
3 years ago
Read 2 more answers
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