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Vikki [24]
3 years ago
13

The general form of the equation of a circle is x^2+y^2−4x−8y−5=0.

Mathematics
1 answer:
lakkis [162]3 years ago
5 0
X² - 4x    + y² - 8y    = 5

Complete the square:
x² - 4x + (4) +  y² - 8y + (16)    = 5 + (4) + (16)
→  (x - 2)²    +  (y - 4)²    = 25

Center: (2,4)
radius: √25 = 5
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Find the average value of the function f(x, y, z) = 5x2z 5y2z over the region enclosed by the paraboloid z = 9 − x2 − y2 and the
Katyanochek1 [597]
The paraboloid meets the x-y plane when x²+y²=9. A circle of radius 3, centre origin. 

<span>Use cylindrical coordinates (r,θ,z) so paraboloid becomes z = 9−r² and f = 5r²z. </span>

<span>If F is the mean of f over the region R then F ∫ (R)dV = ∫ (R)fdV </span>

<span>∫ (R)dV = ∫∫∫ [θ=0,2π, r=0,3, z=0,9−r²] rdrdθdz </span>

<span>= ∫∫ [θ=0,2π, r=0,3] r(9−r²)drdθ = ∫ [θ=0,2π] { (9/2)3² − (1/4)3⁴} dθ = 81π/2 </span>


<span>∫ (R)fdV = ∫∫∫ [θ=0,2π, r=0,3, z=0,9−r²] 5r²z.rdrdθdz </span>

<span>= 5∫∫ [θ=0,2π, r=0,3] ½r³{ (9−r²)² − 0 } drdθ </span>

<span>= (5/2)∫∫ [θ=0,2π, r=0,3] { 81r³ − 18r⁵ + r⁷} drdθ </span>

<span>= (5/2)∫ [θ=0,2π] { (81/4)3⁴− (3)3⁶+ (1/8)3⁸} dθ = 10935π/8 </span>

<span>∴ F = 10935π/8 ÷ 81π/2 = 135/4</span>
4 0
3 years ago
Write in slope form 2y = 24 ​
AlekseyPX

Answer:

  y  = 12

Step-by-step explanation:

The equation of the expression is given as;

              2y  = 24

We are to write in slope form';

    In slope form, an equation is expressed as;

             y = mx + c

where y and x are the intercept

               m is the slope

                c is the intercept

Now to write 2y = 24 in intercept form, we have;

                 2y  = 24

  divide both sides by 2;

                y  = 12

3 0
3 years ago
Find the equation of a line with the following characteristics: slope=1/2;goes through (4,-1)​
gizmo_the_mogwai [7]

Answer:

the answer is 9 14

Step-by-step explanation:

it's correct so then nine times blah equals 9 / 14

3 0
3 years ago
Which expression is equivalent
NeTakaya

Answer:

the first one

Step-by-step explanation:

7 0
3 years ago
Read 2 more answers
a shirt had a logo printed on the front. this logo increases the cost by 25% to £15. what was the original al cost of the shirt
DIA [1.3K]

Answer:

11.25

Step-by-step explanation:

15*(1-25%)=11.25

4 0
3 years ago
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