An object starts from rest, and its acceleration as a function of time is given by a(t)= 2t, measured in m/sec. Find the distance travelled by the object in the first 8 seconds.

Someone answer asap for ! a ball is rolled down a ramp. the height, f(x), in meters, of the ball x seconds after it is released is modeled by the function f(x) = x²- 10x + 25 for all values of x from 0 to 5. which statement about the ball is true? a. the maximum height of the ball is 5 meters b. the height of the ball increases from 0 to 5 meters above the ground. c. the ball has traveled 5 meters when it reaches the bottom of the ramp. d. the ball has been traveling for 5 seconds when it reaches the bottom of the ramp

Find the volume of the solid whose base is the region bounded by f(x), g(x) and the x-axis on the interval [0, 1], and whose cross-sections perpendicular to the y-axis are squares. your work must show the integral, but you may use your calculator to evaluate it. give 3 decimal places for your answe

Acaterer knows he will need 60, 50, 80, 40 and 50 dinner napkins on five successive evenings. he can purchase new napkins initially at 25 cents each, after which he can have dirty napkins laundered by a fast one-day laundry service (i. e., dirty napkins given at the end of the day will be ready for use the following day) at 15 cents each, or by a slow two-day service at 8 cents each or both. the caterer wants to know how many napkins he should purchase initially and how many dirty napkins should be laundered by fast and slow service on each of the days in order to minimize his total costs. formulate the caterer’s problem as a linear program as follows (you must state any assumptions you make): a. define all variables clearly. how many are there? b. write out the constraints that must be satisfied, briefly explaining each. (do not simplify.) write out the objective function to be minimized. (do not simplify.)