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Vilka [71]
2 years ago
9

Find the distance between the points (-7, -10) and (-5,-1)

Mathematics
1 answer:
jek_recluse [69]2 years ago
3 0

Answer:

d=√(x2-x1)² + (y2-y1)²

Step-by-step explanation:

ans is √85 unit

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Is this a reflection
myrzilka [38]

Answer:

yes

Step-by-step explanation:

it is reflected across the y axis

4 0
2 years ago
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
A number,M, is rounded to 1 decimal place. the result is 9.4 complete the error interval for M​
ivann1987 [24]

Answer:

9.35 \le M \le 9.45

Step-by-step explanation:

Given

M = 9.4 to 1 d p

Required

The error interval

The error interval is represented as:

Lower \le M \le Upper

Where

Lower = M - 0.05

Upper = M + 0.05

So, we have:

Lower = M - 0.05

Lower = 9.4 - 0.05

Lower = 9.35

Upper = M + 0.05

Upper = 9.4 + 0.05

Upper = 9.45

Hence, the error interval: Lower \le M \le Upper is:

9.35 \le M \le 9.45

3 0
3 years ago
Can someone answer it please I really need help please I need it right now I was so frustrating please help and please show work
Eduardwww [97]

Answer:

  2 1/4 yards above sea level

Step-by-step explanation:

The midpoint elevation is the average of the endpoint elevations, their sum divided by 2. When elevation is below sea level, it is represented by a negative number.

  (17 3/4 - 13 1/4)/2 = (4 2/4)/2 = 2 1/4 . . . yards above sea level

8 0
3 years ago
Problem
Ganezh [65]

Explanation is in the file

tinyurl.com/wpazsebu

8 0
3 years ago
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