


A rectangular box of height h metres with a square base with side x(t) metres, where initial leng...
I'm not sure about b,c,d. Is there anyone can help with this
question?
A rectangular box of height h metres with a square base with side x(t) metres, where initial length of the side of the base is x(0) 2 metres. The box is initially filled with water to a height of h(0)4 metres. The volume of water is given by Vt)(t) Over time, the sides of the base are decreasing ata ateof0.05 m/s and the water is leaking from...
I only want the answer for No 2
Note: The time it takes to get a two-liter
bottle empty is given in the picture
I only want the answer for No 2
Let h(t) and V(t) be the height and volume of water in a tank at time t. If water drains through a hole with area a at the bottom of the tank, then Torricelli's Law says that dV dt where g is the acceleration due to gravity. So...
5. A pebble falls from the top of a cliff that is 180 m high. The pebble's height above the ground is modelled by h(t) -5t-5t+180 where h is the height in metres at t seconds since the pebble started to fall. a. Find the average rate of change between 1 s and 4 s. b. Find h(3) c. Find the instantaneous rate of change of height at 3 s. d. Explain the meaning of each value calculated in parts...
the height , h(t) in metres of the trajectory of a football is given by h(t) = 2+28t-4.9t^2, where t is the time in flight, in seconds . Determine the maximum height of thefootball and the time wehn the height is reached
A box with a square base and open top must have a volume of 2048 c m 3 . We wish to find the dimensions of the box that minimize the amount of material used. The length of the base is x and the height is h. Since the base is a square, the surface area of just the base would be: Area = The surface area of just one side would be: Area = The surface area of all...
12. During the first 30seconds of its flight, a test rocket's height in metres above its launching point is given by h(t) = 452 – where t is the elapsed time in seconds. (a) Find an equation for the velocity of the rocket and use this to find how long it will take to reach 600m/s. (b) What height will the rocket be at this time? 13. Draw the graphs of the functions in question 12 in the same coordinate...
1. An airplane if flying horizontally at a constant height of 6 km above a fixed observation point. At a certain moment the angle of elevation θ is 30° and decreasing and the speed of the plane is 4 km/h. (a) How fast is 0 decreasing at this moment? (b) How fast is the distance between the plane and the observation point is changing at this moment? 2. Trajectory of a particle is described by parametrical equations as t,y P,...
The height, h, in metres, above the ground of a rider on a Ferris wheel can be modelled by the equation:h= 10 sin ((pi/15 t) - 7.5) + 12 where t is the time, in seconds.At t=0, the rider is at the lowest point. Determine the first two times that the rider is 20 m above the ground, to the nearest hundredth of a second.
Problem 4 4.50 A conical flask contains water to height H=36.8 mm, where the flask diameter is D = 29.4 mm. Water drains out through a smoothly rounded hole of diameter d= 7.35 mm at the apex of the cone. The flow speed at the exit is approxi- mately V = V2gy, where y is the height of the liquid free surface above the hole. A stream of water flows into the top of the flask at constant volume flow...
The length l, width w, and height h of a box change with time. At a certain instant the dimensions are l = 5 m and w = h = 2 m, and l and w are increasing at arate of 3 m/s while h is decreasing at a rate of 4 m/s. At that instant find the rates at which the following quantities are changing.Find Volume.__________ m^3/sFind Surface Area.__________m^2/sFind length of the diagnol.(find answer to two decimal places)__________m/s