Calculus

There are two (main) ways to graph this parabola.

The first is to simply substitute in values of x, find the corresponding y values and then plot those points and connect the points with a curve.

The second way is to 'complete the square' so that we can find where the maximum or minimum occurs and the y-intercept and graph from those two points. This is the process described below.

y = -x2 + 8x + 5

y = -(x2 - 8x) + 5

y = -(x2 - 8x + 16 - 16) + 5

y = -(x2 - 8x + 16) + 16 + 5

y = -(x-4)2 + 21

From this we can see that a maximum occurs at (4,21). To find the y-intercept, substitute in x=0, giving y=5.

From these two points, we get a pretty good idea of what the graph looks like. If you want more accuracy, substitute in more values of x.

89067777782345637

First, you look at the equation long enough to recognize that it's the equation

of a straight line with [ slope = 1 ] and [ y-intercept = 0 ].

Then you draw that line. It passes through the origin, and slopes up toward the

right at 45 degrees.

As another technique, you could use the equation to calculate two points on the line,

then mark the points on the graph, and draw a line between them.

To calculate two points, choose two values for 'x', and then calculate the value

of 'y' for each one.

Let's just pick two numbers out of the blue for 'x':

x = 2 and x = 9 .

Can you use the equation [ y = x ] to calculate the value of 'y' that goes with each one ?

That's right. Good work. When x=2, 'y' is also 2. And when x=9, 'y' is also 9.

So now you have two points on the graph ... (2, 2) and (9, 9).

Using a soft pencil, mark each of those two points on your graph with a small dot.

Then, using the same pencil along with a ruler, draw a line that connects the two

dots. You can extend the line as far as you want to, past either point, in either direction.

(5y + 3)(y - 1)

A function is a relationship that is one-to-one or many-to-one but not one-to-many.

Thus, if a and b are in the domain of the function, then their images in the range, f(a) and f(b) MUST be equal.

IF you use 39.37 inches to a meter (pretty close), there are 60 inches in 5 feet. 60/39.37 = 1.524003048 meters

Intuitively, a continuous function y = f(x) is one where small changes in x result in small changes in y.

More rigorously, consider the function y = f(x) defined on the domain D to the codomain C where both D and C are subsets of R.

Then f(x) is continuous at a point p in D if the limit of f(x) as x approaches p within D is f(p).

The function is said to be continuous is it is continuous at every point in its domain.

The domain and codomain of f can be extended to multiple dimensions provided a suitable metric (eg Pythagorean distance) is used.

8.2 X 7.3 X 10.8 equals 646.488

He needs to continue his therapy--time is the best indicator of how he will deal with his feelings. If you don't feel he's making an honest attempt to change, and is going through the motions only to keep you from leaving, end the relationship. You can't change his behavior for him--he alone has the power to do that. If you decide to stay with him, the best thing for you to do is to set boundaries. Make it absolutely clear that any further incidents of abuse are the dealbreaker of your relationship. Neither of you have the right to physically or verbally abuse the other. Don't use his violent act towards you as ammunition in arguments or as a way to get him to do what you want. You are wise to consider distancing yourself from him. Just because he is in therapy isn't enough for you to waffle about forgetting the hitting incident. He still has a long road to behavioral health, and you have to heal.

0

X-45=12

________

+45 +45

________

x= 57

100 Years in a Century.

f(x)= -x-9

Assuming the question refers to [sin(x)]/2 rather than sin(x/2)

the answer is 1.

So, we want the limit of (sin2(x))/x as x approaches 0. We can use L'Hopital's Rule: If you haven't learned derivatives yet, please send me a message and I will both provide you with a different way to solve this problem and teach you derivatives!

Using L'Hopital's Rule yields: the limit of (sin2(x))/x as x approaches 0=the limit of (2sinxcosx)/1 as x approaches zero. Plugging in, we, get that the limit is 2sin(0)cos(0)/1=2(0)(1)=0. So the original limit in question is zero.

It depends on the density of the sand. Certainly, you are talking about 56 cubic feet, but you will need to know the bulk density of sand to figure out how much that weighs.

-4x-4 equals -16.

Add 4 to both sides; -4x equals -12.

Divide both sides by -4; x equals 3.

20.35 ! Just add them all together in your head - it's not rocket science !

the answer is y minus 10 divided by 2.

∫ f'(x)/(p2 + q2f(x)2) dx = [1/(pq)]arctan(qf(x)/p)

A nice place

x=4

y=5

9x+7y=??

Replace:

9(4)+7(5)= 71

(4+x) (2x-3)