Leo runs 3 miles a day. his goal is to run 33 miles in total. after 8 days, how many more miles does leo have left to run in order to meet his goal? m = miles

Leo will have 9 miles left to meet his goal

Step-by-step explanation:

Step 1: Determine the number of miles he runs a day

Number of miles he runs a day=3 miles

Step 2: Calculate the number of miles he will run in 8 days

This can be expressed as;

Total number of miles he runs in 8 days=number of miles he runs per day×number of days

where;

Number of miles he runs per day= 3 miles per day

Number of days=8 days

replacing;

Total number of miles he runs in 8 days=(3×8)=24 miles

Step 3: Calculate number of miles left after 8 days

After 8 days, Leo will have run 24 miles. To calculate the number of miles left, we express this as;

Number of miles left after 8 days=Total miles he needs to cover to meet his goal-number of miles already covered

where;

Total miles he needs to cover to meet his goal=33 miles

Number of miles already covered=24 miles

replacing;

Number of miles left after 8 days=(33-24)=9 miles

Leo will have 9 miles left to meet his goal

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.