Explanation: A midsegment of a triangle is a segment connecting the midpoints of two sides of a triangle. This segment has two special properties. It is always parallel to the third side, and the length of the midsegment is half the length of the third side.

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4 0

2 years ago

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Find equations of the spheres with center(1, −1, 6)that touch the following planes.a) xy-planeb) yz-planec) xz-plane

Misha Larkins [42]

Given :

Center of sphere , C( 1 , -1 , 6 ) .

To Find :

Find equations of the spheres with center (1, −1, 6) that touch the following planes.a) xy-plane b) yz-plane c) xz-plane .

Solution :

Distance of the point from xy-plane is :

d = 6 units .

So , equation of circle with center C and radius 6 units is :

$(x-1)^2+(y-(-1))^2+(z-6)^2=6^2\\\\(x-1)^2+(y+1)^2+(z-6)^2=36$

Distance of point from yz-plane is :

d = 1 unit .

So , equation of circle with center C and radius 1 units is :

$(x-1)^2+(x+1)^2+(z-6)^2=1^2\\\\(x-1)^2+(x+1)^2+(z-6)^2=1$

Distance of point from xz-plane is :

d = 1 unit .

So , equation of circle with center C and radius 1 units is :

$(x-1)^2+(x+1)^2+(z-6)^2=1^2\\\\(x-1)^2+(x+1)^2+(z-6)^2=1$

Hence , this is the required solution .

4 0

2 years ago

Determine the discriminant for the given equation x^2+4x+5=0. Then describe the roots(how many and what type).

Fed [463]

Discriminant = b^2 - 4ac, where a, b and c come from the form of the quadratic equation as ax^2 + bx + c

Discriminant = (4)^2 - 4(1)(5)
= 16 - 20
= -4

-4 < 0, therefor there are no roots

(If the discriminant = 0, then there is one root
If the discriminant > 0, there are two roots, and if it is a perfect square (eg. 4, 9, 16, etc.) then there are two rational roots
If the discriminant < 0, there are no roots)

3 0

2 years ago