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Q: = }(y? + 2)³/2 for 0 < y < 4.
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Find the slope of the tangent to the curve
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- Solve these prism and cylinder exercises. Where necessary, round the answers to 2 decimal places unless otherwise specified. A solid right cylinder 9.55 centimeters high contains 1910 cubic centimeters of material. Compute the cross-sectional area of the cylinder.Find the length of the segment of the curve y=(1/2) cosh 2x from x= 0 to x= ln(5^0.5). Simplify your answerFind dy/dx and d2 y/dx2 . For which values of t is the curve concave upward? 13. x = et , y = te-t
- A wire has the shape of the curve ?=7?3/2y=7x3/2. Find the length of the wire between ?=0x=0 and ?=1x=1. Give your answer correct to 2 decimal places.Find the distance traveled by a particle with position (x,y) as t varies in the given time interval? x=3sin^2(t) y=3cos^2(t) 0<_t<_2pi What is the length of the curve?Sand falls from an overhead bin and accumulates in a conical pile with a radius that is always four times its height. Suppose the height of the pile increases at a rate of 3cm/s when the pile is 17 cm high. At what rate is the sand leaving the bin at that instant? Let V and h be the volume and height of the cone, respectively. Write an equation that relates V and h and does not include the radius of the cone. Differentiate both sides of the equation with respect to t. (dV/dt)= The sand is leaving the bin at a rate of ?
- Consider the accelertation function of a particle a(t)= -cost + 2e^t measured in meters per second^2. Find the position function given that the initial velocity is 5 m/sec and the initial position is 2 m.Suppose the elevation z above a point (x, y) in a horizontal xy- plane at sea level is z = 5cos (0.01(x? + y²)) meters. The positive x-axis points east, and the positive y-axis point north. A climber is at the point (6, 8, 2.70). If the climber uses a compass reading to walk southwest, will he ascend or descend? At what rate? Give your answer rounded to the nearest hundredth, and explain what the units are.The inductance L (in microhenrys) of a straight nonmagnetic wire in free space is L = 0.00021(ln 2h/ r − 0.75) where h is the length of the wire in millimeters and r is the radius of a circular cross section. Approximate L when r = 2 ± 1/16 millimeters and h = 100 ± 1/100 millimeters.
- A farmer wants to repaint a thin, cylindrical water tank on their property. He only needs to paint the outer surface, not the top or the bottom of the cylinder. The tank has a height of 120 centimeters.and the base radius of the tank is 60 mm. Using linear approximations, estimate the volume of paint needed to add a layer 0.5mm thick to the curved outer surface.The volume of a cylinder can be calculated by V = pi(r^2)hA particle is moving along a straight line with velocity v(t) = t2 - 2t. Its distance from the starting point after 3 seconds is 8 cm. Find s(t), the distance of the particle from the starting point after t seconds.Water is flowing into a conical tank at a constant rate of 3 cubic meters per second. The cone has radius and height 5 meters and 4 meters respectively. Given that ℎ(?) is the height of the water above the bottom of the cone at time ?, find ?2ℎ⁄??2 when the tank is filled to a height of 2 meters