Recall that the player’s height above the floor is given by h = Vt − 16t2, where h is in feet and t is in seconds, and V is the upward velocity at takeoff. Plug t = V/32 into the function to verify that the maximum height reached is V2/64.

Q: The bacteria in a culture can be assumed to multiply at a rate that at any given moment is…

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Q: is Y=2/X +1 a function?

A: We have given equation  Y = 2/X +1  An equation is a function if for every value of x there is a…

Q: a) The tallest building in the world is located in Dubai and is the Burj Khalifa which measures 828…

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Q: Estimate √3.9 using a linear approximation at a=4.

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Q: A conical tank (diameter= 4m, height=5 m) is initially full of water. At time zero, water discharges…

A: Given  Diameter of the tank = 4m Height of the tank = 5m

Q: Assume that a runner runs a 100 meter sprint in 12.3 seconds. He accelerates steadily in the first…

A: The runner accelerates steadily in the first 25 meters. Let the acceleration be a m/s2 and suppose…

Q: Charlie is flying a kite with Lucy. The wind is blowing west at aconstant 8.8 ft/sec, while the kite…

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Q: The rock hits the surface after 5.38 seconds. With what velocity will the rock hit the surface?

A: Given H=15t-2.79t2 Velocity can be obtained with  differentiation of height. V=dH/dt

Q: Assume S=0.6Y+19 describes the projected relationship between  S⁢ , sales of a company (in millions…

A: Given that the model S=0.6Y+19 describes the projected relationship between S , sales of a company…

Q: A rock is thrown straight up in the air from an initial height h., in metres, with initial velocity…

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Q: A ball is thrown from the roof of a building that is 50 meters tall. The initial velocity of the…

A: To find the maximum height that the ball reaches. First, we need to find the projectile equation of…

Q: Recall that the player’s height above the floor is given by h = Vt − 16t2, where h is in feet and t…

A: First differentiate the function, h = Vt − 16t2 with respect to t to compute dhdt.  Solve the…

Q: Suppose that the revenue (in dollars) from the sale of a product is given by R = 60x + 0.9x? –…

A: Since you have asked multiple questions in a single request, we would be answering only the first…

Q: A boy 1.6 metres tall is walking away from a lamp post 10 metres tall. if the boy is walking at the…

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Q: If a bullet from a pistol is fired straight up from the ground, its height t seconds after it is…

A: the bullet from a pistol is fired straight up from the ground, its height t seconds after it is…

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.