In a certain city, the temperature (in F^{\circ}) at t hours aft

mronjo7n 2021-11-16 Answered
In a certain city, the temperature (in F) at t hours after 9 AM is modeled by the function T(t)=50+14sin(πt12). Find the average temperature during the period from 9 AM to 9 PM.
You can still ask an expert for help

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

Solve your problem for the price of one coffee

  • Available 24/7
  • Math expert for every subject
  • Pay only if we can solve it
Ask Question

Expert Answer

George Blue
Answered 2021-11-17 Author has 18 answers
Step 1
The temperature function is given as
T(t)=50+14sin(πt12)F
t is time in hours
The analysis is started at 9 AM so lete a that instant t=0
At 9 PM, t=12
Step 2
The average value of a function is given by
fav=1baabf(x)dx
Tav=1120012[50+14sin(πt12)]dt
=112[50t+14(cosπt12π12)]012
=112[15(120)14(12π){(cosπ×1212)cos0}]
=1514π[cosπcos0]
=1528π
Tav=6.0873F
Not exactly what you’re looking for?
Ask My Question

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

You might be interested in

asked 2021-09-08
Lynbrook West , an apartment complex , has 100 two-bedroom units. The montly profit (in dollars) realized from renting out x apartments is given by the following function.
P(x)=12x2+2136x41000
To maximize the monthly rental profit , how many units should be rented out?
What is the maximum monthly profit realizable?
asked 2021-02-05
Use polar coordinates to find the limit. [Hint: Let x=rcosandy=rsin , and note that (x, y) (0, 0) implies r 0.] lim(x,y)(0,0)x2y2x2+y2
asked 2021-09-05

Let f(t)=t+i where π<t<π and has period 2π. Why is it impossible to express the Fourier series of f(t) in real form?
A. Because f(t) is a complex function with Re(f(x))<0
B. Because f(t) is a complex function with Im(f(x))0
C. Because f(t) is a complex function with Im(f(x))=0
D. Because f(t) is a complex function with Re(f(x))>0

asked 2021-01-15
Evaluate the line integral by the two following methods. y) dx + (x+y)dy C os counerclockwise around the circle with center the origin and radius 3(a) directly (b) using Green's Theorem.
asked 2021-09-05

Complex numbers can serve as entries in a matrix just as well as real numbers.Compute the expressions in Problems 51-53 , where
A=[1+i2i223i] and B=[1i2i1+i]
51.A+2B
52.AB
53. BA

asked 2021-01-31
Use the Divergence Theorem to calculate the surface integral SF·dS, that is, calculate the flux of F across S.
F(x,y,z)=(x3+y3)i+(y3+z3)j+(z3+x3)k, S is the sphere with center the origin and radius 2.
asked 2021-02-25
Evaluate Cx2y2dx+4xy3dy where C is the triangle with vertices(0,0),(1,3), and (0,3).
(a)Use the Greens