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The sequence an is defined as follows: a0 = 9, an+1 = 3(an)^4 +4(an)^3 for n > 0. Show that a10 contains more than 1000 nines in decimal notation.
the function w(d)=0.112d approximates the amount, in centimeter,s, of water that results from d cm of snow melting. Find the amount of water that results from snow melting from depthsof 10cm, 38cm, and 57cm.
What is the maximum height attained by the projectile? Show some work.
Use polar coordinates to find lim(x,y)->(0,0) [(x)(y^2)]/[(x^2)+(y^2)] note that (x,y)->(0,0) is replaced with r->0^+. explain why this is a valid replacement.
The force needed to keep a car from skidding on a curve varies jointly as the weight of the car and the square of the speed and inversely as the radius of the curve.
Use cylindrical coordinates to evaluate the triple integral Ex2+y2dV , where E is the solid bounded by the circular paraboloid z=16-4x2+y2 and the xy -plane.
Probability of Having a Disease when Testing Positive. Suppose that 1% of all people have a particular disease. A test for the disease is 99% accurate. This means that a person who tests positive for the disease has a 99% chance of actually having..
A liquid flows with a velocity of 3.28 feet per second through a pipe of cross-section area 250 cm2 and is collected in a tank. The density of the liquid is 1200 kg/m3. Calculate the mass in kilograms of the liquid collected in the tank in one min..
Let F(u,v) be a function of two variables. Find f '(x) for each of the following. Use F_u and F_v for F_u and F_v
A box has square ends and a rectangular base but no top, the volume is 288 cubic cm. What is the minimum total area of the sides and base, and what are the corresponding dimensions?
Write the equation of a line perpendicular to the given line but passing through the given point.
Maria and Thomas are part of a group of 8 women and 8 men who will participate in a chess tournament. The 16 players will be randomly paired up into groups of two.
Suppose that the cost function for a certain product is c=f(q). If the relative rate of change of c (with respect to q)is 1/q, prove that the marginal-cost function and the average-cost function are eaqual.
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