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OverLord2011 [107]
3 years ago
6

Does anyone know the answer to this question?

Mathematics
1 answer:
cestrela7 [59]3 years ago
5 0
The answer is A; g(x) = |x+4| - 2
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Find equations of the spheres with center(3, −4, 5) that touch the following planes.a. xy-plane b. yz- plane c. xz-plane
postnew [5]

Answer:

(a) (x - 3)² + (y + 4)² + (z - 5)² = 25

(b) (x - 3)² + (y + 4)² + (z - 5)² = 9

(c) (x - 3)² + (y + 4)² + (z - 5)² = 16

Step-by-step explanation:

The equation of a sphere is given by:

(x - x₀)² + (y - y₀)² + (z - z₀)² = r²            ---------------(i)

Where;

(x₀, y₀, z₀) is the center of the sphere

r is the radius of the sphere

Given:

Sphere centered at (3, -4, 5)

=> (x₀, y₀, z₀) = (3, -4, 5)

(a) To get the equation of the sphere when it touches the xy-plane, we do the following:

i.  Since the sphere touches the xy-plane, it means the z-component of its centre is 0.

Therefore, we have the sphere now centered at (3, -4, 0).

Using the distance formula, we can get the distance d, between the initial points (3, -4, 5) and the new points (3, -4, 0) as follows;

d = \sqrt{(3-3)^2+ (-4 - (-4))^2 + (0-5)^2}

d = \sqrt{(3-3)^2+ (-4 + 4)^2 + (0-5)^2}

d = \sqrt{(0)^2+ (0)^2 + (-5)^2}

d = \sqrt{(25)}

d = 5

This distance is the radius of the sphere at that point. i.e r = 5

Now substitute this value r = 5 into the general equation of a sphere given in equation (i) above as follows;

(x - 3)² + (y - (-4))² + (z - 5)² = 5²  

(x - 3)² + (y + 4)² + (z - 5)² = 25  

Therefore, the equation of the sphere when it touches the xy plane is:

(x - 3)² + (y + 4)² + (z - 5)² = 25  

(b) To get the equation of the sphere when it touches the yz-plane, we do the following:

i.  Since the sphere touches the yz-plane, it means the x-component of its centre is 0.

Therefore, we have the sphere now centered at (0, -4, 5).

Using the distance formula, we can get the distance d, between the initial points (3, -4, 5) and the new points (0, -4, 5) as follows;

d = \sqrt{(0-3)^2+ (-4 - (-4))^2 + (5-5)^2}

d = \sqrt{(-3)^2+ (-4 + 4)^2 + (5-5)^2}

d = \sqrt{(-3)^2 + (0)^2+ (0)^2}

d = \sqrt{(9)}

d = 3

This distance is the radius of the sphere at that point. i.e r = 3

Now substitute this value r = 3 into the general equation of a sphere given in equation (i) above as follows;

(x - 3)² + (y - (-4))² + (z - 5)² = 3²  

(x - 3)² + (y + 4)² + (z - 5)² = 9  

Therefore, the equation of the sphere when it touches the yz plane is:

(x - 3)² + (y + 4)² + (z - 5)² = 9  

(b) To get the equation of the sphere when it touches the xz-plane, we do the following:

i.  Since the sphere touches the xz-plane, it means the y-component of its centre is 0.

Therefore, we have the sphere now centered at (3, 0, 5).

Using the distance formula, we can get the distance d, between the initial points (3, -4, 5) and the new points (3, 0, 5) as follows;

d = \sqrt{(3-3)^2+ (0 - (-4))^2 + (5-5)^2}

d = \sqrt{(3-3)^2+ (0+4)^2 + (5-5)^2}

d = \sqrt{(0)^2 + (4)^2+ (0)^2}

d = \sqrt{(16)}

d = 4

This distance is the radius of the sphere at that point. i.e r = 4

Now substitute this value r = 4 into the general equation of a sphere given in equation (i) above as follows;

(x - 3)² + (y - (-4))² + (z - 5)² = 4²  

(x - 3)² + (y + 4)² + (z - 5)² = 16  

Therefore, the equation of the sphere when it touches the xz plane is:

(x - 3)² + (y + 4)² + (z - 5)² = 16

 

3 0
3 years ago
The circumference (C) of a circle is 16 cm. Which formula can you use to find the diameter (d) if you know that C = πd?
elixir [45]
Okay i'm confused on the question but i do know the answer of the diameter
 if that help the diameter would be d=5.09cm
i hope this helps 
5 0
3 years ago
Read 2 more answers
Rabekah is filling a cube-shaped box with small cubes. the volume of each of these cubes is 1 cubic centimeter. She has already
Vinvika [58]
Well it shows that the main cube is 9 blocks tall. It is a perfect cube, not a rectangular prism or anything, so every side is the same. So 9 cubed. Or, in other words, 9*9*9
8 0
3 years ago
I WILL AWARD BRAINLIEST!!! PLEASE HELP!!
11111nata11111 [884]

Answer:

0,-1

Step-by-step explanation:

bruh u know what a whole number is? also its less than not equal or less.

3 0
3 years ago
Read 2 more answers
Suppose we have a binomial experiment in which success is defined to be a particular quality or attribute that interests us.
mestny [16]

For a binomial experiment in which success is defined to be a particular quality or attribute that interests us, with n=36 and p as 0.23,  we can approximate p hat by a normal distribution.

Since n=36 , p=0.23 , thus q= 1-p = 1-0.23=0.77

therefore,

n*p= 36*0.23 =8.28>5

n*q = 36*0.77=27.22>5

and therefore, p hat can be approximated by a normal random variable, because n*p>5 and n*q>5.

The question is incomplete, a possible complete question is:

Suppose we have a binomial experiment in which success is defined to be a particular quality or attribute that interests us.

Suppose n = 36 and p = 0.23. Can we approximate p hat by a normal distribution? Why? (Use 2 decimal places.)

n*p = ?

n*q = ?

Learn to know more about binomial experiments at

brainly.com/question/1580153

#SPJ4

3 0
2 years ago
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