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A vitamin company produces supplements for anyone who enjoys athletic activities. Two of their products are the SimplyProtein Nutrition Bar and the Myoplex Deluxe Shake. One SimplyProtein Nutrition Bar contains 33 grams of protein, 300 calories, 13 grams of sugar, and 45 milligrams of sodium. One Myoplex Deluxe Shake contains 42 grams of protein, 300 calories, 2 grams of sugar, and 450 milligrams of sodium. An athlete is preparing for the Shamrock Shuffle 8K race in Chicago. He is planning to use the SimplyProtein Nutrition Bar and the Myoplex Deluxe Shake in his training. He wants to maximize his protein intake daily while keeping his calories under 1500, sugar under 32 grams, and sodium under 1845 milligrams. How many bars and shakes should he consume daily while maximizing his protein intake? What is the maximum daily protein intake?
Suppose the three vertices A, B and C of a parallelogram ABCD are given. Construct the fourth vertex D.
Prove the triangle inequality starting with: |V+W|^2. You must use Re (less than or equal to) | | and the Schwarz inequality.
Explain why an Abelianization fo G is unique up to isomorphism. Construct an Abelianization of G as follows: Let G' be the subgroup fo G generated by all commutators [x,y] = xyz^-1 y^-1, where x, y are real members of G.
Graph the linear equation for the indicated values of the independent variable.Show this on a Graph as well as the formula
Determine the dimensions of largest possible area of a rectangular garden - What are the dlmensions area if $1200 is to be spent for fencing material?
Sampling distribution of sample mean- key informaiton. What is the probability that the sample mean will be between 28 and 46?
A regular hexagon is divided into 6 equilateral triangles. he altitude of each triangle is 6cm. What is the perimeter of the hexagon?
Use this tree diagram and the probability determined in part (a) to calculate the probability that she should receive at least one payment exactly on time.
Develop a tree diagram for tossing two, eight-sided gaming dice to figure out how many possibilities there are. Define Tree Diagram and Dice Tossing
The Snell law to find the index of refraction
Let f be Lebesgue integrable on [0,1]. Prove that the limit, as k goes to infinity, of the integral from 0 to 1 of (x^k)f(x)dx is equal to 0.
Water is flowing at the rate w of into a tank in the form of a cone of altitude h and base radius and with its vertex in the downward direction. How fast is the water level rising when the water is a certain depth x ?
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