Let a =
1 3 2
3 1 2
4 3 2
and b =
2 1 3
2 2 1
1 3 1
represent the bus routes of two companies between three cities.
a. let c = a ⋅ b. find matrix c, and explain the meaning of entry c1,3.
b. nina wants to travel from city 3 to city 1 and back home to city 3 by taking a direct bus from company a on
the way to city 1 and a bus from company b on the way back home to city 3. how many different ways are
there for her to make this trip?
c. oliver wants to travel from city 2 to city 3 by taking first a bus from company a and then taking a bus from
company b. how many different ways can he do this?
d. how many routes can oliver choose from if he travels from city 2 to city 3 by first taking a bus from
company b and then taking a bus from company a?

dc=6 square root of 3 and ac is 12 square root 3

c and d

step-by-step explanation:

square root of 3/2 = 18/c

cross multiply to get 18*2=√3*c

36/√3 * √3/√3 = c

c= 36*√3/3

c=12√3

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.

well what did you do it matters what you did : )

step-by-step explanation: