Find the equation of a circle whose center is (5,-2) and has a radius of 4.
Given: Center = (5, -2) : h = 5 k = -2 r = 4 Formula: (x-h)^2 +(y-k)^2 = r^2 Solution: (x - 5)^2 + (y -(- 2)) ^2 = 4^2 (x - 5)^2 + (y +2)^2 = 16
A ladder is leaning against a wall. The foot of the ladder is 7 feet away from the wall. If the ladder makes an angle of 50 degrees at ground level, what is the height of the wall?
Figure: the figure must be a right triangle. where the leg of the right triangle would be the height of the wall, the base of the triangle is the distance of the ladder and the angle of elevation is 50 degrees Given: base = 7ft angle theta = 70 degrees Find: height(h) Formula: tan theta = opposite /adjacent tan 50 deg = h/7ft .multiply both sides by 7ft 7 ft*tan 50 deg = h h = 8.34 ft, the height of the wall
Allan won $100,000.00 in a lottery and he decided to put half of it in a certain bank at 5% interest compounded quarterly. He plans to withdraw all his money from the bank in 10 years to build a new house. How much money is he expecting to get from the bank?
Given: Principal = $50,000.00(half of $100,000.00 r = 0.05 t = 10 years n = 4(compounded quarterly) Find: Accrued amount (A) Formula: A = P(1+r/n)^nt Solution: A = $50,000(1+0.05/4)^4*10 A = $50,000(1+0.0125)^40 A = $50,000(1.0125)^40 A = $50,000(1.643619463) A = $82, 180.97 *Note: do not round off the 1.643619463 before multiplying it to 50,000.00. You should multiply the whole thing or else you will lose about $20. Round your final answer instead.