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1. Let a, b, c, d∈ R. If a > 0 and b > 0, then ab > 0. If a > 0 and b ≥ 0, then ab ≥ 0. If a ≥0 and b ≥0, then ab ≥ 0. Need to prove this.
2. Let q ∈ R and x ∈ R - Q. Prove that q + x ∈ R - Q.
3. Prove that ½ + ¼ + 1/8 + ? + 1/2n =1 - 1/2n for all n ∈N.
A medical research team studied the ages of patients who had strokes caused by stress. The ages of 34 patients who suffered stress strokes were as follows.
There is a probability of 0.08 that a vaccine will cause a certain side effect. Suppose that a number of patients are inoculated with the vaccine.
Determine whether the following assertion is true or false: if you integrate the Fourier series for the delta function d(x) term by term you obtain the Fourier series for the step function s(x).
Use the leading coefficient test to determine the behavior of the function.
A company is using linear depreciation and a machine that when new was worth $250,000 is valued at 60,000 after 5 years. Find the linear function that gives the value of the machine as a function of time. What is the value of the machine after 2 year..
A path that passes through a pasture rises 323 feet over a horizontal distance of 4600 feet. Find the slope of the path. Round your answer to two decimal places.
Use mathematical induction to solve the equation.
How we can find out the mathematical model of self adjoint singularly perturbed equation from chemical catalysis and Michaelis-Menten process in biology.
Consider the intersection of level surfaces of F = x^3 + y^3 - u^3 - v^3 and G = xu + yv.
the function w(d)=0.112d approximates the amount, in centimeter,s, of water that results from d cm of snow melting. Find the amount of water that results from snow melting from depthsof 10cm, 38cm, and 57cm.
a study by the information technology department at wpu revealed company employees receive an average of four e-mails
the amount at of atmospheric pollutants in a certain mountain valley grown according to a natural growth model in such
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