Mathematics, 02.07.2019 14:30 Emiann222

The jogging track at francine’s school is 3/4 mile long. yesterday francine completed two laps on the track. if she ran 1/3 of the distance and walked the remainder of the way, how far did she walk?

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Answer from: Jabari8728

1 mile

Step-by-step explanation:

Given: The jogging track at Francine’s school is $\frac{3}{4}$ $\text{mile}$ long. Yesterday Francine completed two laps on the track. If she ran $\frac{1}{3}$ of the distance and walked the remainder of the way.

To Find: how far did she walk

Solution:

Length of jogging track at Francine’s school $=\frac{3}{4}$ $\text{mile}$

Let the distance covered by running be $=\text{x}$

Let the distance covered by walking be $=\text{y}$

Total number of laps completed by Francine

Total distance covered by Francine $=\text{number of laps}\times\text{distance covered in one lap}$

$2\times\frac{3}{4}$

$\frac{3}{2}\text{mile}$

Now,

distance covered by running $=\frac{1}{3}\text{of total distance}$

$\text{x}=\frac{1}{3}\times\frac{3}{2}$

$\text{x}=\frac{1}{2}$ $\text{mile}$

distance covered by walking $\text{y}$ $=\text{total distance}-\text{distance covered by running}$

$\frac{3}{2}-\text{x}$

$\frac{3}{2}-\frac{1}{2}$

$\text{mile}$

Hence, Francine walked for $\text{mile}$

Answer from: Quest

Just a second zzz

Answer from: Quest

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.

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The jogging track at francine’s school is 3/4 mile long. yesterday francine completed two laps on th...