Calculus

There is only one, Newton.

Its area is equal to its length, multiplied by its height

78 - (-49) is the same as 78 + 49 which equals 127

300/1118=

.268 seconds

Think of a pizza that has 12 slices. You will eat the slices from the result of your division.

1. In the first example, lets say you eat 3 out of the 12 slices. That is expressed as 3/12 in the math world.

1. Second example will be 0 divide by 12 (0/12 or zero divided by 12). This means you will get zero of the 12 slices. You have no slices to eat.

2. Third example is division by zero (12/0). First of all this does not exist. You cannot get 12 slices from a pizza that has 0 slices. Think of this as you got to the pizza box and you WANTED to eat 12 slices but all your friends ate all the slices before you. The pizza is gone and does not exist anymore. So 12/0 does not exist in the math world.

Dividing by 0 is undefined. It's not possible.

1.5 hours x 17 days = 25.5 hours = 25 hours 30 minutes

3 * x * x * x * x

what

If the "8 by 8 octagon" refers to the distances between its opposite sides rather than opposite vertices (its principal diagonals), then the side lengths are 8*[sqrt(2) - 1] units of length.

Practice a lot!

y = -2x + 6

slope = m = -2 = -2/1 = rise/run

y-intercept: 6

x-intercept: 3

y = 0

0 = -2x +6

0 + 2x = -2x + 2x + 6

2x = 6

2x/2 = 6/2

x = 3

So we have two points (3, 0) and (0, 6). We can find another point using the slope -2/1.

Use the point (0, 6):

(0 + 1, 6 - 2) = (1, 4)

Draw the line that passes through the points (0, 6), (1, 4), and (3, 0).

When x = 75.964 degrees plus or minus any multiple of 180 degrees.

-4x-2+2=-2+2.

-4x/-4=0/-4

x=0

(3x+2)-(5+7x) = 3x+2-5-7x = -4x-3

3x+2 is -4x-3 times greater than 5+7x.

(3x)^4 +(4x)^3 -(36x)^2 +1 or 3x^4 + 4x^3 -36x^2 +1? Not sure from the way you said it.

In either case the method is the same. Use the power rule for differentiation, d/dx(x^n) = nx^(n-1), to take the derivative of the equation term by term, and then set this equal to zero and solve for x. You will get a cubic function when you do this, so you can try to factor it after you differentiate to simplify the problem.

Assuming the second case (It seems more likely) differentiating gives the following, which I have set equal to zero:

12x^3 + 12x^2 - 72x=0

x(12x^2 +12x-72)=0 Factor out an x

x(12)(x-2)(x+3)=0 Factor some more

This gives horizontal tangents at x=-3,0,and 2. Now all you have to do is plug some easy numbers into the derivative from the intervals between these values. Negative derivative means decreasing, positive means increasing. Good luck!

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x3-x2

Both terms in this expression have x2 in them, so "divide" each term by it using the distributive property in reverse.

x2(x-1) = x3-x2

If you "re-distribute" you should see that they are equal.

There are infinitely many pairs of values (x, y) which will satisfy 4x + 1.5y = 79

The equation can be rearranged:

4x + 1.5y = 79

⇒ 1.5y = 79 - 4x

⇒ y = (158 - 8x) ÷ 3

For any given value of x, plug it into the above equation and the corresponding value of y will be calculated. So, some pairs of values (x, y) that satisfy this are:

(-2, 58), (1, 50), (4, 42), (7, 34)

97 * 10 = 970

x2-b = 9

x2 = 9+b

Square root both sides:

x = the square root of (9+b)

2X - 6X + 5 = 0

subtract 5 from each side

2X - 6X = - 5

do what it says on the left

- 4X = - 5

X = 5/4

check in original equation

2(5/4) - 6(5/4) + 5 = 0

10/4 - 30/4 + 5 = 0

- 20/4 + 5 = 0

- 5 + 5 = 0

0 = 0

checks

509.1

Including the initial digit 3, the 13628th digit of pi is 7.

-8.

9x2 - 6xy + y2 - 81

= (3x - y)2 - 92

= (3x - y - 9)(3x - y + 9)