A population grows from an initial size of 10 people to an amount P(t), given by P(t)=10(3+0.5t+t^3) where t is measured in years from 1996. Find the acceleration in the population t years from 1996.a)60t people per year^2
b)30t people per year^2
c)600t people per year
d)36t people per year^2

Answers

Answer 1

Answer:

The acceleration in the population t years from 1996 is 60t people per year^2.

What is a Function?

A function assigns the value of each element of one set to the other specific element of another set.

It is given that a population grows from an initial size of 10 people to an amount P(t), given by P(t)=10(3+0.5t+t³) where t is measured in years from 1996.

Now, in order to find the acceleration in the population t years from 1996, we need to find the second derivative of the populationfunction, therefore,

$P(t)=10(3+0.5t+t³)\n\nP'(t)=10(0.5+3t^2)\n\nP''(t)=10(6t)\n\nP''(t)=60t$

Hence, the acceleration in the population t years from 1996 is 60t people per year^2.

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Answer 2

Answer: Since the required is the acceleration in the population, the second derivative of the equation is needed.
The first derivative has to be determined first.
dP(t)/dt = 10(0.5+3t^2)
Next, the second derivative can be determined using the first derivative:
d2P(t) = 10(6t) = 60t
Since it's acceleration, the unit is per year^2

THE ANSWER IS a) 60t people per year^2

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How to solve this problem

Answers

Since they are congruent, all will be the same value.

c = 3
∠d = 38° (asked for the angle)
g = 5

If someone eats 3/4 of granola bars per week, what fraction of a box do they eat in per day ? how many boxes do they eat in a year ?

Answers

Answer:

in a day (3/4)÷7=3/28

in a year (3/28)×365=39.107

How many real number solutions does the equation have0=2x^2-20x+50
a. one solution
b. two solutions
c. no solution
d. infinite solutions

Answers

$D =b^2-4ac = 20^2-4*2*50 = 0$
a. one solution

The product of (3+2i) and a complex number is (17+7i)

What is the complex number.

Answers

The question is asking us to find the complex number such that: ( 3 + 2 i ) * x = 17 + 7 i. We know that i^ 2 = - 1. x = ( 17 + 7 i ) / ( 3 + 2 i ) . We have to multiply the numerator and the denominator by ( 3 - 2 i ). Then: x = ( 17 + 7 i ) * ( 3 - 2 i ) / ( 9 - 4 i^2 ) = ( 51 - 34 i + 21 i - 14 i^2 ) / ( 9 + 4 ) = ( 51 + 14 - 13 i ) / 13 = ( 65 - 13 i ) / 13 = 65 / 13 - 13 i / 13 = 5 - i. Answer: The complex number is 5 - i.

Evaluate tan(sin^-1 (-4/5))

Answers

Here, we are required to evaluate tan(sin^-1 (-4/5)).

tan(sin^-1 (-4/5)) = (-4/3)

Sin^-1 (-4/5) = θ

Therefore; ultimately Sin θ = (-4/5)

Since; Sine = opposite / hypothenus

Therefore, adj = √(5²) - (4²)

adj = 3.

However, since tan(sin^-1 (-4/5)) = tan θ

Therefore, tan θ = 4/3

However, since sin θ and tan θ are only negative in the fourth quarter;

Therefore, tan θ = (-4/3)

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$\theta=\sin ^(-1)\left(-(4)/(5) \right )$ is in the fourth quadrant. Hence,

$\tan \theta<0$

From a right triangle (check out the attachment) we get

$\bullet\;\;\cos \theta=(3)/(5)\n\n\n \bullet\;\;\tan \theta=-(4)/(3)\n\n\n\n \therefore~~\boxed{\begin{array}{c} \tan\left(\sin^(-1) \left(-(4)/(5) \right )\right)=-(4)/(3) \end{array}}$

Simplify (10 + 48) ÷ 2 =