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shusha [124]
3 years ago
8

Someone please help me with this

Mathematics
1 answer:
Slav-nsk [51]3 years ago
7 0
So first we need to find out how many days we're looking at. The equation we need to use is ?x5=45 to which the answer is 9.
Now that we know the amount of days we simply multiply. 20x9=180

Therefore Preston has spent 180 minutes reading or 3 hours total
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Find the equation of the sphere centered at (-9,9, -9) with radius 5. Normalize your equations so that the coefficient of x2 is
olganol [36]
<h2><u>Answer</u>:</h2>

(a) x² + y² + z² + 18(x - y + z) + 218 = 0

(b) (x + 9)² + (y - 9)² + 56 = 0

<h2><u>Step-by-step explanation:</u></h2>

<em>The general equation of a sphere of radius r and centered at C = (x₀, y₀, z₀) is given by;</em>

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

<em>From the question:</em>

The sphere is centered at C = (x₀, y₀, z₀) = (-9, 9, -9) and has a radius r = 5.

<em>Therefore, to get the equation of the sphere, substitute these values into equation (i) as follows;</em>

(x - (-9))² + (y - 9)² + (z - (-9))² = 5²

(x + 9)² + (y - 9)² + (z + 9)² = 25      ------------------(ii)

<em>Open the brackets and have the following:</em>

(x + 9)² + (y - 9)² + (z + 9)² = 25

(x² + 18x + 81) + (y² - 18y + 81) + (z² + 18z + 81) = 25

x² + 18x + 81 + y² - 18y + 81 + z² + 18z + 81 = 25

x² + y² + z² + 18(x - y + z) + 243 = 25

x² + y² + z² + 18(x - y + z) + 218 = 0    [<em>equation has already been normalized since the coefficient of x² is 1</em>]

<em>Therefore, the equation of the sphere centered at (-9,9, -9) with radius 5 is:</em>

x² + y² + z² + 18(x - y + z) + 218 = 0

(2)  To get the equation when the sphere intersects a plane z = 0, we substitute z = 0 in equation (ii) as follows;

(x + 9)² + (y - 9)² + (0 + 9)² = 25

(x + 9)² + (y - 9)² + (9)² = 25

(x + 9)² + (y - 9)² + 81 = 25        [<em>subtract 25 from both sides</em>]

(x + 9)² + (y - 9)² + 81 - 25 = 25 - 25

(x + 9)² + (y - 9)² + 56 = 0

The equation is therefore, (x + 9)² + (y - 9)² + 56 = 0

6 0
3 years ago
How many times does 7 go in to 37
Tcecarenko [31]
The answer would be= 5.2857142857
8 0
3 years ago
Read 2 more answers
Brainliest if you guess my age :)
LenaWriter [7]

Answer:

14

Step-by-step explanation:

or 16

5 0
3 years ago
Read 2 more answers
IM SOOOO STUCKKKK HELLPPPPPPPPPPP!!
KonstantinChe [14]

Answer:

18

Step-by-step explanation:

x² = 16² + 30² - 2(16)(30)cos 30°

x² = 256 + 900 - 960(0.866)

x² = 1156 - 831.36

x² = 324.64

x = 18.02

Approx. 18

Please mark my answer as brainliest

3 0
3 years ago
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There are 4 blue marbles, 8 red marbles and 5 green marbles. Write a part to whole ratio comparing green marbles.
fredd [130]

Answer:

5:17

Step-by-step explanation:

there are 17 total marbles and 5 that are green. The part is 5 and the whole is 17.

4 0
2 years ago
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