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- Find the constant of proportionality. y is directly proportional to x. If x=30, then y=15.a tank initialy holds 80 gallon of a brine solution containing 1/8 lb of salt per gallon. at t=0, another brine solution containing 1 lb of salt per gallon is poured into the tank at the rate of 4 gallon/min,while the well-stirred mixture leaves the tank at the rate of 8 gallon/min. find the amount of salt in the tank when the tank contains exactly 40 gallon of solutionThe velocity of a partical moving along x axis is defined by v= kx3-4x2+6x where v is in miles/sec , x is in miles and k is constant. If k = 1 compute the value of acceleration when x = 2 miles?
- A projectile is launched from ground level with initial velocity of v0 feet per second. Neglecting air resistance, its height in feet t seconds after launch is given by s=-16t^2*v0t. Find the time that the projectile will reach a height of 192 feet and return to the ground when v0=112 feet per secondA radioactive element decays at a rate of 5% annually. There are 40 grams of the substance present. Find an equation that models the amount X of the substance present at any time t.A projectile is launched from ground level with an initial velocity of v0 feet per second. Neglecting air resistance, its height in feet t seconds after launching is given by s=-16t^2+v0t. Find the time(s) that the projectile will (a) reach a height of 96 ft and (b) return to the ground when v0=112 feet per second.
- Substituting t=0 for the inital equation qoul get <-1,02>, and again with the derivative foem, which would get <0,0,0>. Is that right?An object is propelled straight up from ground level with an initial velocity of 80 feet per second. Its height at time t is modeled by s(t) = -16t2 + 80t, where the height, s(t), is measured in feet and the time, t, is measured in seconds. In which time interval will the object be more than 64 feet above the ground?How did you apply the concept of maxima/minima in answering the problem? Angelo, who is in a rowboat 2 kilometers from a straight shoreline wishes to go back to his house, which is on the shoreline and 6 kilometers from the point on the shoreline nearest Angelo. If he can row at 6 kph and run at 10 kph, how should he proceed to get to his house in the least amount of time?
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