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The tangent line to the graph of g(x)=2x^3-7x at (1,-5) intersects the curve at another point. Find the coordinates of the other point. Round all non-terminating decimals in the calculation to seven significant digits. Round your final answer to two decimals in the calculation.
The mean life M of an atom in a radioactive substance is given by M = k 0∫∞te-kt dt, where k is a constant. For the radioactive carbon isotope 14C the value of k = 0.000121 year-1. Use this to find the mean life of a 14C atom.
A chemist has two alloys, one of which is 5% gold and 20% lead and the other which is 30% gold and 40% lead. How many grams of each of the two alloys should be used to make an alloy that contains 34 g of gold and 104 g of lead?
the cost varies linearly with the distance and is $366 per month for 300 km driven per month, and $510 per month for 1500 km driven per month. write the equation expressing cost in terms of distance.
Evaluate the integral ∫01 ∫0√1-x2 ∫√x2+y2√2-x2-y2 xy dz dy dx by changing to spherical coordinates. Evaluate the integral ∫∫∫E(x2 + y2) dV where E is the part of the sphere x2 + y2+z2 = 1 above the xy-plane.
Consider the shaded region bounded by y = f(x) and y = g(x) as shown. Set up the integral needed to find the volume of the solid obtained by rotating the region around the x-axis.
What is the maximum time it will take to be transported across the city with wind velocity of 8 miles per hour (to the nearest hour)?
The probability density function for the lifetime of a bulb is f(t) =(1/6) e^{-t/6}, t is less than 0. What is the probability that both of the bulbs will fail within 4 hours?
Sketch both graphs. Find and label the intersection points. Find the area between the graphs using integration. Give the full integral, including limits, in proper notation.
The Friendly Auto Mart sold seven of these trucks and has two of the new transmissions in stock. What is the probability that the auto dealer will need to order more new transmissions?
Let's play three yard football (The games are shown on Thursday afternoon between 4:45 and 5 on the SASN -Short Attention Span Network). The home team starts with the ball on the 1 yard line. The transition probabilities are given in the table
Sketch the situation. What is the net force charge on q3? What is the unit vector pointing in the direction of the net force?
Augmented matrices to solve the word problem
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