Mathematics, 23.07.2019 09:00 bossboybaker

Water is pumped into a tank at a rate modeled be w(t) = 2000e^(-t^2/20) liters per hour for 0 ≤ t ≤ 8, where t is measured in hours. water is removed at a rate modeled by r(t) liters per hour, where r is differentiable and decreasing on 0 ≤ t ≤ 8. selected values of r(t) are shown in the table above. at time t = 0, there are 50,000 liters of water in the tank. (a) estimate r'(2). show the work that leads to your answer. include units of measure. (b) use a left riemann sum with the four subintervals indicated by the table to estimate the total amount of water removed from the tank during the 8 hours. is this an overestimate or underestimate of the total amount of water removed? give a reason for your answer. (c) use your answer from part (b) to find an estimate of the total amount of water in the tank, to the nearest liter, at the end of 8 hours. (d) for 0 ≤ t ≤ 8, is there is a time t when the rate at which water is pumped into the tank the same as the rate at which water is removed from the tank? explain why or why not.

Answers: 1

Show answers

Answers

(a) $\displaystyle R'(2) \approx \frac{R(3) - R(1)}{3-1} = \frac{950 - 1190}{2} = -120\text{ liters/hr}^2$

(b) The integral $\int_0^8 R(t)\, dt$ gives the total amount of water removed.

$\displaystyle\int_0^8 R(t)\, dt \approx (1-0)R(0) + (3-1)R(1) + (6-3)R(3) + (8-6)R(6) \\ \\
= 1(1340) + 2(1190) + 3(950) + 2(740) \\ \\ 
= 8040 \text{ liters}$

This is an overestimate since we are using a left Riemann sum on a decreasing function R.

(c) The integral $\int_0^8 W(t)\, dt$ gives the total amount of water added at the end of 8 hours.

$\text{Total} = \text{initial} + \text{added} + \text{removed} \\ \\ \approx 50000 + \int_0^8 W(t)\, dt + 8040 \\ \\
= 50000 + 7836.19532 + 8040 \\ \\
\approx 49786\text{ liters}$

(d) If we have the equation W(t) = R(t)

, then

.
Let

. Then

is continuous as it is a difference of two continuous functions (R(t) being differentiable implies continuity).

We have $f(0) = W(0) - R(0) \ \textgreater \ 0,\ f(8) = W(8) - R(8) \ \textless \ 0$ .

Therefore, Intermediate Value Theorem says that there is a time $t\in(0,8)$ for which $f(t) = 0 \iff W(t) - R(t) = 0 \iff W(t) = R(t)$ . At this value of

, the rate of water being pumped into the tank will be equal to the rate of water removed.

Answer from: Quest

step-by-step explanation:

5×5×5+2(8)÷2(2)+3(3)

15+16÷4+9

31÷13

do 31÷13 and u will get ur answer

Answer from: Quest

step-by-step explanation: the declaration of the rights of man and of the citizen (french: déclaration des droits de l'homme et du citoyen de 1789), set by france's national constituent assembly in 1789, is a human civil rights document from the french revolution.[1]

the declaration was drafted by the abbé sieyès and the marquis de lafayette, in consultation with thomas jefferson.[2] influenced by the doctrine of "natural right", the rights of man are held to be universal: valid at all times and in every place, pertaining to human nature itself. it became the basis for a nation of free individuals protected equally by the law. it is included in the beginning of the constitutions of both the fourth french republic (1946) and fifth republic (1958) and is still current. inspired by the enlightenment philosophers, the declaration was a core statement of the values of the french revolution and had a major impact on the development of freedom and democracy in europe and worldwide.[3]

the 1789 declaration, together with the 1215 magna carta, the 1689 english bill of rights (1689), the 1776 united states declaration of independence, and the 1789 united states bill of rights, inspired in large part the 1948 united nations universal declaration of human rights

Another question on Mathematics

Mathematics, 21.06.2019 14:30

Each morning papa notes the birds feeding on his bird feeder. so far this month he has see. 59 blue jays, 68 black crows, 12 red robin's and 1 cardinal. what is the probability of a blue jay being the next bird papa sees

Answers: 3

Answer

Mathematics, 21.06.2019 14:40

Multiplying an even number of negative numbers gives an answer that is choose from:

Answers: 3

Answer

Mathematics, 21.06.2019 17:20

Solve -2(4y + 6) = 52. 5 -5 8 -8 and !

Answers: 1

Answer

Mathematics, 21.06.2019 18:30

If, while training for a marathon, you ran 60 miles in 2/3 months, how many miles did you run each month? (assume you ran the same amount each month) write your answer as a whole number, proper fraction, or mixed number in simplest form. you ran __ miles each month.

Answers: 1

Answer

You know the right answer?

Water is pumped into a tank at a rate modeled be w(t) = 2000e^(-t^2/20) liters per hour for 0 ≤ t ≤...

Questions