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2 years ago

Robyn had 8 apples. She ate3/8 of them. What is the number of apples she ate?

Mathematics

2 answers:

Leni [432]2 years ago

8 0

Since she only has 8 apples and she ate 3 of 8, she ate 3 apples.

arlik [135]2 years ago

3 0

3 apples, since there are 8 apples in total, and the denominator is 8, you would just take the numerator as your answer

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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

Given the figure below, find the values of x and z.

iragen [17]

Answer:

x=6 and z=107

Step-by-step explanation:

From the figure or diagram we can say that

z+15x-17=180 ---(1)

z+11x+7=180 ---(2)

Subtracting (1) and (2)

z+15x-17-(z+11x+7)=180-180

4x-24=0

4x=24

x=6

Substitute x=6 in (2)

z+11(6)+7=180

z+66+7=180

z=180-73

z=107

4 0

1 year ago

1) A line with gradient 2 passes through (0, 4). Write down the equation of the line.

blondinia [14]

For the attached image, note that slope is the same thing as gradient.

1) y = 2x + 4

2) Substituting in x = 1 and y = 1,

1 = 4(1) + c

1 = 4 + c

c = -3

So, the equation is y = 4x - 3

7 0

1 year ago

Someone plz help me litterly no one would bother to help me so plz I beg of u due today

goldfiish [28.3K]

<h2>PLEASE MARK BRAINLIEST!</h2>

Answer:

I'm going to help youuuuu.

Step-by-step explanation:

{1}

Your answer is A) because the rise/run is -2/4x, which simplifies to -1/2x, which is option A).

{2}

Dario's salary is B) $12 per hour. This is because, in 5 hours, Dario makes 60 dollars. If you find the unit rate of $60 in 5 hours, the answer is $12 per hour.

{3}

A) Between x = -6 and x = -2

I hope this helps! I am sorry if any of these are incorrect!

- sincerelynini

8 0

3 years ago

F(x) = 2x + 3g(x) = 2x² + 6x + 13Find: (gºf)(x)

Butoxors [25]

Answer:

The function (gof)(x) is;

$(g\circ f)(x)=8x^2+36x+49$

Explanation:

Given the functions;

$\begin{gathered} f(x)=2x+3 \\ g(x)=2x^2+6x+13 \end{gathered}$

Solving for the function;

$(g\circ f)(x)=g(f(x))$

so, we have;

$\begin{gathered} g(f(x))=2(f(x))^2+6(f(x))+13 \\ g(f(x))=2(2x+3)^2+6(2x+3)+13 \\ g(f(x))=2(4x^2+12x+9)^{}+6(2x)+6(3)+13 \\ g(f(x))=8x^2+24x+18^{}+12x+18+13 \\ g(f(x))=8x^2+24x^{}+12x+18+18+13 \\ g(f(x))=8x^2+36x+49 \end{gathered}$

Therefore, the function (gof)(x) is;

$(g\circ f)(x)=8x^2+36x+49$

5 0

3 months ago