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Answers by Grigori S.

Let's rewrite your expression:                          2t+4/(12 -3t^2) = 2(t+2)/3(4 - t^2) = 2(t+2)/3(2-t)(2+t) = 2/3(2-t).   Thus, when t approaches -2 your limit will be 2/12 = 1/6.

Another way to solve the problem. Your function has the first coefficient with negative sign, which means it may only maximum. The time the ball reaches the ground is double of the time needed to reach to its maximum position. To find that time just calculate derivative of your function and...

Unit rate for the bathroom faucet - 8/12 ounces/min = 0.75 oz/min = 3/4 oz/min Unit rate for the kitchen faucet - 6/10 = 3/5 oz/min - two rates show different coefficients of proportionality between amounts of water leaked and time.   Unit rate or both faucets = (3/4) + (3/5)...

To calculate then uncertainty of the equivalent capacitor Ceq you have to differentiate the expression for the capacitor shown by Richard, and replace the symbol of differential by Δ symbol (means uncertainty or error of measurement). Let           ...

The sky is blue because of Raleigh scattering  of the sunlight  in the Earth atmosphere. This type of scattering (while the other portion of the light reaches the Earth's surface) is described by the function inversely proportional to fourth degree of the light wavelength: ∼λ-4)...

boat speed (answer)

 GUIDE PROBLEMS Let d be the distance traveled by the boat, v0 - speed of the boat in still water, v - speed of the current, t1 = 1/5, and t2 = 3/5. To find the speed of the boat in still water we have to write two equations: one for motion up the river and another one – against...

Use rules of exponents. First of all         (x5)-8 = x -40   Then if your next term is x4  you will have x-40 x4 = x-36  (you are adding the exponents)   If you have x -4  then your final answer is x -44.

f(y) is  a parabola which is open down, and has two horizontal, intercepts: y=0 and y=2 with maximum at y = 1. Because g(y) is a straight line, area bounded by the line for 0 ≤y,≤1 is 1/2. Thus, the area bounded by two graphs is the integral of  f(y) from 0 to 1 minus 1/2. The answer...

Word Problems (answer)

Let x be the amount of hours spent by Samantha when she works alone, and 3x - time spent by Logan. First, You have to find how much work can be done each of these girls per unit of time. For Samantha it is 1/x, for Logan - 1/3x. Because 45 minutes is 3/4 of an hour, together they could have...