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4 years ago

What is the difference between the product of 12 and 8and the sum of 12 and 8

Mathematics

1 answer:

Sunny_sXe [5.5K]4 years ago

3 0

The product (found when multiplying both numbers together) of 12 and 8 is 96.

The sum (found when adding both numbers together) of 12 and 8 is 20.

The difference (found when subtracting the sum from the product) of 96 and 20 is 76!

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Question is in the picture:::

Leviafan [203]

Answer:

160

Have a great day!

6 0

3 years ago

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

3 years ago

The population of a certain animal species you are studying decreases at a rate of 3.5% per year. Only 80 of the animals in the

kotegsom [21]

The function:
f ( x ) = x * 0.965^t
where x is the initial amount and t is the number of the years
80 = x * 0.965^3
80 = x * 0.89632
x = 80 : 0.89632 ≈ 89
Answer:
The initial amount of animals was <span>89.</span>

4 0

3 years ago

I mostly need help writing a linear inequality, I think I might be able to graph it though.

damaskus [11]

Answer:

The answer to your question is:

Step-by-step explanation:

Data

Grocery store = G = $9 /h

Mowing lawns = M = $6/ h

Between two jobs ≥ $150

Write a linear inequality

9G + 6M ≥ 150

See the picture below.

8 0

3 years ago

dalia saved $3,000 last year.she saved $600 in the month of January.what percent of the total amount of money she save last year

storchak [24]

Dalia saved 20%of her entire years savings in January.

3000 is her entire savings

300 is 10 percent of her entire savings, 300+300=600

so 10%+10%=20%

hope this helped

5 0

3 years ago