Calculus

51

A graph is a function if any vertical line intersects it at most once.

To solve for 2 unknown variables you need at least 2 independent equations. You have only 1.

To solve an equation, the goal is to get the variable by itself. In this case the variable is q.

-6=8q-4

first you want to get 8q by itself because the 8 and the q are together right now. So add 4 to each side to cancel it out on the side that has a -4.

-6+4=8q

simplify.

-2=8q

then to get rid of the 8, you have to divide both sides by 8 and then you get q by itself.

-2/8=q

simplify again.

-1/4=q

q=-1/4 :)

You are solving for x and y.

If x is set equal to 1 and y is set equal to 4, then you have 5-20=-15.

You can graph this by placing a point on the graph corresponding to x and y. That is, on the x axis you would go over 1 and on the y axis you would go up 5.

Now if x is set equal to 5, then that is 25, so y must be set equal to 10. This is 25-40=-15. Then on the same graph, you go over 5 on the x axis and go up 10 on the y axis.

Now you can draw a line between the two.

All you have to do now is solve the equation for another set of numbers, and then put that point on the graph. With three points, you have sufficient information.

6

x=-1.6

2

∫ f'(x)/√(af(x) + b) dx = 2√(af(x) + b)/a + C

C is the constant of integration.

All of the angles between the sides need to be the same. The sides can be of any length, but because the angles are the same they will always be in the same ratio to each other.

Your equation is a trimonial (made up of 3 parts) so your equation will end up being two sets of parentheses. In the first parentheses at the beginning goes the 2x, and at the begining of the second parentheses is x (because when you multiply 2x by x you get 2x^2 (two x squared) next you need to find two numbers that multiply to get six and also when you add them together you get seven. However since the beginning number is 2 (from the 2x) one of those two numbers has to be multiplied by 2 in order to get seven. The numbers needed are 2 and 3 with the two being the one that is multiplied by two. Therefore the second two needs to be i the second paretheses and the three needs to be in the first. Your equation will end up looking like this:

(2x+3)(x+2)

1800 m divided 1000 = 1.8 km

For the x intercepts, y = 0 ie 0 = 2x2 + 2x - 4

or x2 + x - 2 = 0 so that (x + 2)*(x - 1) = 0

So the intercepts are (-2,0) and (1,0)

89

If you counted one number every second between now, December 19, 2009 at 17:06:13, and one billion seconds time, you would reach one billion in 11574 days, 1 hour, 46 minutes, 40 seconds, reaching your target on Tuesday, August 27, 2041 at 18:52:53.

6cos(2t)

If a function is even ie if f(-x) = f(x). Such a function would be symmetric about the y-axis. So f(x) is a many-to-one function. The inverse mapping then is one-to-many which is not a function.

In fact, the function need not be symmetric about the y-axis. Symmetry about x=k (for any constant k) would also do.

Also, leaving aside the question of symmetry, the existence of an inverse depends on the domain over which the original function is defined. Thus, y = f(x) = x2 does not have an inverse if f is defined from the real numbers (R) to R. But if it is defined from (and to) the non-negative Reals there is an inverse - the square-root function.

I would suggest you plot it using, say GeoGebra. (Very easy to use.) On the left side of the y-axis the graph never falls below y=-1, I think. It climbs indefinitely on the right side. It extends indefinitely to the left, and to the right. But, as I say, if you learn GeoGebra, many problems like these will become much easier.

(1,-2)

There are an infinite number of ordered pairs that answer that question correctly.

Since you're not letting me see the list of choices that goes with the question, the

probability of my coming up with the correct one from that list is zero.

A trapezium (US: trapezoid).