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A farmer is constructing a rectangular pen by placing a fence on the boundary for dealing with his cattle. He will use a portion of the north side of his 100 feet long barn for one side of the pen and will need to construct a dividing fence perpendicular to the barn to make two enclosures for various purposes. If he has 360 feet of fencing, what are the dimensions (length and width) of the pen which will maximize the total area of the pens? Justify your answer.
Let T : V → W be a surjective linear map. For a subspace U ⊆ V, define the restriction T|u ∈ L (U, W) by T|u (u) = T (u) . Prove that there exists a subspace U of V such that T|u is an isomorphism.
The average number of television sets in the sample households turns out to be 2.56, and the SD is 0.73. What is the observed value for the average number of television sets per household?
Show that if (a_n)^infinity evaluated at n=1, and (b_n)^infinity evaluated at n=1 are equivalent sequences of rationals, then (a_n) ^infinity evaluated at n=1 is a cauchy sequence if and only if (b_n)^infinity evaluated at n=1 is a cauchy sequence..
A high-speed train makes a 320 mile nonstop run between two major cities in 512 hours. The train travels 80 mph in the country, but safety regulations require that it travel only 20 mph when passing through smaller, intermediate cities. How many h..
if the height of the basketball hoop is 10ft the angle of elevation between claire and the goal is 35deg and the angle
The dimensions of a closed rectangular box are measured as 95 cm, 52 cm, and 12 cm, respectively, with a possible error of 0.2 cm in each dimension. Use differentials to estimate the maximum error in calculating the surface area of the box.
The flux capacitor (the equipment necessary for time travel) needs 85 grams of Plutonium to have enough power to travel through time. How long can Doc Brown store his Plutonium for to have enough to time travel.
Using the Quotient rule, find the gradient of the function:
If the sound intensity of something at 40 feet away is read as 75 decibels, what would the calculated intensity be at 80 feet away?
Which of the following is NOT a characteristic of an ideal statistician?
If the mountain is increasing in height at 2 feet per hour when it is 500 feet high, how fast is the lava flowing (how fast is the volume of the mountain increasing)? ( V = 1/3 πr2h)
demand for walnut fudge ice cream at the swan ice cream dairy can be approximated by a normal distribution with a mean
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