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MAVERICK [17]
3 years ago
6

Solve the equation. X+3.5 = 10 A.X = 13.5 B. X = 7.5 C. X = 6.5 D. X = 30.5

Mathematics
2 answers:
Juliette [100K]3 years ago
6 0

Answer:

the answer is C

Step-by-step explanation:

its making write more so yeah

elena-s [515]3 years ago
5 0

Answer:

x=6.5

Step-by-step explanation:

subtract 3.5 from 10 and it gives you 6.5

:)

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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
Find the slope (0, -3) and (9, 0) PLEASE SHOW YOUR WORK, WILL MARK BRAINLEIST
Flura [38]
<h3>Answer: slope = 1/3</h3>

===================================================

Work Shown:

Use the slope formula to get

m = (y2 - y1)/(x2 - x1)

m = (0 - (-3))/(9 - 0)

m = (0 + 3)/(9 - 0)

m = 3/9

m = 1/3

----------------

Basically we subtract the y coordinates, and do the same for the x coordinates as well (subtract in the same order). Afterward, divide the two results. Reduce the fraction as much as possible.

A slope of 1/3 means we move up 1 unit each time we move to the right 3 units.

The slope being positive means the line goes uphill as you read from left to right.

6 0
3 years ago
Please I need help with this question.<br>No 22. Is very important.<br>Thank you.​
kvv77 [185]

Answer:

C. 132m^3

Step-by-step explanation:

Height = 4

Length = 6

Breadth = 7

Note : We were asked to find volume of the cuboid

Since, it has a base in the shape of a right angle triangle , we need to find the Area of the trapezium before calculating the total volume.

 Step 1

Find the area of the trapezium

Area of a trapezium = \frac{1}{2} (a+b)h

\frac{1}{2} (4+7)*4

\frac{1}{2} (11)4\\

\frac{1}{2} *44\\= 22

 Step 2

Calculate the volume of the cuboid

Volume of a cuboid =length× breadth × height

In this case , the volume will be our length ×  Area of a trapezium

 V= 6 × 22

V = 132m^3

6 0
3 years ago
Where do martians leave thier spaceships
kari74 [83]
They leave it on the moon.
8 0
3 years ago
Read 2 more answers
I am a french soldier who became a major ally to the Continental Army, and buddies with George Washington! Who am I
horsena [70]

Answer:Marquis Lafayette

Step-by-step explanation:

This shouldn't be in mathematics?

8 0
3 years ago
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