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2 years ago

The farmers wife baked 9 pies on Monday and 5 on Tuesday. How many more pies did she bake on Monday?

Mathematics

1 answer:

insens350 [35]2 years ago

6 0

Answer:

Step-by-step explanation:

9 - 5 = 4

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Find the integral <br> ∫√(9+x)/(9-x)

densk [106]

I suppose you mean

$\displaystyle \int \frac{\sqrt{9+x}}{9-x} \, dx$

Substitute y = √(9 + x). Solving for x gives x = y² - 9, so that 9 - x = 18 - y², and we have differential dx = 2y dy. Replacing everything in the integral gives

$\displaystyle \int \frac{2y^2}{18 - y^2} \, dy$

Simplify the integrand by dividing:

$\dfrac{2y^2}{18 - y^2} = -2 + \dfrac{36}{18 - y^2}$

$\implies \displaystyle \int \left(\frac{36}{18-y^2} - 2\right) \, dy$

For the first term of this new integral, we have the partial fraction expansion

$\dfrac1{18 - y^2} = \dfrac1{\sqrt{72}} \left(\dfrac1{\sqrt{18}-y} + \dfrac1{\sqrt{18}+y}\right)$

$\implies \displaystyle \frac{36}{\sqrt{72}} \int \left(\frac1{\sqrt{18}-y} + \frac1{\sqrt{18}+y}\right) \, dy - 2 \int dy$

The rest is trivial:

$\displaystyle \sqrt{18} \int \left(\frac1{\sqrt{18}-y} + \frac1{\sqrt{18}+y}\right) \, dy - 2 \int dy$

$= \displaystyle \sqrt{18} \left(\ln\left|\sqrt{18}+y\right| - \ln\left|\sqrt{18}-y\right|\right) - 2y + C$

$= \displaystyle \sqrt{18} \ln\left|\frac{\sqrt{18}+y}{\sqrt{18}-y}\right| - 2y + C$

$= \boxed{\displaystyle \sqrt{18} \ln\left|\frac{\sqrt{18}+\sqrt{9+x}}{\sqrt{18}-\sqrt{9+x}}\right| - 2\sqrt{9+x} + C}$

6 0

1 year ago

8. Personal Financial Literacy Diana is

Vikki [24]

Answer:

3402

Step-by-step explanation:

7 yards is 21 feet, so Diana's cost is ...

(162/ft)(21 ft) = 3402

___

<em>Comment on the number</em>

This problem statement doesn't say what the cost units are.

7 0

2 years ago

The cost C to produce x number of tennis rackets is C = 190 + 18. The tennis rackets are sold wholesale for $23

andre [41]

Answer:

19 tennis rackets

Step-by-step explanation:

4 0

2 years ago

3:1 =6:x what is the value of x

AleksAgata [21]

Answer:

x = 2

Step-by-step explanation:

$\frac{3}{1} = \frac{6}{x}$

$3x = 6$

$x = 2$

8 0

2 years ago

Read 2 more answers

What is the answer to this question

madreJ [45]

Answer:

Step-by-step explanation: c=0.10m+30

Plzz give me brainliest

4 0

2 years ago