What is 2,108 x 35 please write in comments below

Find the standard equation of a sphere that has diameter with the end points given below. (3,-2,4) (7,12,4)

DiKsa [7]

Answer:

The standard equation of the sphere is $(x-5)^{2} + (y-5)^{2} + (z-4)^{2} = 53$

Step-by-step explanation:

From the question, the end point are (3,-2,4) and (7,12,4)

Since we know the end points of the diameter, we can determine the center (midpoint of the two end points) of the sphere.

The midpoint can be calculated thus

Midpoint = $(\frac{x_{1} + x_{2} }{2}, \frac{y_{1} + y_{2} }{2}, \frac{z_{1} + z_{2} }{2})$

Let the first endpoint be represented as $(x_{1}, y_{1}, z_{1})$ and the second endpoint be $(x_{2}, y_{2}, z_{2})$ .

Hence,

Midpoint = $(\frac{x_{1} + x_{2} }{2}, \frac{y_{1} + y_{2} }{2}, \frac{z_{1} + z_{2} }{2})$

Midpoint = $(\frac{3 + 7 }{2}, \frac{-2+12 }{2}, \frac{4 + 4 }{2})$

Midpoint = $(\frac{10 }{2}, \frac{10}{2}, \frac{8 }{2})\\$

Midpoint = $(5, 5, 4)$

This is the center of the sphere.

Now, we will determine the distance (diameter) of the sphere

The distance is given by

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

$d = \sqrt{(7 - 3)^{2} +(12 - -2)^{2} + (4- 4)^{2}$

$d = \sqrt{(4)^{2} +(14)^{2} + (0)^{2}$

$d = \sqrt{16 +196 + 0$

$d =\sqrt{212}$

$d = 2\sqrt{53}$

This is the diameter

To find the radius, r

From $Radius = \frac{Diameter}{2}$

$Radius = \frac{2\sqrt{53} }{2}$

∴ $Radius = \sqrt{53}$

r = $\sqrt{53}$

Now, we can write the standard equation of the sphere since we know the center and the radius

Center of the sphere is $(5, 5, 4)$

Radius of the sphere is $\sqrt{53}$

The equation of a sphere of radius r and center $(h,k,l)$ is given by

$(x-h)^{2} + (y-k)^{2} + (z-l)^{2} = r^{2}$

Hence, the equation of the sphere of radius $\sqrt{53}$ and center $(5, 5, 4)$ is

$(x-5)^{2} + (y-5)^{2} + (z-4)^{2} = \sqrt{(53} )^{2}$

$(x-5)^{2} + (y-5)^{2} + (z-4)^{2} = 53$

This is the standard equation of the sphere

6 0

3 years ago

Georgie has a bushel basket of apples to sell at her fruit stand.1 out of every 5 can not be sold because they are not ripe yet.

Vinil7 [7]

20 % of apples are not ripe

Solution:

Georgie has a bushel basket of apples to sell at her fruit stand

1 out of every 5 can not be sold because they are not ripe yet

To find: percent of her apples that are not ripe

From given statement,

1 out of every 5 is not sold because it is not riped yet

So, 1 out of evry 5 apples are not riped

The fraction is given as:

$\text{Apples that are not ripe } = \frac{1}{5}$

We have to find the percent of apples that are not ripe

Percentage is given as:

$\text{Percent of apples that are not ripe} = \text{apples that are ripe } \times 100\\\\\text{Percent of apples that are not ripe} = \frac{1}{5} \times 100 = 20 \%$

Thus 20 % of apples are not ripe

6 0

4 years ago

Solve for the value of each letter.

creativ13 [48]

Answer:

Step-by-step explanation:

1] 6x + 10 = 28 {subtract 10 from both sides}

6x + 10 -10 = 28 - 10

6x = 18 {Divide both sides by 6}

6x/6 = 18/6

x = 3

2] -2m - 4 = 8 {Add 4 to both side}

-2m - 4 + 4 = 8 + 4

-2m = 12 {Divide both sides by -2}

-2m/-2 = 12/-2

m = -6

3] x + x + 2x = 48 {add the like terms}

4x = 48 {divide both sides by 4}

4x/4 = 48/4

x = 12

4] 3y +4 +3y - 6 = 34 {add the like terms}

6y - 2 = 34 {Add 2 to both side}

6y - 2 + 2 = 34 +2

6y = 36 {divide both sides by 6}

6y/6 = 36/6

y = 6

5]9(w - 6) = 36 {divide both sides by 9}

[9(w - 6)]/9 = 36/9

w - 6 = 4 {Add 6 to both sides}

w - 6 + 6 = 4 + 6

w = 10

4 0

3 years ago

Read 2 more answers

Which is the direct linear variation equation for the relationship?

jenyasd209 [6]

I'm going to guess but I believe it is A

7 0

3 years ago

3 (5р — 3) = 5 (p — 1)

Akimi4 [234]

Answer:

15p-9=5p-5

Step-by-step explanation:

i expanded the brackets I think this is correct if you wanted to expand it

8 0

3 years ago