Find the next three terms of the arithmetic sequence 5, 9, 13, 17, … . Question 9 options:

a)

21, 23, 25

b)

41, 45, 49

c)

21, 41, 61

d)

21, 25, 29

The next three terms of the arithmetic sequence 5, 9, 13, 17 is 21, 25, 29.

Given that,

Based on the above information, we can see that

There is the addition of 4 in each next number i.e.

5 + 4  = 9

9 + 4 = 13

13 + 4 = 17

17 + 4 = 21

21 + 4 = 25

25 + 4 = 29

Therefore, the option d is correct

Hence, the other options are incorrect.

Therefore we can conclude that the next three terms of the arithmetic sequence 5, 9, 13, 17 is 21, 25, 29.

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the image of (6, 9) under a dilation is (4, 6). the scale factor is

answer: ratio of volume of cone (with 3 times the height and equal diameter) to volume of cylinder is 2 to 1. the value of π is not used.

step-by-step explanation:

radius is diameter/2 = 4.

area of circle is π r^2.

volume of cylinder is height × area of base = hπr^2 = 3(4^2) π = 48π cubic inches.

not knowing the formula for volume of cone, i calculate it using calculus (which is for calculating things).

volume of cone is integral 0 to h area(y) dy. area(y) is π r(y)^2. r(y) runs r to zero as y runs zero to h, r(0) = r, r(h) = 0.

r(y) = r - r/h y

area(y) = π (r - r/h y)^2 = π (r^2 - 2r^2y/h + r^2y^2/h^2) = π r^2(1-2y/h+y^2/h^2)

antiderivative area(y) = π r^2 (y-y^2/h+y^3/(3h^2))

integral 0 to h = π r^2(h-h^2/h+h^3/(3h^2) - (0)) = π r^2(h - h + h/3) = π r^2(h/3) = π/3 r^2 h

volume of this cone is π/3(4^2)18 cubic inches.

= 6 16 π = 96π cubic inches.

cone has twice the volume, 96/48.

cone height is 6 times the cylinder.

ratio of volume formula: π r^2 cancels.

cone over cylinder ratio is 6h/3 to h, 2 to 1.