Proofs

6 and 1

Because Corresponding Parts of Congruent Triangles, there are five ways to prove that two triangles are congruent. Show that all sides are congruent. (SSS) Show that two sides and their common angle are congruent. (SAS) Show that two angles and their common side are congruent. (ASA) Show that two angles and one of the non common sides are congruent. (AAS) Show that the hypotenuse and one leg of a right triangle are congruent. (HL)

The question doesn't tell us where on earth the park is, so there's no way we can account for the convergence of the meridians, since the effect is less at the equator and most near the poles. So consider it a straight x-y problem on a plane.

If the park is placed at the origin of coordinates (0.0),
Flor lives at the point ( -3, 4 ), and Joey lives at the point ( 2, 8 ).

x-difference = 5, y-difference = 4

Distance between the points
= square root of [ (x-difference)2 + (y-difference)2 ]

= square root of (52 + 42 )
= square root (25 + 16 )
= square root (41)
= 6.403 miles (rounded)

it is the total (estimated) area of the universe, measured in either kilometers or meters

The 50/50 chance means there are two outcomes, and each on is equally likely. A coin has a 50% chance of coming up heads and 50% chance of coming up tails. If we have a number of events or outcomes, and little information to based which one is more likely to occur, we can assume that they are equiprobable events or outcomes. You can learn more by searching wikipedia under equiprobable.

Ramanujan number is the smallest natural number that can be can be expressed as a sum of two perfect cubes in two different ways:-

123 + 13 = 1728+1 =1729 103 + 93 = 1000+729 =1729

It is a field of math that uses calculus, specifically, differential calc, to study geometry. Some of the commonly studied topics in differential geometry are the study of curves and surfaces in 3d

The diagonals arenotthe sides. They're lines you draw from one angle of the parallelogram to the angle opposite it. So if you have parallelogram ABCD, your diagonals are AC and BD, because AB, BC, CD, and DA are all sides.

If the hypotenuse is the square root of three, then the legs are (root 6)/2.

If the hypotenuse is 12, then the legs are 6(root 2).

This is because, for any given right isosceles triangle, the length of the hypotenuse x is root two times the length of the legs.

Any line that enters a circle (and is not a tangent) must cross its boundary twice; once to enter, once to exit. Since a secant is a line segment that joins two different points on a curve, such a line as above is a secant.

There is NO equation for the area of a sphere

Assuming you mean surface area, the surface area of a sphere of radius r is 4πr^2.

100000000000 seconds = 1666666666.6666667 minutes = 1666666666 minutes and 40 seconds

1666666666 minutes = 27777777.766666667 hours = 27777777 hours and 46 minutes

277777777 hours = 1157407.375 days and 9 hours

1157407 days = 3168 years and 295 days

So 100000000000 seconds = 3168 years, 295 days, 9 hours, 46 minutes and 40 seconds ago.

An example:

Laser beams are sometimes modelled as being infinitely thin but in reality they do have some width and this width changes with respect to distance from the laser source. Using algebra it is possible to calculate the distance where the laser beam has a minimum width. This is useful because laser devices are used to read information on cd's and dvd's so minimizing the beam width at the cd/dvd will allow for more data to be stored on the cd/dvd.

Another example:

A fat man wants to take a boat ride. If he knows the dimensions of the boat then he can calculate the buoyant force on the boat and compare it to the gravitational force due to his mass. If the former is less than the latter, the boat will sink and he will get wet which will ruin his new pants (they dissolve in water)

Final example:

You have a cannon that shoots blocks of cheese and you want to shoot some smelly cheese through someone's bedroom window. You can use algebra to calculate the angle your cannon should make with the ground in order to hit your target and hence, give someone a smelly surprise.

sampling theorem is defined as , the sampling frequency should be greater than or equal to 2*maximum frequency, and the frequency should be bounded..

i,e

fs=2*fmax

where fs= sampling frequency

Let's start out with the basic inequality 1 < 3 < 4.

Now, we'll take the square root of this inequality:

1 < √3 < 2.

If you subtract all numbers by 1, you get:

0 < √3 - 1 < 1.

