All categories

3 years ago

I need the solution

Mathematics

1 answer:

shutvik [7]3 years ago

8 0

$\dfrac{8c^3}{6(c+d)}\div\dfrac{2c^2}{3c+3d}=\dfrac{4c^3}{3(c+d)}\div\dfrac{2c^2}{3(c+d)}\\\\=\dfrac{4c^3}{3(c+d)}\cdot\dfrac{3(c+d)}{2c^2}=\dfrac{4c^3}{2c^2}=2c$

You might be interested in

Evaluate using integration by parts

PolarNik [594]

Rather than carrying out IBP several times, let's establish a more general result. Let

$I(n)=\displaystyle\int x^ne^x\,\mathrm dx$

One round of IBP, setting

$u=x^n\implies\mathrm du=nx^{n-1}\,\mathrm dx$

$\mathrm dv=e^x\,\mathrm dx\implies v=e^x$

gives

$\displaystyle I(n)=x^ne^x-n\int x^{n-1}e^x\,\mathrm dx$

$I(n)=x^ne^x-nI(n-1)$

This is called a power-reduction formula. We could try solving for $I(n)$ explicitly, but no need. $n=5$ is small enough to just expand $I(5)$ as much as we need to.

$I(5)=x^5e^x-5I(4)$

$I(5)=x^5e^x-5(x^4e^x-4I(3))=(x-5)x^4e^x+20I(3)$

$I(5)=(x-5)x^4e^x+20(x^3e^x-3I(2))=(x^2-5x+20)x^3e^x-60I(2)$

$I(5)=(x^2-5x+20)x^3e^x-60(x^2e^x-2I(1))=(x^3-5x^2+20x-60)x^2e^x+120I(1)$

$I(5)=(x^3-5x^2+20x-60)x^2e^x+120(xe^x-I(0))$

Finally,

$I(0)=\displaystyle\int e^x\,\mathrm dx=e^x+C$

so we end up with

$I(5)=(x^4-5x^3+20x^2-60x+120)xe^x-120e^x+C$

$I(5)=(x^5-5x^4+20x^3-60x^2+120x-120)e^x+C$

and the antiderivative is

$\displaystyle\int2x^5e^x\,\mathrm dx=(2x^5-10x^4+40x^3-120x^2+240x-240)e^x+C$

8 0

2 years ago

Describe when to use a series and when to use an equation.

anyanavicka [17]

Answer:

An equation is used when we have paired sets of data to describe how the values in one pair change when we alter the values in the other set.

On the other hand, a series gives a general formula of determining the value of the nth observation when the values have been arranged in increasing order

Step-by-step explanation:

An equation such as; y = 3x+5 models the relation between the response variable y and the predictor variable x. It tells us how y changes when x is altered by a certain magnitude. The value 3 is described as the slope while 5 is the y-intercept.

On the other hand, a series such as; score = 2 + 3n provides a general formula that can be used to determine the score of the nth individual in a sample or population.

5 0

3 years ago

Earl runs 75 meters in 30 seconds .How many meters does Earl run per second

belka [17]

Answer:

2.5 meters per second

Step-by-step explanation:

75/30 = 2.5

I'd choose 25 because the person who wrote the answers probably forgot to add decimal points

6 0

3 years ago

A sno-cone machine priced at $139 is on sale for 20% off. What is the price of the sno-cone machine after the discount? *

lawyer [7]

So percents are just written as 20% = 0.2 so keep that in mind

139 divided by 0.2 is 95 , which would be the price after the discount :)

hope this helps!
give me brainliest

7 0

2 years ago

The back of Dante's property is a creek. Dante would like to enclose a rectangular area, using the creek as one side and fencing

Allushta [10]

The correct value is 720 ft of fencing.

Answer:

Max Area = 64800 sq.ft

Step-by-step explanation:

A square will always give us the maximum area.

Thus, one side would be;

720/4 = 180 feet

So, we want a square 180 ft by 180 ft

however, from the question, we are to use the creek as one side. So, we'll take the 180 ft that we don't need because of the creek and then add it to the opposite side to get 180 + 180 = 360 ft.

Thus,we now have a rectangle with dimensions: 180 ft by 360 ft

Area is given by;

area = length × width

Maximum Area = 180 × 360

Max Area = 64800 sq.ft

6 0

3 years ago