9 questions to be answered I want the answers separately and the work
A box with a square base and open top must have a volume of 87808 cm . We wish to find the dimensions of the box that minimize the amount of material used. First, find a formula for the surface area of the box in terms of only x, the length of one side of the square base. [Hint: use the volume formula to express the height of the box in terms of x.] Simplify your formula as much as possible. A(x) = Next, find the derivative, A' (a) A' (x) = Now, calculate when the derivative equals zero, that is, when A'(x) = 0. [Hint: multiply both sides by a 2 . ] A' (x) = 0when x = We next have to make sure that this value of a gives a minimum value for the curfa the second derivative test. Find A"(x) A" (z) = A stone is dropped (initial velocity is 0) from the edge of a roof (this would be the initial height), an hits the ground with a velocity of -120 feet per second. How high (to the nearest foot) is the roof? Evaluate A"(x) at the -value you gave above. Note: the acceleration of an object due to earth's gravity is 32 - sec2 NOTE: Since your last answer is positive, this means th that value, so the zero of A' (x) must indicate A microwaveable cup-of-soup package needs to be constructed in the shape of cylinder to hold 500 cubic centimeters of soup. The sides and bottom of the container will be made of styrofoam costing $ 0.03 (3 cents) per square centimeter. The top will be made of glued paper, costingestion 12 per square centimeter. Find the dimensions for the package that will m Helpful information: What point with strictly positive z-coordinate that lies on the parabola y = 3x - 7 is closest to the h : height of cylinder, r : radius of cylinder point P(0, 3)? Enter an ordered pair of exact numbers, with all fractions simplified and denominators rationalized. Volume of a cylinder: V = mr h Area of the sides: A = 2rrh Area of the top/bottom: A = 172 To minimize the cost of the package: (round all answers to 2 decimal places as needed) Evaluate the integral 19 2 210 + 5 Radius: cm 16 2 4 ) da Height: cm Minimum cost: cents A small house was built on an island off a perfectly straight shoreline. The point B on the shoreline that is closest to the island is exactly 7 miles from the island. Eight miles east of B is the closest source of fresh water to the island. A pipeline is to be built from the island to the source of fresh water by laying pipe underwater in a straight line from the island to a point Q on the shoreline between B and the water source, and then laying pipe on land along the shoreline from Q to the source. It costs 7000 dollars per mile to lay the pipe under the water and 4375 dollars per mile to lay pipe on land. How far east of B should Q be located in order to minimize the total construction costs? A ball is shot from the ground straight up into the air with initial velocity of 50 ft/sec. Assuming the air resistance can be ignored, how high, to the nearest hundredth of a foot, does it go? The acceleration due to gravity is 32 Jit underwater A particle is moving with acceleration a(t) = 18t + 8 ft -2 . Its position at time t = 0 seconds is s(0) = 4 feet, and its velocity at time t = 0 seconds is v(0) = 11 ft/s. What is its position at time underground t = 8 seconds? feet Find a formula for the cost of laying the pipe in terms of z C(z) = A stone is thrown straight up from the edge of a roof, 700 feet above the ground, at a speed of 12 Find the value for a that will minimize the total cost. feet per second. All answers are to the nearest tenth. A. Remembering that the acceleration due to gravity is -32J, how high is the stone 2 seconds later? B. At what time does the stone hit the ground? C. What is the velocity of the stone when it hits the ground? ( Please note that the video below has units in *meters* rather than feet, so a = -9.8 in the video.) Question Help: 1 Vidan
