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Induction
#1. Prove by induction that 8 + 11 + 14 + ... + (3n + 5) = n(3n + 13)/2 for all n Î N.
A child lies on the ground and looks up at the top of a 17-ft tree nearby. the child is 14 ft away from the tree. what is the angle of elevation from the child to the top of the tree?
How do I determine the short-run profit maximizing price and quantity? How do I determine the maximum profit accruable to the firm?
Make a chart of the possible dimensions for a rectangle with an area of 196 m2. What are the optimum dimensions of the rectangle for minimizing the perimeter?
An aircraft is flying horizontally at a constant height of 4000 ft
A long, current-carrying solenoid with an air core has 1750 turns per meter of length and a radius of 0.0180 m. A coil of 125 turns is wrapped tightly around the outside of the solenoid. What is the mutual inductance of this system?
A 100% concentrate is to be mixed with a mixture having a concentration of 30% to obtain 65 gallons of a mixture with a concentration of 80%. How much of the 100% concentrate will be needed?
A random sample of 20 items from the first population showed a mean of 100 and a standard deviation of 15. A sample of 16 items for the second population showed a mean of 94 and a standard deviation of 8.
Kate and John buy a block of land for $140,000 by paying $10,000 deposit and then taking out a loan for the remainder. The loan will be repaid with quarterly instalments over 15 years with interest at j4 = 7.7%.
This month she doesn't know yet how many mixing vats she will need to order. Let y = number of mixing vats required. Write an equation using y that she can use to determine the total amount of her order. Assume no chemicals are ordered, only vats.
Solve the following system of equations using the Substitution method: Solve the following system of equations using the elimination method:
Different ways to schedule appearances of 4 performers. There are 4 performers who will present their comedy this weekend at a comedy club
the sides in cm of a triangle are x-y, 2into square root of xy and x+y respectively.show that the triangle is a right angled triangle and state the triangle law.
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