If √3 is rational, then it can be expressed as a fraction of two integers, m/n. This next part is the only remotely tricky part of this proof, so pay attention. We're going to assume that m/n is in its most reduced form; i.e., that the value for n is the smallest it can be and still be able to represent √3. Therefore, √3n must be an integer, and n must be the smallest multiple of √3 to make this true. If you don't understand this part, read it again, because this is the heart of the proof.

Now, we're going to multiply √3n by (√3 - 1). This gives 3n - √3n. Well, 3n is an integer, and, as we explained above, √3n is also an integer; therefore, 3n - √3n is an integer as well. We're going to rearrange this expression to (√3n - n)√3 and then set the term (√3n - n) equal to p, for simplicity. This gives us the expression √3p, which is equal to 3n - √3n, and is an integer.

Remember, from above, that 0 < √3 - 1 < 1.

If we multiply this inequality by n, we get 0 < √3n - n < n, or, from what we defined above, 0 < p < n. This means that p < n and thus √3p < √3n. We've already determined that both √3p and √3n are integers, but recall that we said n was the smallest multiple of √3 to yield an integer value. Thus, √3p < √3n is a contradiction; therefore √3 can't be rational and so must be irrational.

Q.E.D.

There are 22 ways to make change from a dollar using nickels, dimes, and quarters.

1. 4 q

2. 10 d

3. 20 n

4. 2 q , 5 d

5. 3 q , 2 d , 1 n

6. 1 q , 7 d, 1 n

7. 9 d, 2 n

8. 8 d, 4 n

9. 7 d, 6 n

10. 6 d , 8 n

11. 5 d , 10 n

12. 4 d , 12 n

13. 2 d , 16 n

14. 1 d , 18 n

15. 5 n , 3 q

16. 3 n , 1 q , 6 d

17. 7 n , 1 q , 4 d

18. 9 n , 1 q , 3 d

19. 11 n , 1 q , 2 d

20. 13 n , 1 q , 1 d

21. 14n , 3 d

22. 15n , 1 q

There are many sequences with this property: The sequence with every term equal to 0 has this property. In fact the sequence can be anything you like as long you make sure the 58th term is the sum of the first 10 terms.

A more specific case:

If you are dealing with an arithmetic sequence, i.e. a sequence of the form s(n)=a+bn for constants a and b, we can derive a relationship between a and b:

s(1)+s(2)+...+s(10)=10a+55b

and

s(58)=a+58b

From this, it follows that if s(1)+s(2)+...+s(10)=s(58), then we have 10a+55b=a+58b, which implies that 3a=b. Again, there are infinitely many sequences with this property, but if it is an arithmetic sequence, it will be of the general form s(n)=a+3an=a(3n+1)

A three dimensional oval is simply called an egg, or more mathematically, an ovoid. A three dimensional ellipse (a more symmetric oval) is called a prolate spheroid, or oblate spheroid, depending on how the ellipse is rotated.

Psycho-educational testing is a subset of psychological testing. Psychological testing may include assessment of intellectual functioning, achievement, learning disorders, personality, vocational aptitude and interest, and behaviors associated with neurological impairment. Usually, psycho-educational testing is an assessment that is focused on educational performance and that includes tests that measure intellectual functioning, perceptual-motor development, academic achievement, and personality screening with the goal of determining if the student has a learning disability and/or qualifies for special education services. This type of testing is provided by the public school system and also by private psychologists and, in some states, other mental health professionals, such as licensed professional counselors.

Invertible counterpoint The contrapuntal design of two or more voices in a polyphonic texture so that any of them may serve as an upper voice or as the bass. Invertible counterpoint involving two (three, four) voices is called double (triple, quadruple) counterpoint. http://www.answers.com/topic/invertible-counterpoint-music

Stress testing means increasing the load ,and cheking the performance at each level.

Load testing means at a time giving more load by the expectation and checking the performance at that leval.

Volume testing means first we have to apply initial load,then at certain time increase the load and check the performance.

Unit testing is a software testing method by which individual units of source code are tested to determine whether they are fit for use.

Deductive reasoning

In mathematics, a proof is a deductive argument for a mathematical statement. Deductive reasoning, unlike inductive reasoning, is a valid form of proof. It is, in fact, the way in which geometric proofs are written.

Such terms are called axioms, or postulates.Exactly which terms are defined to be axioms depends on the specific system used.