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Doss [256]
3 years ago
15

Select the basic integration formula you can use to find the indefinite integral.

Mathematics
1 answer:
kondaur [170]3 years ago
3 0

Answer:

\int \dfrac{du}{u}=\log|u|+C

\int u^n du=\dfrac{u^{n+1}}{n+1}+C

\int \dfrac{du}{u\sqrt{u^2-a^2}}=\dfrac{1}{a}\csc^{-1}(\dfrac{x}{a})+C

Step-by-step explanation:

a.

\int \dfrac{du}{u}=\log|u|+C    [\because \int \dfrac{dx}{x}=\log |x|+C]

b.

\int u^n du=\dfrac{u^{n+1}}{n+1}+C    [\because \int x^n dx=\dfrac{x^{n+1}}{n+1}+C]

c.

\int \dfrac{du}{u\sqrt{u^2-a^2}}=\dfrac{1}{a}\csc^{-1}(\dfrac{x}{a})+C        [\because \dfrac{adx}{x\sqrt{x^2-a^2}}=\csc^{-1}(\dfrac{x}{a})+C]

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Solve the equation 5y-6=10
BaLLatris [955]

Answer:

y = 3.2

Step-by-step explanation:

Simplifying

5y + -6 = 10

Reorder the terms:

-6 + 5y = 10

Solving

-6 + 5y = 10

Solving for variable 'y'.

Move all terms containing y to the left, all other terms to the right.

Add '6' to each side of the equation.

-6 + 6 + 5y = 10 + 6

Combine like terms: -6 + 6 = 0

0 + 5y = 10 + 6

5y = 10 + 6

Combine like terms: 10 + 6 = 16

5y = 16

Divide each side by '5'.

y = 3.2

Simplifying

y = 3.2

8 0
2 years ago
Read 2 more answers
Find the slope of this line: (15,7) (3,-2)<br><br> Help
Oliga [24]

Answer:

m=\frac{3}{4}

Step-by-step explanation:

\mathrm{Slope\:between\:two\:points}:\quad \mathrm{Slope}=\frac{y_2-y_1}{x_2-x_1}

\left(x_1,\:y_1\right)=\left(15,\:7\right),\:\left(x_2,\:y_2\right)=\left(3,\:-2\right)

m=\frac{-2-7}{3-15}

\mathrm{Refine}

m=\frac{3}{4}

5 0
3 years ago
31 billion in scientific notation
umka2103 [35]
31 to the 9th power (31 9... i cant make the number small lol)
5 0
3 years ago
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PLEASE HELP ME WITH BOTH OF THESE PROBLEMS THIS IS DUE SOON PLEASE HELP ME
iogann1982 [59]

Answer:

Step-by-step explanation:

4.

a)

P = 2width + 2length

8x = 2x + 2 length; 8x-2x = 2 length; 6x=2 length

length = 3x

b)

sides= 1/4 of 3x = 3x/4

perimeter of square = 4* side = 4*3x/4 = 3x

c)

x= 4

P rectangle =8x= 8*4= 32

P square = 3x = 3*4 = 12

32-12 = 20 cm greater is the P rectangle than P of square

d)

A rectangle = 2x*x = 2*4*4 = 32

A square =(3x/4)² = (3*4/4)² = 9

32-9 = 23 cm² greater is the A rectangle than A of square

5.

4Comic+1 Nonfiction

4comic = 8y so 1 comic = 2y

1 nonfiction = (3+7y)+ 2y

a)

1 nonfiction = 7y+2y+3 = 9y+3

b)

total= 8y+9y+3 = 17y+3

if y=4

total = 17*4 +3  = $71

7 0
3 years ago
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A stock has had returns of 7 percent, 25 percent, 17 percent, −13 percent, 25 percent, and −6 percent over the last six years. W
Tems11 [23]

Answer: Geometric average return would be 0.10% and arithmetic average return would be 9.17%.

Step-by-step explanation:

Since we have given that

Returns are as follows:

7%, 25%, 175, -13%, 25% and -6%.

Geometric return is given by

\sqrt[6]{(1+0.07)(1+0.25)(1+0.17)(1-0.13)(1+0.25)(1-0.06)}-1\\\\=\sqrt[6]{(1.17)(1.25)(1.17)(0.87)(1.25)(0.94)}-1\\\\=0.097\%=0.10\%

Arithmetic average return would be

\dfrac{7+25+17-13+25-6}{6}=9.17\%

Hence, geometric average return would be 0.10% and arithmetic average return would be 9.17%.

7 0
2 years ago
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