Calculus Please Check my answer

The rate at which water flows into a tank, in gallons per hour, is given by a differentiable function R of time t. The table below gives the rate as measured at various times in an 8-hour time period.

t---------0-----2------3-------7----8
(hours)

R(t)--1.95---2.5---2.8----4.00--4.26
(gallons per
hour)

Use a trapezoidal sum with the four sub-intervals indicated by the data in the table to estimate definite integral 0 to 8 of R(t) dt. Using correct units, explain the meaning of your answer in terms of water flow.

(2) (2.5+1.95)/2)+(1)(2.8+2.5)/2)+(4)(4+2.8)...
Simplified gives a water flow of 24.83 gallons over eight hours.

Is there some time t, 0 < t < 8, for which we are guaranteed that R' (t) = 0? Justify your answer.
No and this is shown by a graph of the function.

The rate of water flow R(t) can be estimated by W(t) = ln( t^2 + 7 ). Use W(t) to approximate the average rate of water flow during the 8-hour time period. Indicate units of measure.
[W(8)-W(0)]/(8-0) =(4.26268-1.94591)/8 = 0.2986 gallons/hour

f is a continuous function with a domain [−3, 9] such that
f(x) =
3 for -3 <= x < 0
-x+3 for 0 <= x <= 6
-3 for 6 < x <= 9

n what interval is g increasing? Justify your answer.
when f(x)>0 due to the fundamental theorem

For 0 ≤ x ≤ 6, express g(x) in terms of x. Do not include +C in your final answer.
6 + (-x^2/2 + 3x)+3

  1. 👍
  2. 👎
  3. 👁

Respond to this Question

First Name

Your Response

Similar Questions

  1. math

    A tank contains 50 gallons of a solution composed of 90% water and 10% alcohol. A second solution containing 50% water and 50% alcohol is added to the tank at rate of 4 gallons per minute. As the second solution is being added,

  2. math

    A large mixing tank currently contains 100 gallons of water into which 6 pounds of sugar have been mixed. A tap will open pouring 20 gallons per minute of water into the tank at the same time sugar is poured into the tank at a

  3. calculus

    A conical water tank with vertex down has a radius of 12 feet at the top and is 23 feet high. If water flows into the tank at a rate of 20 {\rm ft}^3{\rm /min}, how fast is the depth of the water increasing when the water is 17

  4. Calculus

    Water flows from the bottom of a storage tank at a rate of r(t) = 400 − 8t liters per minute, where 0 ≤ t ≤ 50. Find the amount of water that flows from the tank during the first 45 minutes.

  1. calculus

    A conical water tank with vertex down has a radius of 12 feet at the top and is 28 feet high. If water flows into the tank at a rate of 30 ft^3/min, how fast is the depth of the water increasing when the water is 16 feet deep?

  2. Math

    A conical water tank with vertex down has a radius of 10 feet at the top and is 22 feet high. If water flows into the tank at a rate of 30 {\rm ft}^3{\rm /min}, how fast is the depth of the water increasing when the water is 14

  3. math - calc

    A conical water tank with vertex down has a radius of 12 feet at the top and is 26 feet high. If water flows into the tank at a rate of 30 {\rm ft}^3{\rm /min}, how fast is the depth of the water increasing when the water is 12

  4. AP Calc. AB

    If a cylindrical tank holds 100,000 gallons of water, which can be drained from the bottom of the tank in an hour, then Torricelli's Law gives the volume of water remaining in the tank after t minutes as V(t)=100,000(1-(t/50))^2,

  1. Calculus

    If a tank holds 5000 gallons of water, which drains from the bottom of the tank in 40 minutes, then Torricelli’s Law gives the volume V of water remaining in the tank after t minutes as 12 V 􏰘 5000(1 􏰜 40 t) 0 􏰡 t 􏰡

  2. math

    A conical water tank with vertex down has a radius of 13 feet at the top and is 28 feet high. If water flows into the tank at a rate of 10 {\rm ft}^3{\rm /min}, how fast is the depth of the water increasing when the water is 17

  3. Math

    A rectangular tank 40cm wide by 50 cm long by 30 cm high is filled up with water up to 2/3 of its height .water flows from a tap into the tank at a rate of 0.5 liter per minute. Find the amount of water in the tank after 30

  4. CALC

    A 200-gallon tank is currently half full of water that contains 50 pounds of salt. A solution containing 1 pounds of salt per gallon enters the tank at a rate of 6 gallons per minute, and the well-stirred mixture is withdrawn from

You can view more similar questions or ask a new question.