Calculus

In real-world situations, the best that you can do is approximate using numerical methods. For instance, you could take an aerial photograph of the region, overlay a grid, and then use methods such as "The trapezoid rule" or "Simpson's rule". Any calculus text should cover how to use these and you can also find a description of these methods at:

http://en.wikipedia.org/wiki/Trapezoidal_rule

http://en.wikipedia.org/wiki/Simpson%27s_rule

If, however, it is a math problem and you are given functions of the curves (or rivers), then you just integrate the difference (in absolute value) of the two functions. For instance, if we have the curves f and g on [a,b], and f is greater than or equal to g on the interval, then we just integrate f-g over [a,b].

pooo000ooo000ooo000ooo000ooo000ooo000ooo000ppp

Sqroot x > x if x<1.

Start on the left-hand side.

cos(x) + tan(x)sin(x)

Put tan(x) in terms of sin(x) and cos(x).

cos(x) + [sin(x)/cos(x)]sin(x)

Multiply.

cos(x) + sin2(x)/cos(x)

Make the denominators equal.

cos2(x)/cos(x) + sin2(x)/cos(x)

Add.

[cos2(x) + sin2(x)]/cos(x)

Use the Pythagorean Theorem to simplify.

1/cos(x)

Since 1/cos(x) is the same as sec(x)- the right-hand side- the proof is complete.

factor x2-14x+46 What two numbers multiply to give 46, and (since the 14 is negative) are 14 apart?

Well, 46 only factors into [1 2 23 46], so there are no integer answers.

This calls for the quadratic formula

(-b±√(b2-4ab))/2a

(14±√(196-184)/2

(14+√(12))/2 and (14-√(12))/2

(14+3.464)/2 and (14-3.464)/2

17.464/2 and 10.536/2

8.7321 and 5.2679 are both approximations of the answers. ■

hyperbola

xy=total cost

well y=.04x is most likey a linear equation with the .04 as the slope of the line and there is no y intercept or the y intercept is 0

x=1.875

Three US quarts is about 0.002839059 cm3

25

When calculating mean, you sum every number in some data set and divide by how many numbers are in the set.

For every zero added to the data, the sum doesn't change but the number which you divide the sum by increases by one.

For example, if your homework grades in a class are:

82, 76, 90, 85, 92

Your mean homework grade then is

(82 + 76 + 90 + 85 + 92) / 5 = 425 / 5 = 85

Say you forget to do your next homework assignment, so you get a zero. To calculate your new mean grade, instead of adding up the numbers again, just increase the denominator by one:

425 / (5 + 1) = 425 / 6 = about 71

3

Take the derivative of the equation with respect to x:

dy/dx = d(x^2-2sin(x)+3)/dx

=d(x^2)/dx-2*d(sin(x))/dx+d(3)/dx

=2x-2*cos(x)

That's your tangent equation.

At x=0 ---> 2*0-2*cos(0) = -2

There's your slope.

Yes, as x-y2=0

1m = 1000 mm

1 cu m = 1m x 1m x 1m

= 1000mm x 1000mm x 1000mm

= 1,000,000,000 cu mm

=> 1 mm3 = 1/1000000000 m3

Carl Gauss lived in Germany from 1777 to 1855.

This equation has no meaning. 47 cubed is 103,823, but the rest of the equation is worthless without a value for x and t. At present, X and T do not have values, so you can not evaluate this expression.

Solve for y, getting the equation into the form of y = mx + b. m will then be the slope, and b will be the y intercept.

You don't, if you're only looking for real number results. If you are including imaginary numbers, x2+4 = (x+2i)*(x-2i).

Parallel lines go the same way and are always the same distance from each other (eg you and a mate walking side by side).

Skew lines pass each other but don't meet, eg when you walk under a bridge and the train passes over. You are heading different ways, but you don't actually (just pass by)

-3x + 2x > 6

-x > 6

x < 6

{x| x < 6 } or ( -∞, 6)

Depends on how close you need to be. 2.9, or 2.99, or 2.999 etc

Yes it is linear, it is a horazontal line, or 0 slope