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Ray Of Light [21]
3 years ago
13

Question 5. I need help please

Mathematics
1 answer:
Nonamiya [84]3 years ago
7 0
The answer would be C. 72
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Plz help im an idiot
MrMuchimi

Answer:

3.)138

4.) 149

Step-by-step explanation:

you add the two inside measures together.

5 0
3 years ago
Read 2 more answers
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
This figure represents the base of a fish tank that is 8 inches high.
Igoryamba

The volume of the fish tank is 408 in³

To solve the volume of the fish tank, we need to understand what is the volume of plane shapes.

<h3>What is the volume of plane shapes?</h3>

The volume of plane shapes resembles a 3-dimensional space showing the area enclosed by the shape.

From the figure given:

The figure can be differentiated into two shapes;

  • A rectangle
  • A triangle

The volume of the rectangle is known as:

  • = Length × Breadth
  • = 7 inches × 6 inches
  • = 42 inches²

The volume of the triangle is:

  • = 1/2 × base × height
  • = 1/2 × 3 × 6
  • = 9 inches²

The total volume of the base of the fish tank now is:

  • = 42 inches² + 9 inches²
  • = 51 inches²

Now, the volume of the fish tank is:

  • = Height × base of the fish tank
  • = 8 inches × 51 inches²
  • = 408 in³

Learn more about the volume of plane shapes here:

brainly.com/question/20475473

7 0
2 years ago
A recursive rule for a sequence is given. Find the first four terms of the sequence.
tigry1 [53]

Answer:  

So...

   a0 = -2

   a1 = (a0)2 - 4  =  4 - 4  =  0

   a2 = (a1)2 - 4 = ((a0)2-4)2 - 4 =...=  02 - 4  = -4  

       For an+1, you may use the previous term (an) if you have just calculated it, rather than calculating it recursively again

   a3 = (-4)2 - 4 = 12

 

The first four terms in the sequence are -2, 0, -4, 12.

Step-by-step explanation:

This recursive sequence is defined as follows:

 a0 = -2      [the first term]

 an+1 = an2 - 4     [for all other terms, n≥0; note that you cannot find a0 using this line]

 

Note that this is not "BASE" for a number base, but it is "SUB" for subscript, indicating the term.  Sometimes, sequences are written with the first term being a1 and sometimes sequences are written with the first term being a0.  This is because there are situations that make one or the other more convenient (for example, starting with elapsed time t=0 makes sense).

 

To find the value of later terms, a recursive definition requires that you find the value of the previous term, which requires that you find the value of the previous term, which requires that you find the value of the previous term, which requires that you find the value of the previous term, ... which requires that use the value of the first term.

 

That's why (joke) that the dictionary definition of "recursive" is "see recursive."

4 0
3 years ago
Rewrite the following equation in slope-intercept form. 18x − 19y = -20
pantera1 [17]
Slope intercept form

6 0
3 years ago
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