Rewrite 105,000 in scientific notation.

Use integration by parts to find the integrals in Exercise. ∫(4x-12)e-8x dx.

stepladder [879]

Answer:

$e(2x^{2} -12x)-4x^{2}+C$

Step-by-step explanation:

We have been given an indefinite integral as $\int \left(4x-12\right)e-8x\:dx$ . We are asked to find the given integral.

Let us solve our given problem.

$\int \left(4x-12\right)e\:dx-\int 8x\:dx$

Take out constant:

$e\int \left(4x-12\right)\:dx-8\int x\:dx$

$e(\int 4x\:dx -\int 12\right\:dx)-8\int x\:dx$

$e(\frac{4x^{1+1}}{2} -12x)-8*\frac{x^{1+1}}{1+1}+C$

$e(\frac{4x^{2}}{2} -12x)-8*\frac{x^{2}}{2}+C$

$e(2x^{2} -12x)-4x^{2}+C$

Therefore, our required integral would be $e(2x^{2} -12x)-4x^{2}+C$ .

5 0

3 years ago

Simplify (3x - 5) - (5x + 1). 0-2x + 6 -2x - 6 2x - 6 2x + 6 fast please!

mamaluj [8]

-2x-6

EXPLANATION

(3x-5) = (-2x) - 6

3 0

3 years ago

A square of side length s lies in a plane perpendicular to a line L. One vertex of the square lies on L. As this square moves a

user100 [1]

Answer:

Part (A) The required volume of the column is $s^2h$ .

Part (B) The volume be $s^2h=\frac{s^2h}{2}+\frac{s^2h}{2}$ .

Step-by-step explanation:

Consider the provided information.

It is given that the we have a square with side length "s" lies in a plane perpendicular to a line L.

Also One vertex of the square lies on L.

Part (A)

Suppose there is a square piece of a paper which is attached with a wire through one corner. As you blow it up it spins around on the wire.

This square moves a distance h along L, and generate a corkscrew-like column with square.

The cross section will remain the same.

So the cross section area of original column and the cross section area of twisted column at each point will be the same.

The volume of the column is the area of square times the height.

This can be written as:

$s^2h$

Hence, the required volume of the column is $s^2h$ .

Part (B) What will the volume be if the square turns twice instead of once?

If the square turns twice instead of once then the volume will remains the same but divide the volume into two equal part.

$s^2h=\frac{s^2h}{2}+\frac{s^2h}{2}$

Hence, the volume be $s^2h=\frac{s^2h}{2}+\frac{s^2h}{2}$ .

5 0

3 years ago

Please help please ASAP please help please I’ll mark you as a brnlist

FrozenT [24]

Answer:

i think its no triangle can be formed.... if it aint right im sorry 7th grade was a long time ago

Step-by-step explanation:

3 0

3 years ago

Situation A

Colt1911 [192]

The equation a = 100 + 75d represents Maria's account balance.

Step-by-step explanation:

Given that,

Maria opened a new savings account with an initial deposit of $100.
She deposits $75 into this savings account every two-weeks.

You need to find the equation to represent Maria's account balance, a after she has completed d deposits.

Let 'd' be the number of deposits Maria made after the initial deposit.
Let 'a' be the total account balance after 'd' deposits.

Therefore, the equation for the total account balance can be framed as the sum of the initial deposit and amount deposited after that.

To find the amount that was deposited after the initial deposit :

⇒ $75 × number of times Maria deposited.

⇒ 75 × d

The equation is written as,

⇒ a = 100 + 75d

Hence the equation a = 100 + 75d represents Maria's account balance.

7 0

4 years ago