Determine if the given sequence is an arithmetic sequence. if it is, identify the common difference.-8, -11, -14, -17, a. yes the common difference is -3b. yes the common difference is 3c. no there is no common differenced. yes the common difference is 8/11

A. Yes, the common difference is -3

Step-by-step explanation:

First of all, this would be an arithmetic sequence, because there is a constant value being added (or effectively subtracted, if the value is negative) to each subsequent number in the sequence.

To find the common difference, ie. what value is added, we must take a term from the sequence and subtract the previous term from it.

Using the first two terms, -8 and -11:

-11 - (-8) = -11 + 8

= -3

You can check if this is right by taking another term from the sequence and trying to add the common difference, then seeing if this value matches the next term.

Taking the third and fourth terms, -14 and -17:

- 14 + (-3) = -14 - 3

= -17

The fourth term is also -17.

This is correct; thus, it is an arithmetic sequence, with a common difference of -3 (answer A)

It is a common mistake for people to answer B, however always remember that what we are looking for is what value, added to a given term, will give us the next term.

Since adding a negative number effectively means subtracting it, then this will apply to sequences that become more negative (or decrease) rather than more positive (or increase).

Also remember to use brackets in order to clearly set out working as this can lead to little mistakes, particularly where many negative signs are involved.

Hope that helped :)

f(x) is going down by 4

step-by-step explanation:

(its either that or its going left by 4)

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.