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MATH 16A QUIZ 4-
(1) Find the point (x, y) on the curve y = x2 for which 2x + y is minimized, and explain why it is an absolute minimum.
(2) I have 200 feet of fencing to construct a rectangular fence for my cows. I want both the length and width of my fence to be at least 2 feet. What is the smallest area I can enclose?
(3) Find the derivative of f(x) = 4√x(2x2 - 1)3.
(4) Find the derivative of f(x) = (x3-1/x3+1) at x = 0.
Calculation of Probability - Normal Distribution - find the probability that a randomly selected employee
1. Let V be a real vector space. We know that V has an additive identity, called 0. Suppose there is a vector u ∈ V with the property that u+v=vforeveryv∈V. Showthatu=0. (Thisshowsthatarealvector space can only have one additive identity.)
a triangular lot has dimensions 20.6 m, 31.4 m and 38.3 m. Find the angles at the corners of the property.
1. Consider R3with two orthonormal bases: the canonical basis e=(e1,e2,e3) and the basis f=(f1,f2,f3), where f1=(1,1,1)/(3^(1/2)) ,f2=(1,-2,1)/(6^(1/2)) ,f3=(1,0,-1)/(2^(1/2))
Suppose the population standard deviations for men and for women both were about 100. Construct a 95% confidence interval to estimate the difference in the population mean scores on this event for men and women.
The current in a circuit is i = 2.00 cos 100t. Find the voltage across a 100-microfarad(uF) capacitor after 0.200 s, if the initial voltage is Zero (one microfarad(uF)=10 to the power of -6 F).
Use integer programming to establish whole numbers for the solution variables.
Show the mass as triple integral and solve the integral using spherical polar coordinate and Use the spherical coordinate integral to evaluate
Find the future value of the ordinary annuity. Interest is compounded annually, unless otherwise indicated.
The function P(t) = 145e-0.092t models a runner's pulse, P(t), in beats per minute, t minutes after a race, where 0 ≤ t ≤15. Graph the function using a graphing utility. TRACE along the graph and determine after how many minutes the runner's puls..
Does the data indicate that the mean remission time using the new drug is different from 12.5 week at a level of significance of 0.01 - test the claim that the mean body mass index (BMI) of men is equal to the mean BMI of women.
A wire 210 inches long is cut into two pieces. One piece formed into a square, and the other into a circle. If they have the same area, what are the lengths of the two pieces of wire.
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