The members of a marching band form a rectangle with initial
length L0=40 feet and initial width W0=20 feet. As their song
begins, they begin marching so that the length of the rectangle
increases at a rate of 3 feet per second, and the width of the
rectangle increases at a rate of 2 feet/second.
(a) Write an equation for area A of the rectangle of the marching
band in terms of length L and width W.
(b) Use implicit differentiation to find an expression for da/dt in
terms of W, L, dw/dt, and dl/dt.
(c) Write expressions for L(t) and W(t) in feet, in terms of time t
in seconds.
(d) How fast is the area of the rectangle increasing t=5 seconds
after their song begins? Give units.
(a) evaluated expression for
area of rectangle
(b) evaluated the expression for dA/dt in terms of W, L, dW/dt , dL/dt
(c) evaluated expression for L(t) and W(t)
(d) calculated the rate of change of Area at t=5 sec
which is 200 feet²/sec
The members of a marching band form a rectangle with initial length L0=40 feet and initial...
I) (a) Find the derivative: ( +1)(3x2 -88) (b) Use implicit differentiation to determine d from the Cobb-Douglass production equation 90x1/3y2/5432 (a) The width of a rectangle is increasing at a rate of 10 inches per minute, and the length is decreasing at a rate of 3 inches per minute. Determine the rate of change in area when the rectangle has a width of wdt hes and leng of 2o iches, is the ainreasing o decreasing? [Hint: Let w() and...
A loop of wire in the shape of a rectangle of width w and length L and a long, straight wire carrying a current I lie on a tabletop as shown in the figure below.(a) Determine the magnetic flux through the loop due to the current I. (Use any variable stated above along with the following as necessary: μ₀ . )ΦB=(b) Suppose the current is changing with time according to I=a+b t, where a and b are constants. Determine the...
Problem 4: The length and width of a basketball court is determined and found to be 94.07 feet by 50.01 feet. Each measurement has an uncertainty of 0.88 feet. Find the area, Am. On a separate piece of paper, write the equation for area: A = l × w . Find the value of A, ΔA, and Am. Problem 5: A bowling ball was timed with a stopwatch and the travel time was estimated at 2.40 seconds with an uncertainty...
please show work
7. Find the vertex of the following function 10. A high school baseball player throws a ball straight up into the air for his math class. The height h at a certain time t can be modeled by the following function At what time will the ball hit the ground? B) (-2.-17) k(t)-16t +96t +6 o) (2,-17) a)t--0.061 seconds b) 4.512 seconds clt-5323 seconds d)?-6.062 seconds B. Find the vertex of the folowing graph: (1 -4) 9....