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Use Lagrange multipliers to find the maximum and minimum values of the function subject to the given constraints. (If a value does not exist, enter NONE.)
f(x,y,z) = x4 + y4 + z4; x2 + y2 + z2 = 1
Six liters of liquid soap were bought for $11.40 per liter. The soap was repackaged in 150-mililliliter plastic containers. The cost of each container was $.26. Each container of soap sold for $3.29 per bottle. Find the profit on the 6 liters of l..
The probability of a bit error in a memoryless binary symmetric communication channel is 10^-3. Find the probability of a block of 1000 bits
Find the directional derivative at P(-2,2,-1) in the direction of Q(18,-2,4). Find the direction of maximum decrease at P. (your answer does not have to be unit vector.) What is the maximum rate of decrease?
A farmer wants to fence o a rectangular ?eld and then divide the ?eld in half with a fence down the middle (see diagram below). If he can only aord 240 ft. of fencing material, what is the width y which gives the maximum area of the ?eld?
What is the largest domain over which this function is defined? For this domain, what is the corresponding range of the function?
A cup of coffee at 187 degrees is poured into a mug and left in a room at 70 degrees. After 4 minutes, the coffee is 133 degrees. Assume that the differential equation describing Newton's Law of Cooling is (in this case) dT/dt=k(T-70).
A company has fixed costs of 20,000,and the cost of producing one unit of their product is $10. the unit sell for $20. write an equation for the total cost. write an equation for the total revenue. graph these equations to find the break even poin..
The height of a ball (in feet) t seconds after it is thrown straight upward is determined by h(t)=16t^2+48t+7. How long did it take the ball to hit the ground?
A 23-ft ladder is leaning against a building. If the base of the ladder is 6 ft from the base of the building, what is the angle of elevation of the ladder? How high does the ladder reach on the building?
What is the probability that the mean annual snowfall during 40 randomly picked years will be between 105 inches and 112 inches?
a container in the shape of an inverted right circular coner has a radius of 8 inches at the top and a height of 10 inches. At the instant when teh water in the container is 8 inches deep the surface level is falling at the rate of -1.3in/s. FInd ..
Write a system of two equations in two unknowns for each problem. Solve each system by substitution.
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