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3 years ago

(a²-4) (9-b²) +24ab algebraic factorization

Mathematics

1 answer:

Anastasy [175]3 years ago

7 0

Answer: -a2b2 + 9a2 + 24ab + 4b2 - 36

Step-by-step explanation:

A+B) • (A-B) =

A2 - AB + BA - B2 =

A2 - AB + AB - B2 =

A2 - B2

AB = BA is the commutative property of multiplication.

- AB + AB equals zero and is therefore eliminated from the expression.

Pharaphrase it if used.

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If (8, −9) and (6, −3) are the endpoints of the diameter of a circle, what is the equation of the circle?

Umnica [9.8K]

$(x-7)^{2} + (y+6)^{2} = 10$ is the equation of the required circle.

Step-by-step explanation:

Step 1 :

Let A = (8,-9) and B = (6,-3) be the endpoints of the diameter of the given circle.

We need to determine the circle's equation with this diameter

Step 2 :

The mid point of the diameter will be center of the required circle.

Let M = (x,y) be the mid point of the circle.

So we have x = (8+6)÷ 2 , y = ((-9) + (-3)) ÷ 2

M = ( 7, -6) is the midpoint of the diameter and the center of the circle.

Step 3 :

The radius of the circle is distance between midpoint and any one of the end point of the diameter that is distance between point A(8,-9) and M ( 7,-6)

Distance between the 2 points $(x_{1} ,y_{1}) and (x_{2} ,y_{2})$ is given by

$\sqrt{(x_{2}-x_{1})^{2}+ (y_{2}-y_{1})^{2} }$

So distance between A(8,-9) and M ( 7,-6) = $\sqrt{(7-8)^{2}+ (-6-(-9))^{2} }$

= $\sqrt{(1)^{2}+ (3)^{2} } = \sqrt{10 }$

Hence the radius r is $\sqrt{10}$

Step 4 :

The equation of circle with center (a,b) = (7,-6) and radius r = $\sqrt{10}$ is given by

$(x-a)^{2} + (y-b)^{2} = r^{2}$

=> $(x-7)^{2} + (y-(-6))^{2} = (\sqrt{10} )^{2}$

=> $(x-7)^{2} + (y+6)^{2} = 10$ is equation of the required circle.

Step 5 :

Answer :

$(x-7)^{2} + (y+6)^{2} = 10$ is equation of the required circle.

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If it diameter we’re reduced by half it’s volume would be

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Well lets work it out.
Diameter = 2 * Radius
Diameter * 1/2 = 1/2 * 2 * Radius
That would mean that the Radius would also be halved.
(1/2 * Radius)^2 * pi * height = volume, and 0.5^2 = 1/4, so its volume is reduced by a fourth

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Answer:

h/g

Step-by-step explanation:

we know that

The cotangent of angle G is equal to divide the adjacent side angle G to the opposite side angle G

cot(G)=h/g

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(a²-4) (9-b²) +24ab algebraic factorization​

(a²-4) (9-b²) +24ab algebraic factorization