Why is the correct answer D? Please explain thoroughly.

Step-by-step explanation:

When computing the right Riemann sum corresponding to the integral from "a" to "b", the k-th value of x is

 x[k] = a + k·∆x

as k goes from 1 to n, where the interval width (∆x) is (b-a)/n.

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Here, we have a=0, b=5, ∆x = 5/n and x[k] = 5k/n. So, the integral ...

becomes the sum ...

This matches the given sum, so the above integral is the answer to the question.

step-by-step explanation:

in which figure is point g a centroid

see explanation

step-by-step explanation:

a

(6r + 7) + (13 + 7r) ( remove brackets and collect like terms )

= 6r + 7 + 13 + 7r

= 13r + 20

b

remove brackets and collect like terms

13 - r - 1 + r

= 12 - r

c

remove brackets and collect like terms

= - 8 - r + 2r - 4

= - 12 + r

d

remove brackets and collect like terms

= 7r - - - 6r

[-   - = - - = - ]

= r -