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ELEN [110]
2 years ago
14

(x+1)(6x-5) find the indefinite Integral

Mathematics
1 answer:
Elan Coil [88]2 years ago
3 0

~~~~\displaystyle \int (x+1)(6x-5)~ dx\\\\\\=\displaystyle \int (6x^2-5x+6x-5)~ dx\\\\\\=\displaystyle \int(6x^2+x-5)~ dx\\\\\\=6\displaystyle \int x^2 ~ dx +\displaystyle \int  x~dx - \displaystyle \int~ 5~ dx\\\\\\=6\cdot \dfrac{x^{2+1}}{2+1} + \dfrac{x^{1+1}}{{1+1}}- 5x+C~~~~~~~~~~~~~~~~~;\left[\displaystyle \int x^n ~ dx= \dfrac{x^{n+1}}{n+1}+C,~~ n \neq -1\right]\\\\\\=6\cdot \dfrac{x^3 }{ 3} + \dfrac{x^2}2 - 5x+C\\\\\\=2x^3 +\dfrac{x^2 }{2 } - 5x +C

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The function f(x) varies inversely with x and f(x)=8 when x=3
Sedaia [141]

Answer:

12

Step-by-step explanation:

we know that

A relationship between two variables, x, and y, represent an inverse variation if it can be expressed in the form y*x=k or y=k/x

In this problem we have

For x=3 -----> f(x)=8

so

Find the value of k

f(x)*x=k

substitute the value of x and f(x)

8*3=k

k=24

therefore

the equation is equal to

f(x)=24/x

For x=2 -------> substitute in the equation and find the value of f(x)

f(x)=24/2=12

6 0
3 years ago
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zavuch27 [327]
Thank u for posting a picture!
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8 0
3 years ago
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How to solve this problem I don’t get it at all
Zarrin [17]
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8 0
3 years ago
1.    An AP has a common difference of 3.  Given that the nth term is 32, and the sum of the first n terms is 185, calculate the
netineya [11]

Answer:

The value of n is 10

Step-by-step explanation:

The formula of the nth term of the arithmetic progression is a_{n} = a + (n - 1)d

  • a is the first term
  • d is the common difference between each 2 consecutive terms
  • n is the position of the term

The formula of the sum of nth terms is S_{n} = \frac{n}{2} [2a + (n - 1)d]

∵ An AP has a common difference of 3

∴ d = 3

∵ The nth term is 32

∴ a_{n} = 32

→ Substitute them in the 1st rule above

∵ 32 = a + (n - 1)3

∴ 32 = a + 3(n) - 3(1)

∴ 32 = a + 3n - 3

→ Add 3 to both sides

∴ 35 = a + 3n

→ Switch the two sides

∴ a + 3n = 35

→ Subtract 3n from both sides

∴ a = 35 - 3n ⇒ (1)

∵ The sum of the first n terms is 185

∴ S_{n} = 185

→ Substitute the value of S_{n} and d in the 2nd rule above

∵ 185 = \frac{n}{2} [ 2a + (n - 1)3]

∴ 185 = \frac{n}{2} [2a + 3(n) - 3(1)]

∴ 185 = \frac{n}{2} [2a + 3n - 3]

→ Multiply both sides by 2

∴ 370 = n(2a + 3n - 3)

∴ 370 = 2an + 3n² - 3n

→ Substitute a by equation (1)

∴ 370 = 2n(35 - 3n) + 3n² - 3n

∴ 370 = 70n - 6n²+ 3n² - 3n

→ Add the like terms in the right side

∵ 370 = -3n² + 67n

→ Add 3n² to both sides

∴ 3n² + 370 = 67n

→ Subtract 67 from both sides

∴ 3n² - 67n + 370 = 0

→ Use your calculator to find n

∴ n = 10 and n = 37/3

∵ n must be a positive integer ⇒ 37/3 neglecting

∴ n = 10

∴ The value of n is 10

4 0
2 years ago
X + 2y = -4 in graph
MariettaO [177]

Equation Answer:

y = -½x - 2

Graph:

3 0
2 years ago
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