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- The velocity of a ball thrown upward into the air is given by , where is time measured in seconds and velocity is in feet per second. Calculate the displacement (change in position) of the ball between t=1 and t=4Letf(x) = 6 + 5x². Findƒ (1) and: f(1) ƒ(6) Round your answers to three decimal places. (+) = i 6.138 ƒ(1) *ƒ(6)* equal to ƒ(1) ƒ(6)* Are they equal?The function of demand and supply of goodsP = 14 - 2Q and P = 5 + 2Q. When againstgoods are taxed at t = 2 per unit, then calculate: b. Tax burden borne by consumers and producers.
- The height of a hill is given by h(x, y) = 2xy- 3x2- 4y2- 18x+ 28y+12. Here, x is the distance east and y is the distance north of the origin, both measured in meters. A function like this is often used to produce topographic maps. Where is the top of the hill and how high is it?Suppose that f(x) = x² – 5x + 7 has roots a and B. Use symmetric functions to find a + B, aß, a² + B², and a³ + B³.The dosage of a pediatric medication depends on the weight of the child. The function U(k) = 25k + 20 gives the number of units of medication for the weight of the child in kilograms. Compute U(4.2), U(12), and U(15).