Note that if you multiply your equation by x and rearrange the terms you can write the equation as    x*y'+2y-6x=0.    If you let M(x,y) = 2y-6x and N(x,y)=x then you have a differential equation of the following form   N(x,y)*y'+M(x,y)=0...

Slope is the change in y divided by the change in x. Your change in y is 2-(-5)=7, and your change in x is 4-0=4. So your slope is 7/4.

If you want to transform a function f(x) z units to the right then what you need to find is f(x-z). In your case this becomes f(x-15).

First guess to find a root. If you plug in x=1 you will find that this is a root. So (x-1) is a factor to your expression. Do long division on your initial expression by (x-1). Then your factors will be (x-1) and whatever you get from long division. But your answer from long division will be quadratic...

In one hour the first person washes 10% (1/10) of the windows whereas the second person washes 12.5% (1/8) of the windows. So together in a single hour they can wash 22.5% of the house. We want to find how long it will take for them to wash 100% of the house. So the total amount of hours it would...

Va=Vb-6 Vat=(VB-6)t=190 Vbt=220 (Vb-6)t-Vbt=190-220 -6t=-30 t=5 Vb*5=220 Vb=44 Va=Vb-6=44-6=38

12 hours.   The first student does 7.2/18 of the work when the two students are working together, or 40% of the work. The other student therefore does 60% of the work. Compared to the first student, the second one work 60/40 or 1.5 times faster. Since 18/1.5=12, the second student would...

x^4+22x^2+21=(x^2+21)(x^2+1)   Zeros at x^2=-21 and x^2=-1 so x=+-i sqrt(21) and x=+-i

Any three consecutive numbers will do. Call n the first number, n+1 the second and n+2 the third. Then, putting your words into an equation we have   2(n) + (n+1) = 3(n+2) - 5 3n + 1 = 3n +1   As you can see, this equation works for any n...

Another example might be if you need to create some kind of enclosure. Lets say you have a limited amount of fencing available and you want to make a rectangular enclosure. What should the dimensions of your rectangle be in order to maximize the area encompassed by the enclosure? I'm not sure what...

I also don't know what you mean by the golden rule for an antiderivative. However, one of the most useful formulas when taking the antiderivative of a single term of the form xn is ∫xndx = xn+1/(n+1).