Determine whether the graph defines a function of x. Yes or No

Move values to the lines to complete the sentence about triangle p’ q’ r’

Citrus2011 [14]

Do u have an attachment?? :)

5 0

2 years ago

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

An observer (O) spots a plane (P) taking off from a local airport and flying at a 33° angle horizontal to her line of sight and

docker41 [41]

Answer:

the distance of the Bird (B) from the plane (P) is = 10779 ft

Step-by-step explanation:

From the given information:

a diagrammatic representation is attached below for better understanding and solution to the question.

From the diagram;

Let the Bird (B) be represent as A

The plane (P) be represented by B

The observer be represented by O

and the tower T be represented by C

we will see that:

$\overline {AB} \ \| \ \overline {OC}$

Also;

$\angle ABO = \angle BOC = 33^0$

AO = BC = 7000

Let consider the trigonometry of triangle BAO

tan θ = opposite/adjacent

tan 33° = 7000/x

0.6494 = 7000/x

x = 7000/0.6494

x = 10779.18

x = 10779 ft ( to the nearest whole number)

Thus; the distance of the Bird (B) from the plane (P) is = 10779 ft

7 0

3 years ago

A wire is ⅝ meters long. it is divided into 2 equal parts. what is the length of each part

mote1985 [20]

Answer:

5/16m long.

Step-by-step explanation:

5/8 ÷ 2/1
5/8 × 1/2
=5/16m long.

7 0

2 years ago

Read 2 more answers

HELP ME PLZ I WILL MARK LCM

Nataly [62]

Answer:

18

Step-by-step explanation:

Find the multiples of 9

9,18,27,36

Find the multiples of 6

6,12,18,24

The first common multiple is 18

8 0

3 years ago

Read 2 more answers