Tutor profile: Rafay S.

Thomas has several dimes and nickels. He has a total of 23 coins. The total value of the coins is $1.55. Write the equations representing the total number of coins and their values in terms of nickels and dimes.

Let x be the number of nickels Let y be the number of dimes x + y = 23 0.05x + 0.10y = 1.55

Find the first derivative of the following function. f(x) = 2x^3 + 3x^2 + 5

f'(x) = 6x^2 + 6x

Captain American is fighting Thanos on top of Burj Khalifa. Thanos unfortunately punches Captain America and sends him tumbling over the building. Captain America's fall from the top of the building can be modelled by the function h = -9.8t^2 + 828, where h represents Captain America's height in metres during his fall and t represents the number of seconds since he started falling. Iron Man is fighting on the ground and sees that Captain is falling so he quickly flies to save him. Iron Man's flight can be modelled by h = 35t - 2. Will Iron Man be able to catch Captain America before he hits the ground? If yes, then at what height will they be when Iron Man catches Captain America?

This is a system of 2 equations. 1. h = -9.8t^2 + 828 2. h = 36t - 71 Iron Man will be able to catch Captain America when their graphs intersect. To find if the graphs intersect: Substitute, equation 2 into equation 1 36t - 71 = -9.8t^2 + 828 Rearrange and collect like terms 0 = -9.8t^2 -36t + 899 Use quadratic formula to solve for t t = ( -(-36) +/- sqrt( (-36)^2 - 4*(-9.8)*(899) ) ) / 2*(-9.8) t = -11.59 and t = 7.91 Since time cannot be negative, we will take t = 7.91 seconds. Iron Man will catch Captain American 7.91 seconds after his fall. To figure out the height when Iron Man will catch Captain America, we plug in t = 7.91 into either equation 1 or equation 2. h = 36(7.91) -71 h = 213.76 They will be 213.76 m from the ground