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Inessa [10]
3 years ago
14

Help super important

Mathematics
1 answer:
const2013 [10]3 years ago
3 0
Hello.

Taking a look at our screenshot provided, we can conclude that we need to find the missing angle degree out of 90 degrees, as we are dealing with a right angle.

Let's set this up as an Algebraic formula and solve for the variable;
5x + 15 + 50 = 90

First, let's combine like-terms (15 and 50).

5x + 65 = 90

Now, isolate our variable by subtracting 65 from each side of the equation.

90 - 65 = 25
65 - 65 = 0

5x = 25

Now, divide both sides by 5 to solve for x, our missing angle degree.

x = 5

Your answer is A.) 5

I hope this helps!
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shutvik [7]

Answer:

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Step-by-step explanation:

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7 0
3 years ago
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Integral of 17/(x^3-125)
daser333 [38]

Answer:

17/75 ln│x − 5│− 17/150 ln(x² + 5x + 25) − 17/(5√75) tan⁻¹((2x + 5) / √75) + C

Step-by-step explanation:

∫ 17 / (x³ − 125) dx

= 17 ∫ 1 / (x³ − 125) dx

= 17 ∫ 1 / ((x − 5) (x² + 5x + 25)) dx

Use partial fraction decomposition:

= 17 ∫ [ A / (x − 5) + (Bx + C) / (x² + 5x + 25) ] dx

Use common denominator to find the missing coefficients.

A (x² + 5x + 25) + (Bx + C) (x − 5) = 1

Ax² + 5Ax + 25A + Bx² − 5Bx + Cx − 5C = 1

(A + B) x² + (5A − 5B + C) x + 25A − 5C = 1

Match the coefficients and solve the system of equations.

A + B = 0

5A − 5B + C = 0

25A − 5C = 1

A = 1/75

B = -1/75

C = -2/15

So the integral is:

= 17 ∫ [ 1/75 / (x − 5) + (-1/75 x − 2/15) / (x² + 5x + 25) ] dx

Simplify:

= 17/75 ∫ [ 1 / (x − 5) − (x + 10) / (x² + 5x + 25) ] dx

Factor ½ from the numerator of the second fraction:

= 17/75 ∫ [ 1 / (x − 5) − ½ (2x + 20) / (x² + 5x + 25) ] dx

Split the fraction:

= 17/75 ∫ [ 1 / (x − 5) − ½ (2x + 5) / (x² + 5x + 25) − ½ (15) / (x² + 5x + 25) ] dx

Multiply the last fraction by 4/4:

= 17/75 ∫ [ 1 / (x − 5) − ½ (2x + 5) / (x² + 5x + 25) − 30 / (4x² + 20x + 100) ] dx

Complete the square:

= 17/75 ∫ [ 1 / (x − 5) − ½ (2x + 5) / (x² + 5x + 25) − 15 / ((2x + 5)² + 75) ] dx

Split the integral:

= 17/75 ∫ 1 / (x − 5) dx − 17/150 ∫ (2x + 5) / (x² + 5x + 25) dx − 17/5 ∫ 1 / ((2x + 5)² + 75) dx

The first integral is:

∫ 1 / (x − 5) dx = ln│x − 5│

The second integral is:

∫ (2x + 5) / (x² + 5x + 25) dx = ln(x² + 5x + 25)

The third integral is:

∫ 1 / ((2x + 5)² + 75) dx = 1/√75 tan⁻¹((2x + 5) / √75)

Plug in:

= 17/75 ln│x − 5│− 17/150 ln(x² + 5x + 25) − 17/(5√75) tan⁻¹((2x + 5) / √75) + C

4 0
3 years ago
There are 418 students at a school. Han estimates that they each drink about 5 glasses of water each day.
Sauron [17]

Answer:

Step-by-step explanation:

a) together, they all drink about 2,090 glasses of water in one day. (418 * 5 = 2,090).

b) 2,090 * 7 (7 days in 1 week) = They drink about 14,630 glasses of water in one week.

c) 14,630 * 4 (4 weeks in 1 month) = About 58,520 glasses of water in one month.

d) 1,000,000/58,520 ≈ 17. It would take all of the students about 17 months to drink 1,000,000 glasses of water.

Hope that helps!

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2 years ago
How do I do this? (Will give brainliest) (explanation if you could)
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What is 9-(-5) please help me​
elena-14-01-66 [18.8K]

9-(-5)=

9 + 5 (because - - = +)

14

thus 9-(-5) = 14

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