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Rzqust [24]
3 years ago
14

$80 at 12%for 2years

Mathematics
1 answer:
Ivan3 years ago
8 0

<em>Look</em><em> </em><em>at</em><em> </em><em>the</em><em> </em><em>attached</em><em> </em><em>picture</em><em>⤴</em>

<em>Hope</em><em> </em><em>it</em><em> </em><em>will</em><em> </em><em>help</em><em> </em><em>y</em><em>o</em><em>u</em><em>.</em><em>.</em>

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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
What is the area of this figure?<br><br><br> 49.5 in²<br><br> 66.5 in²<br><br> 84 in²<br><br> 91 in²
zubka84 [21]

The given figure can be divided in two parts 1) Square with side 7 in 2) A right triangle with base 12 in and height 7 in.

1) Area of square = side^{2}

Side of the square is 7 in.

Area = 7^{2} =49in^{2}

2) Area of triangle = \frac{1}{2} .base . height

Area of triangle =\frac{1}{2} (12)(7) =42in^{2}

Area of polygon= Area of square+ Area of triangle

Area of polygon = 49+42 =91 square in.

Area = 91in^{2}

3 0
3 years ago
Read 2 more answers
The dimensions of a right rectangular prism are 3/2 ft, 1/2 ft, and 2ft. What is the volume of this prism ?
r-ruslan [8.4K]

Answer:

v=1.5

Step-by-step explanation:

1.5*0.5*2=1.5

can i have brainliest

5 0
3 years ago
Will give brainlest<br> What is the result of adding these two equations? − 2x+7y= −5 −2x−4y= 6
Inga [223]

Answer:

All you have to do is combine the like terms. Once you do that you get: -4x+3y=-11

4 0
3 years ago
Jefferson Park sits on one square city block that measures 300ft on each side. Sidewalks join opposite corners. About how long i
Alexxandr [17]
You have a 300 feet side length square and you need to calculate the length of the diagonal. When you split the square along one diagonal you get triangles, so you can apply Pythagoras' Theorem, with the hypotenuse as the needed diagonal.
a²+b²=c²
300²+300²=c²
2*300²=c²
√(2*300²)=c
√(2) * √(300²)=c
√(2) * 300=c
c~424.26 ft which is the solution/option c
5 0
3 years ago
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