geno3141

One formula for the area of a triangle is: Area = ½·a·b·sinC

where C is the angle between the two sides a and b.

In this problem, a = 100, b = 53.2, and C = 40°.

Area =  ½·100·53.2·sin40°     -->      Area = 1700 (rounded)

Product means times and decreased means subtract:

-5 · x - 11 = 15

-5x - 11 = 15              To remove - 11 and 11 to both sides.

-5x - 11 + 11 = 15 + 11

-5x = 26                     To remove -5 which is multiplied to x, divide by -5

-5x/-5 = 26/-5

x = -5.2

Since you have x^12, take the 12th root of each side:

(x^12) ^ (1/12) = (2^18) ^ (1/12)

When you have an exponent to an exponent (a power to a power), multiply them:

     12 * 1/12 = 1         and          18 * 1/12 = 18/12 = 3/2 = 1 + 1/2

So, you get: x^1 = 2^(3/2)     which is x = 2^(3/2) = 2√2.

How to reduce: 2^(3/2):

2^(3/2) = 2^(1 + 1/2)

To multiply numbers with the same base, you add their exponents; also, if you have a problem with exponents are added, the problem can be split into two numbers that are added.

So, 2^(1 + 1/2) = (2^1) · (2 ^ (1/2) )

2^1 = 2         and         2 ^ (1/2) = √2

The final answer is x = 2√2.

To reduce a square root, determine if a perfect square (not 1) divides into the number.

Since 4 divides into 8 and since √(4) = 2 :

√(8) = √(4·2) = √(4)·√(2) = 2√(2)

You will need to know where the area is (under the normal curve of distribution); is it from the mean to the right?; is it evenly distributed on both sides of the mean? etc.

Everything in the previous answer is correct.

Math also includes pictures and patterns. How to find the area and volume of objects. And how to give the rules for how one item changes into another. 

Math determines how items move (think of games) and how music can be stored on CDs and computers.

Robots are controlled by computer programs; and computer programs depend upon math. 

And, this is only the beginning!

There is a formula that says: d(a^u)/dx = a^u·ln(a)·du/dx

(If you don't have this formula, then we'll have to go back to more basic formulas.)

(Assumes: a>0 and u is a differentiable function of x. The inclusion of du/dx makes it a chain rule problem.)

For your problem, a = 5, u = -1/x.   

--> a^u = 5^(-1/x) 

--> ln(a) = ln(5)

--> du/dx = d(-1/x)/dx = d(-x^-1)/dx = x^-2 

y' = 5^(-1/x) · ln(5) · (x^-2)

Calculus is used when you want to use the rate of change; for instance, if you know the rate of the change in the temperature in a room (along with knowing other variables), you can predict the temperature (and the rate of change of temperature) at a previous time or at a future time.

It is used to predict instantaneous rate of change.

For example, it is not hard to calculate you average speed over a period of time: speed = (final location - initial location) / (final time - initial time). 

Specific example: you are on an interstate and you pass mile marker 100 at 1:00. Later you pass mile marker 170 at 2:00. Your average speed was (170 - 100) / (2:00 - 1:00) = 70 miles / 1 hour = 70 miles per hour.

However, how do you calculate the speed of the car at the instant it drove off the road; at the instant it left the road, its final location was the same as its initial location (one point, so the distance it travelled that instant was 0 feet) and its final time was the same as its initial time (so its time was 0 seconds). Placing these values in the speed formula, you get 0 / 0. Calculus gives ways to handle these "indeterminate" expressions.

Calculus also gives ways to calculate areas and volumes (these have uses in solving problems that really have nothing to do with area and volume in the usual meanings).

Among other uses, scientific notation is used to express very large and very small quantities:

98 000 000 000 becomes 9.8 x 10^10  and  0.000 000 000 07 becomes 7 x 10^-11

In algebra, they are both said to be undefined.

However, in calculus, n/0 (with n≠0) will either approach ∞ or -∞ depending upon the sign of n and in which direction 0 is being approached.

0/0 is said to be "indeterminate" as its value depends upon the problem; in one problem it may be 0, in another 27, in another -42.

0/0 is undefined in the sense that it does not have one specific value; indeterminate in the sense that any number can be used as the answer (0/0 = 12 because 0 = 12*0; same for any number, not just 12).

There is a change of base formula that will allow you to change from any base to base 10:

Using common logs (that is base 10 logs):

It is: log(base) number = log(number) / log(base).

Example: If you want to find the log (in base 2) of 47:    log(base 2) 47 = log(47) / log(2)

This will work for any base:

If you want to find the log (in base 8) of 119:    log(base 8) 119 = log(119) / log(8)

This also works if you want to use natural logs:

Use the formula: log(base) number = ln(number) / ln(base).

Example: log(base 2) 47 = ln(47) / ln(2).