Write the explicit formula
for the sequence 8, 4,0,-4,8
then find the 10th term in
the sequence

The required explicit formula is A(n)= 4-4n

10th term of arithmetic sequence is (-36)

Step-by-step explanation:

Given arithmetic sequence is 8,4,0,-4,-8

The arithmetic sequence is given by a,a+d,a+2da+(n-1)d

Comparing both the sequence we get,

a=8 and a+d=4

For value of d:

d+a=4

d=4-8=(-4)

The explicit formula is given by : A(n)= a+(n-1)d

A(n)= a+(n-1)d

A(n)= 8+(n-1)(-4)

A(n)= 8-4n+4

A(n)= 4-4n

Therefore, The required explicit formula is A(n)= 4-4n

To find value of 10 th term:

Take n=10 in explicit formula

A(10)= 4-4(10)

A(10)= -36

Therefore, 10th term is (-36)

4

step-by-step explanation:

6 (donuts) divided by 3 is 2.

so 2/3 means 2 times 2, which is 4/6.

you get two and your friend gets four.

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.