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Ksju [112]
2 years ago
11

Integrate this two questions ​

Mathematics
1 answer:
tankabanditka [31]2 years ago
5 0

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.

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On a cold February morning, the radiator fluid in Stanley’s car is -18 degrees When the engine is running, the temperature goes
Rasek [7]

Remark

This is an arithmetic progression. You have the first and last terms and the difference.

Givens

a = - 18

L = 60

d = 4.5        

Equation

L = a + (n - 1)d

Solve

60 = -18 + (n - 1) * 4.5   Add 18 to both side

60 + 18 = (n - 1) * 4.5      

78 = (n - 1) * 4.5           Divide both sides by 4.5

78/4.5 = n - 1

17.3333 = n - 1             Add 1 to both  sides.

18.3333 = n

Conclusion

It will that 18 1/3 or 18.33333 minutes to get the from -18 to 60 degrees.


3 0
2 years ago
What is the value of x? <br> -2/7x+6+1/7x=18 <br> x=
Alenkinab [10]
- \frac{2}{7} x + 6 + \frac{1}{7} x = 18

First, simplify \frac{2}{7} x to \frac{2x}{7} / Your problem should look like: -\frac{2x}{7} + 6 + \frac{1}{7} x = 18
Second, simplify \frac{1}{7} x to \frac{x}{7} / Your problem should look like: - \frac{2x}{7} + 6 + \frac{x}{7} = 18
Third, simplify - \frac{2x}{7} + 6 + \frac{x}{7} to - \frac{x}{7} + 6 / Your problem should look like: -\frac{x}{7} + 6 = 18
Fourth, regroup terms. / Your problem should look like: 6 - \frac{x}{7} = 18
Fifth, multiply both sides by 7. / Your problem should look like: 42 - x = 126
Sixth, subtract 42 from both sides. / Your problem should look like: -x = 126 - 42
Seventh, simplify 126 - 42 to 84. / Your problem should look like: -x = 84
Eighth, multiply both sides by -1. / Your problem should look like: x = -84

Answer: x = -84

4 0
3 years ago
G = x-c/x solve for x
Elan Coil [88]

Answer:

x=\frac{c}{1-g}

Step-by-step explanation:

Step 1: Multiply both sides by x,

 gx=−c+x

Step 2: Add -x to both sides.

gx+−x=−c+x+−x

gx−x=−c

Step 3: Factor out variable x.

x(g−1)=−c

Step 4: Divide both sides by g-1.

\frac{x(g-1)}{g-1} =\frac{-c}{g-1\\}

x=\frac{c}{1-g}

Hope this helps!

5 0
3 years ago
Read 2 more answers
What is h(-2)<br> H(-1.75)<br> H(1)
ruslelena [56]

h(x)=\left\{\begin{array}{cccc}-2&if&-2\leq x

3 0
3 years ago
NEEEEDD HEEELLLPPPP
rusak2 [61]

Option 2: \frac{x-12}{4} is the correct answer

Step-by-step explanation:

Given fraction is:

\frac{2x-24}{8}

In order to simplify, we can see that the function is already in compact form

So,

We can simplify the given fraction.

We can see that the numerator can be further simplified

\frac{2(x-12)}{8}\\=\frac{x-12}{4}

Hence,

Option 2: \frac{x-12}{4} is the correct answer

Keywords: Polynomials, expressions

Learn more about polynomials at:

  • brainly.com/question/9196410
  • brainly.com/question/9178881

#LearnwithBrainly

8 0
3 years ago
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