Colleen’s parents recently purchased a ranch. The ranch raises horses, cows and sheep. Colleen’s parents want to breed Bernedoodles to help out around the farm. Since she has never raised puppies before, Colleen wants to learn as much about her new puppy as possible. In particular, she wants to know how much a Bernedoodle puppy weighs when it is born. To find out, Colleen decided to track the weight of her first puppy who was born just before they purchased the ranch. She found that her puppy grew steadily by about 73 grams each day, and she assumes that he has been doing so since he was born. Seven days after he was born, the puppy weighed 811 grams.

Your Task: Determine how much the puppy weighed the day he was born using three different representations of the puppy's growth: a graph, an x → y table, and write equations. Then, assuming the puppy will continue to grow at the same rate, determine when the puppy will weigh 3900 grams.

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.

answer:   2 multiplied by x =24

step-by-step explanation:

you can use a^2+ b^2=c^2

46

step-by-step explanation:

given

height = 168 cm

formula

height =2.47*f+54.13

solution

168 = 2.47f + 54.13             subtract 54.13 from both sides

168 - 54.13   = 2.47f             combine

113.87 = 2.47f                     divide by 2.47

113.87 / 2.47 = f                   combine

46.1 = f  

answer: 46 cm