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skad [1K]
3 years ago
11

Including 6% sales tax, an inn charges $135.68 per night. Find the inns nightly cost

Mathematics
2 answers:
Angelina_Jolie [31]3 years ago
6 0

Answer:

144 dollars

Step-by-step explanation:

Andru [333]3 years ago
4 0
135.68(1+0.06)^1= 144
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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
How many proper subsets does the set T = {i, c, j, e} have?
Gala2k [10]
Number of proper subsets = 2^number of elements- 1
= 2^n - 1
No of elements = 4
2^4-1 = 16-1 = 15
5 0
3 years ago
Help help help help help
Blizzard [7]

Answer:

x = 12

Step-by-step explanation:

Becuase 6/12 = 2 and 9 + 2 = 11

12

7 0
2 years ago
Please help! I'll rate 5 stars, if possible give brainliest, and give a thanks.
muminat

Answer:

2x+20 + x+40 = 180

Step-by-step explanation:

The angles are supplementary so they add to 180

2x+20 + x+40 = 180

3 0
3 years ago
Read 2 more answers
At a bake sale, as student spent $11.00 buying 3 brownies and 5 cookies. His friend spent $3.95 buying 1 brownie and 2 cookies.
dybincka [34]

Answer:

$2.25

Step-by-step explanation:

Let "b" be the price of 1 brownie and "c" the price of 1 cookie.

At a bake sale, a student spent $11.00 buying 3 brownies and 5 cookies. Symbolicaly,

3 b + 5 c = 11.00   [1]

His friend spent $3.95 buying 1 brownie and 2 cookies. Symbolicaly,

1 b + 2 c = 3.95

b = 3.95 - 2c   [2]

If we replace [2] in [1], we get

3 (3.95 - 2c) + 5 c = 11.00

11.85 - 6c + 5c = 11.00

c = 0.85

If we replace c = 0.85 in [2], we get

b = 3.95 - 2 (0.85) = 2.25

8 0
3 years ago
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