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iren2701 [21]
3 years ago
6

The temperature of water in the Solar steam power system for time 0 equal to or less than t equal to or less than 10, is modeled

by the differentiable function S, where t is measured in hours. Selected values of S(t) are given in the table above and represent the temperature in degrees celsius of the water in the solar steam power system.
(a) use the data in the table to evaluate the definitive integral of S'(t)dt where a=10 and b=0. using correct units interpret the meaning of the definitive integral in the context of this problem.
(b) For 0 less than or equal to t less than or equal to 6, approximate the average temperature of the water in the system using a right Riemann approximation. determine if the approximation is an overestimate or an underestimate. justify your answer.
(c) For 10 less than or equal to t less than or equal to 20 the change in temperature of the water in the system can be modeled by the equation S'(t)=-
\sqrt{2x} ( \frac{ {x}^{2}  - 100}}{x}
using this model determine the total change in the temperature of the system for the given interval. interpret your answer in the context of this problem​

Mathematics
2 answers:
Nana76 [90]3 years ago
7 0

Answer:

did anyone find it?

Step-by-step explanation:

GenaCL600 [577]3 years ago
3 0

Answer:

https://secure-media.collegeboard.org/apc/ap12_calculus_bc_q1.pdf

Step-by-step explanation:

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2 years ago
The general solution to the second-order differential equation y′′+10y=0 is in the form y(x)=c1cosβx+c2sinβx. Find the value of
allsm [11]

Answer:β=√10 or 3.16 (rounded to 2 decimal places)

Step-by-step explanation:

To find the value of β :

  • we will differentiate the y(x) equation twice to get a second order differential equation.
  • We compare our second order differential equation with the Second order differential equation specified in the problem to get the value of β

y(x)=c1cosβx+c2sinβx

we use the derivative of a sum rule to differentiate since we have an addition sign in our equation.

Also when differentiating Cosβx and Sinβx we should note that this involves function of a function. so we will differentiate  βx in each case and multiply with the differential of c1cosx and c2sinx respectively.

lastly the differential of sinx= cosx and for cosx = -sinx.

Knowing all these we can proceed to solving the problem.

y=c1cosβx+c2sinβx

y'= β×c1×-sinβx+β×c2×cosβx  

y'=-c1βsinβx+c2βcosβx

y''=β×-c1β×cosβx + (β×c2β×-sinβx)

y''= -c1β²cosβx -c2β²sinβx

factorize -β²

y''= -β²(c1cosβx +c2sinβx)

y(x)=c1cosβx+c2sinβx

therefore y'' = -β²y

y''+β²y=0

now we compare this with the second order D.E provided in the question

y''+10y=0

this means that β²y=10y

β²=10

B=√10  or 3.16(2 d.p)

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Rina8888 [55]

Answer:

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Step-by-step explanation:

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