Chapter 7.1, Problem 25E

Cacaulte the derivative

d 3) (2a)* = (Derivative of an exponential %3D function)

The windchill index announced during the winter by the weather bureau measures how cold it "feels" for a given temperature t (in degrees Fahrenheit) and wind speed w (in miles per hour). It is calculated by the formula C(t, w) = 35.74 + 0.6215t - 35.75w 0.16 + 0.4275tw0.16 + '.+ If the temperature is 31 degrees and the wind speed is 10 miles per hour, estimate the change in the windchill temperature if the wind speed increases by 4 miles per hour and the temperature drops by 5 degrees. (Round your answer to two decimal places.)

Instruction: Analyze each situation and show your complete solution. Highlight or box your answers in your computation.

Boyle's Law expresses the relationship between the pressure, P, and the volume, V, of a gas under constant temperature. PVC where C is a constant Suppose the pressure and volume change with respect to time. (a) Write the equation that relates how fast the the pressure and volume are changing with respect to time. Use Leibniz notation for any derivatives, in addition to upper case letters for P and V. (b) Suppose the pressure is increasing by 20 atmospheres per minute when the volume is 600 cubic centimeters and the pressure is 150 atmospheres. How fast is the volume changing? dv dt -units-

三I Homework: Find the derivative of the function. x2 y = x ³ _ +32x +3 40 y' =

Find the normalizing constant c so that ce-x14 dx = 1. -0- c =

(경) 8 -1 x, X(0) = -2 %3D X' = 6. X(t) = %3D Need Help? Read It Watch It

A mouse on a tightrope is moving such that its position relative to some fixed point is given by x(t)=−2/3t^3+9t^2−36t+18 where x is measured in centimeters and tt is measured in seconds.Write an expression for the mouse's velocity. v(t)=v(t)=  What is the mouse's velocity when t=4t=4? cm/s Write an expression for the mouse's acceleration. a(t)=a(t)=   What is the mouse's acceleration when t=4t=4? cm/s2