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Explain the equation a^2 + b^2 = c^2?

Pythagorean triples uses this formula a^2+ b^2= c^2, what does the ^ mean?

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^ means "raised to the power of."
a^2 is "a raised to the power of 2" or "a squared."

Posted on Jul 12, 2013


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The sum of two square numbers is equal to a squar

9+16=25 =5^2
You can write 3^2+4^2=5^2
(3,4,5) form a Pythagorean triple.
If you construct a right triangle with legs =3 and 4, the hypotenuse will be 5, because in a right triangle the Pythagorean theorem holds true.
It says (leg_1)^2+l(leg_2)^2=(hypotenuse)^2
Other Pythagorean triples are (5,12,13), (9,40,41)
Here is a link to more info on Pythagorean triples

Pythagorean Triples Advanced

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Write the equation in standard form for the circle passing through ( - 6,2) centered at the origin

The equation of a circle is (x-h)^2 + (y-k)^2 = r^, where h and k are the x and y coordinates of the centre of the circle. However the centre is the origin, so we have x^2 + y^2 = r^2.

Now, we need to figure out r. However, we can calculate r because it is the distance from the origin to (-6,2). We can use Pythagorean Theorum, a^2 + b^2 = c^2, were a is -6 and b is 2. We get 6^2 + 2^2 =c^2. c^2= 40.

Thus, the formula of the circle is x^2 + y^2 = 40.

Good luck.

Apr 14, 2014 |

1 Answer

What does the equation mean a^2 b^2 = c^2?

With the insertion of a plus sign it's "a squared plus b squared is equal to c squared." Applied to the Pythagorean Theorem it's "the sum of the squares of the sides is equal to the square of the hypotenuse."

Jul 12, 2013 | Office Equipment & Supplies

1 Answer


Pythagorean Theorem?
The formula should be L=(P-2W)/2 or L= (P/2)-W
P is the perimeter of the rectangle, L its length, and W the width. But where do you hook the Pythagorean Theorem here? In other words, where is the question you are asking?

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How do i factor

This calculator is unable to factor a polynomial expression.
In general there are a few factoring methods
  1. Factor by grouping terms
  2. Factor by completing the square (quadratic polynomial)
  3. Factor by finding two integers such their sum is equal to the coefficient of the middle term, and their product is equal to the third (constant term). This is valid for a quadratic polynomial where the leading coefficient (of the x^2 term) is equal to 1. X^2+SX+P
A cubic equation can be solved algebraically, although two solutions may be complex. Use the Cardano formulas. A quartic equation can be solved by the formulas for the quadratic equation, if you transform the quartic equation to look like A(X^2)^2 + B(X^2) +C=0

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I knowi can find a linear equation if i have: two points {for example A(0,0) and B(1,1) the equation is y=x} or one point {for example C(0,2)} and a slope {for example m=2) the equaton is y=2x+2 can my...

The general answer is no. However the calculator can be used to find the slope and the y-intercept. You write the formula for the rate of change (a) and use the calculator to calculate it. Then you use the formula to find the y-intercept.
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The total cost of C of producing n articles per hour in a factory is given by the formula C = a + bn where a and b are constants When 10 articles are produced the total cost is 320 when two are produced...

For this type of problem, a equals the constant cost of operation (monthly rent..etc) and b equals the cost to manufacture the items.

first equation: 320 = a + b(10)
second equation: 520 = a +b(20)

320 = a + 10b
520 = a + 20b subtract equation 2 from equation 1

200 = -10b divide by -10

20 = b plug b into one of the equations

320 = a +(20)(10) multiply

320 = a +200 subtract 200

120 = a

Let me know if i need to explain further.

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Change csc to 1/sin. Find a common denominator and add the two left terms.
1/sin - sin = (1 -sin^2)/sin. Rewrite formula
(1 - sin^2)/sin = cos^2/sin Divide out the /sin.
1 - sin^2 = cos^2 Rearange.
1 = cos^2 + sin^2 Yes, that's true. It's like the Pythagorean formula.

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