A relation contains the ordered pairs (3, 8), (6, 10), (9, 12), and (a, b). For which values of a and is the relation a function? . A. = 3 and b = 14
B. a = 6 and b = 12
C. = 9 and b = 9
D. a = ll and = 8

value of a = 11

value of b = 8

Therefore, option D is correct.

Step-by-step explanation:

We know that a function is a relation where each input or x-value of the X set has a unique y-value or output of the Y set.

In other words, we can not have duplicated inputs as there should be only 1 output for each input.

Given the ordered pairs of a relation

(3, 8), (6, 10), (9, 12), and (a, b).

Now, we have to choose the ordered pair containing values of 'a' and 'b' such that there is no duplicated or repeated x-value in the domain of a relation.

It is clear that

WE CAN NOT chose a = 3 and b = 14 because then x = 3 would be repeated. Hence, option A is INCORRECT.

WE CAN NOT chose a = 6 and b = 12 because then x = 6 would be repeated. Hence, option B is INCORRECT.

WE CAN NOT chose a = 9 and b = 9 because then x = 9 would be repeated. Hence, option C is INCORRECT.

But, if we choose a = 11 and b = 8, then the relation would be a function because each input or x-value of the X set will have a unique y-value or output of the Y set.

i.e.

(3, 8), (6, 10), (9, 12), (a, b)

(3, 8), (6, 10), (9, 12), (11, 8)

Thus, the ordered pairs (3, 8), (6, 10), (9, 12), (11, 8) represent the function because each input or x-value of the X set will have a unique y-value or output of the Y set.

Hence,

value of a = 11

value of b = 8

Therefore, option D is correct.

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.