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3 years ago

Write this product in its simplest form -5a•6a^8

Mathematics

1 answer:

timofeeve [1]3 years ago

6 0

The rule for the product of similar bases with exponents:

(a^b)(a^c)=a^(b+c)

(-5*6)(a^1)(a^8)

(-30)(a^(1+8))

-30a^9

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Whats the intrgral of <img src="https://tex.z-dn.net/?f=%20%5Cint%20%20%5Cfrac%7Bx%5E2%2Bx-3%7D%7B%28x%5E3%2Bx%5E2-4x-4%29%5E2%7

rosijanka [135]

$\displaystyle\int\frac{x^2+x-3}{(x^3+x^2-4x-4)^2}\,\mathrm dx$

Notice that $x^3+x^2-4x-4=x^2(x+1)-4(x+1)=(x-2)(x+2)(x+1)$ . Decompose the integrand into partial fractions:

$\dfrac{x^2+x-3}{(x-2)^2(x+2)^2(x+1)^2}$
$=\dfrac1{3(x+1)}-\dfrac{11}{32(x+2)}-\dfrac1{3(x+1)^2}-\dfrac1{16(x+2)^2}+\dfrac1{96(x-2)}+\dfrac1{48(x-2)^2}$

Integrating term-by-term, you get

$\displaystyle\int\frac{x^2+x-3}{(x^3+x^2-4x-4)^2}\,\mathrm dx$
$=-\dfrac1{48(x-2)}+\dfrac1{3(x+1)}+\dfrac1{16(x+2)}+\dfrac1{96}\ln|x-2|+\dfrac13\ln|x+1|-\dfrac{11}{32}\ln|x+2|+C$

5 0

3 years ago

Which of the following is the graph of y=sqr root -x-3

Elan Coil [88]

Answer:

The graph in the attached figure

see the explanation

Step-by-step explanation:

we have

$y=\sqrt{-x-3}$

we know that

The radicand must be greater than or equal to zero

$(-x-3)\geq 0$

solve for x

Adds 3 both sides

$-x\geq 0+3$

$-x\geq 3$

Multiply by -1 both sides

Remember that, when you multiply or divide both sides of an inequality by a negative number, you must reverse the inequality symbol

$x\leq -3$

The domain of the function is the interval (-∞,-3]

For x=-3 ---> the value of y=0

The range is the interval {0,∞)

therefore

The graph in the attached figure

3 0

3 years ago

Write the equation for the graph in slope-intercept form.

Maslowich

Answer:

y = - $\frac{3}{4}$ x + 1

Step-by-step explanation:

y = mx + b

Find two point on the graph (0,1) (4,-2); 1 is the y intercept

y = mx + 1

$\frac{1 + 2}{0 - 4}$ = $\frac{3}{-4}$

y = - $\frac{3}{4}$ x + 1

6 0

2 years ago

Read 2 more answers

Li rolls a number cube labeled 1 to 6 a total of 24 times. How many times can she expect to roll a 1

scoundrel [369]

Li can expect to roll a one 4 times.

Since there are six possibilities (1, 2, 3, 4, 5 & 6), you divide 24 and 6 to get 4.

8 0

2 years ago

Read 2 more answers

Please helpp!

ycow [4]

Answer:

The result is the number of years, approximately, it'll take for your money to double. For example, if an investment scheme promises an 8% annual compounded rate of return, it will take approximately nine years (72 / 8 = 9) to double the invested money

8 0

2 years ago