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iVinArrow [24]
2 years ago
5

Order 10,16,18,24,14,17,26,15,14,

Mathematics
1 answer:
Anettt [7]2 years ago
6 0
Order : 6 9 9 10 12 15 15 17 18

Mean: 12.33

Median: 12

mode: 9 and 15

range: 12
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A 21-inch rope is to be cut into two pleces so that one piece is 8 inches longer than twice the other. How long is each piece, i
Serhud [2]

Answer:

4 1/3 inches   Smaller piece

16 2/3 inches   Larger piece

Step-by-step explanation:

x + (2x + 8) = 21

3x + 8 = 21

3x = 13

x = 13/3

x = 4 1/3 inches   Smaller piece

2x + 8 = 8 2/3 + 8

2x + 8 = 16 2/3 inches   Larger piece

8 0
3 years ago
Help me please and thank you
AURORKA [14]

Answer:

B

Step-by-step explanation:

You just count the dots and check the tables.

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 quadratic equation that can be written as the difference of squares has...
quester [9]

Answer: C two solutions

Step-by-step explanation:  

The Difference of Two Squares theorem says that any time an equation may be written as a difference between squares A² - B² = 0 it may be rewritten as two products, the sum and difference of the square roots (A + B) (A - B)

Hope this helped :)

6 0
2 years ago
Read 2 more answers
7➗1/5 <br> As a fraction plz
marishachu [46]

\bf 7\div \cfrac{1}{5}\implies \cfrac{7}{1}\div \cfrac{1}{5}\implies \cfrac{7}{1}\cdot \cfrac{5}{1}\implies \cfrac{35}{1}

5 0
3 years ago
Read 2 more answers
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