Mathematics, 21.01.2021 22:50 whitneynicole1

A small town in Ohio commissioned an actuarial firm to conduct a study that modeled the rate of change of the town's population. The study found that the town's population (measured in thousands of people) can be modeled by the function P(t)= - 1/3t^3 +64t +300 , where tis measured in years.

a. Find the rate of change function P' (t) of the population function.
b. Find P '(1), P(2), P(3) and P' (4). Interpret what the results mean for the town.
c. Find P" (2), and P "(4). Interpret what the results mean for the town's population.

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Answer from: Quest

intensity of the vector is v= √37 ≈ 6.08 units and make angle ∡α ≈ 9.46° with east direction

step-by-step explanation:

required vector is consists of the two componentsvx= 2+4=6 units and vy= 1 unit and vx ⊥ vywe will use pythagorian theorem to find intensity of the vector vv∧2 = vx∧2 + vy∧2 => v = √vx∧2 + vy∧2 = √6∧2 + 1∧2 = √36+1 = √37 ≈ 6.08 unitsthe angle ∡α between vector and east direction we wil find with tanαtanα = 1/6 => α = arc tanα = arc 1/6 => α ≈ 9.46°

hope this

#10 can anyone solve this for will give !

Answer from: Quest

the required function is $y=-x+4$ .

step-by-step explanation:

from the given table it is noticed that the graph passing through (-3,7), (0,4), (3,1) and (8,-4).

it is a linear function because the value of y is decrease by one as the value of x increase by 1.

the slope of the function is

$m=\frac{y_2-y_1}{x_2-x_1}=\frac{4-7}{)}=\frac{-3}{3}=-1$

the slope of the function is -1 and the y-intercept is 4.

the slope intercept form is

$y=mx+b$

where, m is slope and b is y-intercept.

$y=-1x+4$

$y=-x+4$

therefore the required function is $y=-x+4$ . the graph of this function is shown below.

Answer from: Quest

The question is kind of confusing. if it's asking how many variations of answers can you give. then do 4^5 for your answer.this would be something like the first question could be a and the 2nd c or first b next c etc. if you can, ask the teacher for a better confirmation of what it's asking. if i'm assuming correctly what it's asking, it's 625 different variations.

Answer from: Quest

answer: the prove is mentioned below.

step-by-step explanation:

an isometric rigid transformation is a transformation of the plane that preserves lengths and angles.

that is, the pre-image and the image under a rigid transformation will be congruent.

here, given: cb ║ ed and cb ≅ ed

prove that: δ cbf ≅ δ edf

since, cb ║ ed

therefore, by the alternative interior angle theorem,

∠fcb ≅ ∠fed

∠fbc ≅ ∠ fde

and, cb ≅ ed ( given)

therefore, the angles and sides are persevered after transformation.

thus, by the definition of isometric rigid transformation,

δ cbf ≅ δ edf

Given: ̅cb̅̅̅ ∥ ̅ed̅̅̅; ̅cb̅̅̅ ≅ ̅ed̅̅̅ prove: cbf ≅ edf using isometric (rigid) transformation

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A small town in Ohio commissioned an actuarial firm to conduct a study that modeled the rate of chan...

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