Which function describes the arithmetic sequence shown? −1, 1, 3, 5, 7, 9, 11, 13, a) ƒ(x) = 2x − 3 eliminate b) ƒ(x) = 3x − 2 c) ƒ(x) = 2x + 3 d) ƒ(x) = 3x + 2

A)

Step-by-step explanation:

Given:

The arithmetic sequence shown is −1, 1, 3, 5, 7, 9, 11, 13, ...

We have been given 4 options.

A) ƒ(x) = 2x − 3

B) ƒ(x) = 3x − 2

C) ƒ(x) = 2x + 3

D) ƒ(x) = 3x + 2

we will check for all and then find the correct 1

1) we will check for A) ƒ(x) = 2x − 3

When x=1; f(1) = 2×1 - 3 = -1

when x= 2; f(2) = 2×2 - 3 = 1

when x=3; f(3) = 2×3 - 3 = 3

when x=4; f(4) = 2×4 - 3 = 5

Hence the first four terms are similar to the given sequence hence we can conclude that this option is correct.

2) we will check for A) ƒ(x) = 3x − 2

When x=1; f(1) = 3×1 - 2 = 1

when x= 2; f(2) = 3×2 - 2 = 4

when x=3; f(3) = 3×3 - 2 = 7

when x=4; f(4) = 3×4 - 3 = 9

Hence the first four terms are not similar to the given sequence hence we can conclude that this option is incorrect.

3) we will check for A) ƒ(x) = 2x + 3

When x=1; f(1) = 2×1 + 3 = 5

when x= 2; f(2) = 2×2 + 3 = 7

when x=3; f(3) = 2×3 + 3 = 9

when x=4; f(4) = 2×4 + 3 = 11

Hence the first four terms are not similar to the given sequence hence we can conclude that this option is incorrect.

4) we will check for A) ƒ(x) = 3x + 2

When x=1; f(1) = 3×1 + 2 = 5

when x= 2; f(2) = 3×2 + 2 = 8

when x=3; f(3) = 3×3 + 2 = 11

when x=4; f(4) = 3×4 + 3 = 15

Hence the first four terms are not similar to the given sequence hence we can conclude that this option is incorrect.

Hence option A) ƒ(x) = 2x − 3 is the correct function which describes the the arithmetic sequence −1, 1, 3, 5, 7, 9, 11, 13, ..

-4

step-by-step explanation:

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.