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The temperature at 6 P.M. was 31°F. Through midnight, it had dropped 40°F. What was the temperature at midnight?
Visualize a number line. The drop from 31° to 0° is 31°. There are still 9 more degrees to drop. They will be below zero. -9°F is the temperature at midnight.
An elliptical galaxy has gravitational boundaries defiend by 9x 2 +16y 2 +144z 2 =144. A black hole at the center of the galaxy is interacting with dark matter producing a radiatio
I am here to tell you, Alex has a cold.
an insurance salesman sells policies to 5 men, all of identical age in good health. the probability that a man of this particular age will be alive 20 years hence is 2/3.Find the p
Infinite Interval - Improper Integrals In this type of integral one or both of the limits that is upper limit and lower limit of integration are infinity. In these cases the
three times the first of the three consecutive odd integers is 3 more than twice the third integer. find the third integer.
writing sin 3 a.cos 3 a = sin 3 a.cos 2 a.cosa = sin 3 a.(1-sin 2 a).cosa put sin a as then cos a da = dt integral(t 3 (1-t 2 ).dt = integral of t 3 - t 5 dt = t 4 /4-t 6 /6
Derivatives of Trig Functions In this section we will see derivatives of functions other than polynomials or roots of polynomials. We'll begin this process off through taking
Before we find into finding series solutions to differential equations we require determining when we can get series solutions to differential equations. Therefore, let's start wit
Chain Rule : Assume that we have two functions f(x) & g(x) and they both are differentiable. 1. If we define F ( x ) = ( f o g ) ( x ) then the derivative of F(x) is,
Example of Integration by Parts - Integration techniques Some problems could need us to do integration by parts many times and there is a short hand technique that will permit
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