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1. Use mathematical induction to prove that 2-2*7+2*7^2-.....+2(-7)^n=(1-(-7)^n+1)/4 whenever n is a nonnegative integer.
2. Show that 1^3+2^2+....n^3=[n(n+1)/2]^2 whenever n is a positive integer.
3. Use mathematical induction to show that 3 divides n^3+2n whenever n is a nonnegative integer.
Write the expression in the standard form a + b i. First convert to rectangular form--- calculate the magnitude-- find reference angle--then the argument of z---
The natural length of a spring is 10 cm. A force of 25 N stretches it to a length of 20cm. How much work, in units of N-cm, is done in stretching it from a length of 10cm to a length of 15cm?
The Bunny Number Oney rabbit farm noticed that the rate of increase in rabbits on the farm was directly proportional to the number of rabbits at the farm at any time t. It was further noticed that the number of rabbits increased from 200 to 400 in..
What percent of the first chemical will have been converted in 20min? In how many minutes will 60% of the first chemical have been converted?
The resale value of a certain industrial machine decreases at a rate that depends on its age. When the machine is t years old, the rate at which its value is changing is -960e^ -t/5 dollars per year.
Find the equation of parabola describe. Find 2 points of latus rectum.Graph. Find all the complex root. Leave your answer in polar form with the argument in degrees.
Find the value of "a" that makes the following function differentiable at x = 2.
Identify one or more control procedures (either general or application controls, or both) that would guard against each of the following errors or problems.
Independent flips of a coin that lands on heads with probability p are made. What is the probability that the first four outcomes are
What percentage change in the required sample size would this produce?
Find (dy/dx) by implicit differentiation for the following equation:
We may think that this is similar to a Fresnel Integral (sin(x^2)). In that case, we would set z=e^(iz)^2, and then integrate over the special contour with regions I: 0 to R, II:
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