For each sequence write down the formula for the nth number and calculate the 11th number, the nth number, and the 100th number. 85, 67, 49, ...

nth number ; Tn = -18 n + 103

For the 11 th number : T₁₁ = -18 *11 +103 = -95

For the 100 th number : T₁₀₀ = -18 *100 + 103 = -1697

Step-by-step explanation:

The sequence is given as;

85, 67, 49,

This is an A.P with a common difference ,d= -18

The formula for nth term can be written as;

Tn=d*n +???

where d= -18, then Tn= -18*n , Tn = -18 n +?

For;

n =1 Tn = -18*1 = -18 but T₁ = 85 , so you add 103 to -18 to get 85

n=2Tn = -18*2 = -36but T₂= 67 , so you add 103 to  -36 to get 67

Thus,

For the nth number ;

Tn = -18 n + 103

and

For the 11 th number : T₁₁ = -18 *11 +103 = -95

For the 100 th number : T₁₀₀ = -18 *100 + 103 = -1697

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.

step-by-step explanation:

for exempl this   system of equations   y = x - 3

                                                                y = 2x - 5

look   the line : y = x -3     ( red)

                            the line : y = 2x -5 ( bleus)