Abbey always gets zits on her chin and she can't figure out the best method to get rid of them. She decides to test several products to see which clears her face up fastest washing with soap and water, washing with an acne face Wash from the pharmacy, and washing her face with organie oils For one week she just washes her face with water. The next wock she washes every day with soap and water. The following wock she uses the acne wash, and the last week she uses the organic oils Each week she records the number of zits she has on her chin at the end of the day. Independent Variable
Dependent Variable
Hypothesis
control group
Experimental group
Constants
possible threats to accuracy of results?
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correct answer:

b.(19,-2)

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.

irrational, cannot

the answer is c: divide the arc's degree measure by 360°, then multiply by the circumference of the circle.