bqimath

shoot it was 4 inches inscribed in a cone with base radius of 6

A sphere of radius 4 inches is inscribed in a cone with a base of radius 6 inches. In inches, what is the height of the cone? Express your answer as a decimal to the nearest tenth.

Answer:x²

f(0)=0

c=0

f(1)=1,c=0, so a+b=1

f(2)=4

so 4a+2b=4

which is 2a+b=2

a+b=1

2a+b=2

so a=1, b=0

now we substitute:

a=1,b=0,c=0

x²+0x+0=x²

x²

-1/2

x^2+x^2-3x-2x+5+1=2x^2-5x+6

we divide that by six so the constant term is the same:1

(2x^2-5x+6)/6=1/3x^2-5/6x+1

so now we know A=1/3, B=-5/6

A+B=1/3-5/6=-1/2

|z|=1

z=1 or -1

if z=1,

|1+1|+|1-1+1^2|=2+1=3

if z=-1,

|1-1|+|1+1+(-1)^2|=0+3=3

it can only be 3

proof:

|z|=1

z^2=1

|1±z|+|1±z+1|=1±z+1±z+1=3±z±z, one has the be -1 so 3

The number of squares crossed by an ant crawling diagonally across an

l*w rectangle formula is

l+w−gcd(l,w)

.

The rectangle dimensions are

4*4 so l=4, w=4

4+4-gcd(4,4)=8-4=4

Total permutations of 6 distinct children in 6 distinct seats: 6!=720

Fix sibling pair i to sit in the same column.

The pair has two siblings s1 and s2→ 2 ways to order them vertically (top-bottom or bottom-top).

There are 3 columns → 3 possible columns for them to occupy.

The remaining 4 children can be permuted in the remaining 4 seats arbitrarily → 4!=244! = 244!=24 ways.

Therefore,

3×2×4!=3×2×24=144

2 ways to order siblings vertically → 2×2=4

3×4×2=24

6×8=48

6!−408=720−408=312

312 ways