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iren [92.7K]
3 years ago
14

Can anyone help me out in my homework. I would love to talk about these problems ​

Mathematics
1 answer:
katen-ka-za [31]3 years ago
5 0

Step-by-step explanation:

(b) If F_G = m_1g, then

m_1g = G\dfrac{m_1m_2}{r^2}

Note that m_1 cancel out so we get

g = G\dfrac{m_2}{r^2}

Solving for m_2, we get

m_2 = \dfrac{gr^2}{G}

(c) I'm not sure what the problem is asking for but here goes. As r doubles, F_G becomes

F_G = G\dfrac{m_1m_2}{(2r)^2} = \dfrac{1}{4}\left(G\dfrac{m_1m_2}{r^2}\right)

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What should be my first step when subtracting integers is to .A.add the opposite.

<h3>What are the step to follow in order to subtract integers?</h3>

To perform this operation  first number  must be kept as the  minuend, and then then change the operation from subtraction to addition.

Then  proceed with the regular addition of integers, hence What should be my first step when subtracting integers is to add the opposite.

Read more on integers here:

brainly.com/question/17695139

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The expression of integral as a limit of Riemann sums of given integral \int\limits^5_b {1} \, x/(2+x^{3}) dxis 4 \lim_{n \to \infty}∑n(n+4i)/2n^{3}+(n+4i)^{3} from i=1 to i=n.

Given an integral \int\limits^5_b {1} \, x/(2+x^{3}) dx.

We are required to express the integral as a limit of Riemann sums.

An integral basically assigns numbers to functions in a way that describes displacement, area, volume, and other concepts that arise by combining infinite data.

A Riemann sum is basically a certain kind of approximation of an integral by a finite sum.

Using Riemann sums, we have :

\int\limits^b_a {f(x)} \, dx=\lim_{n \to \infty}∑f(a+iΔx)Δx ,here Δx=(b-a)/n

\int\limits^5_1 {x/(2+x^{3}) } \, dx=f(x)=x/2+x^{3}

⇒Δx=(5-1)/n=4/n

f(a+iΔx)=f(1+4i/n)

f(1+4i/n)=[n^{2}(n+4i)]/2n^{3}+(n+4i)^{3}

\lim_{n \to \infty}∑f(a+iΔx)Δx=

\lim_{n \to \infty}∑n^{2}(n+4i)/2n^{3}+(n+4i)^{3}4/n

=4\lim_{n \to \infty}∑n(n+4i)/2n^{3}+(n+4i)^{3}

Hence the expression of integral as a limit of Riemann sums of given integral \int\limits^5_b {1} \, x/(2+x^{3}) dxis 4 \lim_{n \to \infty}∑n(n+4i)/2n^{3}+(n+4i)^{3} from i=1 to i=n.

Learn more about integral at brainly.com/question/27419605

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5 0
1 year ago
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