Calculus

Ada had no job, after her father died when she was nine years of age, her mother tried to force her into slavery. Ada fought it for quite a while, until there was no use. Her aunt from her fathers side, took her and turned her into a slave, used to fix other computers, with that and the knowledge she had with math, she learned how to make a program for her computer. As soon as she made one, she fled the country to become famous. And died at the age of 36, because she had a bad case of measles. :) Your welcome!

Calculus, like any math, is best learned by practice. You can use a Study Deck - see the link to learn how to make and use one! - for the formulae and definitions, but the key to learning is to work problems until you really understand it.

To find the area of the Norman window, you need to divide the perimeter by 2 to get the width of the rectangle, which is 22.5 feet. The radius of the semicircle is half of the rectangle's width, so it's 11.25 feet. The area of the rectangle is 11.25 * 22.5 = 253.13 square feet, and the area of the semicircle is 0.5 * pi * 11.25^2 = 198.93 square feet. So, the total area of the window is 253.13 + 198.93 = 452.06 square feet.

Yes, a piecewise graph can represent a function as long as each piece of the graph passes the vertical line test, meaning that each vertical line intersects the graph at most once. This ensures that each input has exactly one output value.

Your question doesn't make sense. The area of a circle is Pi (approximately 3.14) times the RADIUS squared. An example would be a circle with a diameter of 6 inches and thus the circle would have a radius of 3 inches. Three squared (3 times 3) is 9, and 9 times Pi is approximately 28.3 square inches.

There is no concept of 'most tested students'. This is a misnomer.

Yes, all over the world, the student community is tested on their learning and experieinces. Some topics may need direct testing and some indirect testing. The two types of evaluation- formative and summative come into the picture here.

Turkey is located at 40 degrees N latitude cross 40 degrees E longitude. It is a Eurasian country that stretches across the Anatolian peninsula in Western Asia and Thrace in the Balkan region of southeastern Europe.

Any function of the form aebx - for non-zero a and b - is exponential. For examples, just replace "a" and "b" with any non-zero number.

Equivalently, any function of the form cdx - once again, for non-zero c and d - is exponential. Here, too, you can replace c and d with any number to get examples.

The exponential function describes a quantity that grows or decays at a constant proportional rate. It is typically written as f(x) = a^x, where 'a' is the base and 'x' is the exponent. For example, if we have f(x) = 2^x, each time x increases by 1, the function doubles, showing exponential growth.

3x + 5 = 20

Subtract '5' from both sides

3x = 15

Divide both sides by '3'

x = 5 The answer!!!!!

10xn=50.3

Multiply both sides by 9, giving y + 45 = 0 so y = -45

When doing the log of a base other than 10 or e you put the numbers in as if you were doing a log either of those bases and then divide the answer by log or ln of the base number you want.

Ex.
Log 3 (17)
You enter: log(17) / log(3)
or
ln(17) / ln(3)

3x - y = 0

5y = 15

5y = 15 Divide by '5' on both sides

Hence y = 3

Substitute for 'y' in the first equation./

3x - 3 = 0

3x = 3

Divide both sides by ;3;

x = 1

So in ( x,y) form the answer is ( 1,3).

A DECADE is a period of TEN years.

Hence 6 decades = 6 x 10 = 60 years.

In a Table form

10 years = 1 Decade

10 decades = 1 century ( 100 years)

10 centuries = 1 millenium ( 1000 years).

y=3x

3x + 2y = 8

This is an equation.

It could be the equation of a line.

It is 7+8x simplified

A biconditional statement is a compound statement consisting of a double conditional: "She's going to the party if and only if I'm going." (I'm going if she's going and vice-versa.) Thus, it's basically the conjunction of two conditionals, where the antecedent of either is the consequent of the other.

one solution

write down the 2 equations

eq 1: 2x + y = 5

eq 2: 2y + x = 4

get a value for x from eq 2

x = 4 - 2y

substitute 4 - 2y for x in eq 1

2(4 - 2y) + y = 5

8 - 4y +y = 5

-3y = -3

y=1

substitute 1 for y in eq 2

2(1) + x = 4

2 + x = 4

x = 4-2

x = 2

x^(2) - 4y^(2)

Before calculating , we note

#1 ' There is a negative sign between the two squares. So it will factor

#2 ' '4' is the square of '2' . So we can redraw the terms as ( 2y)^2

Hence

x^(2) - (2y)^2)

This now satisfies the two conditions above. . So it will factor to

( x - 2y)(x + 2y)

Note the different signs in each bracket .

You hve asked for it to be solved!!! To solve you need to equate the terms to a value. In this case use '0'

Hence

(x - 2y)(x + 2y) = 0

Taking each bracket in turn

x - 2y = 0

x = 2y or 2 = x/y or y = x/2

Then

x + 2y = 0

x = -2y or -2/x/y or y = x/-2

Are the possible forms of solution.

NB If you have two squared terms and a positive (+) between them, then it does NOT factor.

NNB Think of the Pythagorean Equation

a^2 + b^2 = h^2 This DOES NOT factor.

However

a^2 = h^2 - b^2 (Algebraic rearrangement) , DOES factor to

a^2 = (h - b)(h + b)

4x^(2) + 28xy + 49y^(2) ->

(2x)^(2) + 28xy + (7y)^2

Split into brackets

( 2x + 7y)(2x + 7y)

If you applyuFOIL you will find toy come to '28xy'.

The clue to this problem is to note that '4' ^ '49' are both squared numbers.

Assuming that the terms, a and AA, are commutative, It is 1 + a^3 + (AA)^3 - 3aAA