Answer:
(x-1)^2+(y+1)^2=3
Step-by-step explanation:
x² + y2 - 2x + 2y - 1 = 0
add the 1 to get it to the other side of the equation
x² + y2 - 2x + 2y = +1
group the x's and y's
(x² -2x) + (y2+2y) = +1
then you'll complete the square on the -2x and + 2y. that just means divide by two and then raise it to the 2nd power.
so (-2/2)^2 and (+2/2)^2
(x²-2x+1)+(y2+2y+1) = 1+1+1
you add the one's to the other side because whatever is done to one side must be done to the other
you'll then need to factor again.
(x-1)^2+(y+1)^2=3
to factor it take one of your squared x's, the sign of the middle term within the parentheses , then the square root of the last term within the parentheses. remeber to put your ^2 (raised to the 2nd power) outside of the parentheses when you finish.
Considering balloon to be an spherical object
Volume of sphere = 
, where r is the radius of sphere.
After 19 minutes ,If radius of balloon changes from r to R, the Volume changes from V to V'.
V'= 
,
As given,rate at which the air leaked out of the balloon (in liters of air per minute) was half of the rate at which Vavilen inflated the balloon.
Also, 
Now, again the radius changes from R to r.So, Volume changes from V' to Back to V.
Time taken by the balloon to deflate = 38 minutes
But there is no relation between time and volume of Balloon.
So, we can't predict at which rate balloon is deflating or inflating.Apart from the statement given in Question:
remember to use SOH CAH TOA. THE SOLUTION THAT I GOT CAME OUT AS 15/8
The exponent symbol when typing is ^. so I so rewrite this for you.
(15x^8 / 24y^5) / (4x^4 / 8y^2)
I assumed you meant 8y squared because you said 8 squared.
now when we divide by a fraction, we can actually multiply by it's reciprocal and get the same thing. The word reciprocal really just means flip it over. so:
(15x^8 / 24y^5) * (8y^2 / 4x^4)
let's reduce the coefficients ( the numbers in front of the x and y) to make it easier.
We have 15/24 which can be reduced to 5/8
and 8/4 which is 2/1
so:
(5x^8 / 8y^5) * (2y^2 / x^4)
multiply numerator and denominator
(10x^8y^2) / (8x^4y^5)
now reduce coeffient. 10/8 is 5/4
reduce x: x^8/x^4 is x^4
reduce y: y^2/y^5 is 1/y^3
now put together
5x^4 / 4y^3
so C
11. x² - 7x = 0
x(x) - x(7) = 0
x(x - 7) = 0
x = 0 or x - 7 = 0
+ 7 + 7
x = 7
Solution Set: {0, 7}
12. 3x² - 4x = 20x + 27
+ 4x + 4x
3x² = 24x + 27
3x² - 24x - 27 = 0
x = -(-24) ± √((-24)² - 4(3)(-27))
2(3)
x = 24 ± √(576 + 324)
6
x = 24 ± √(900)
6
x = 24 ± 30
6
x = 4 ± 5
x = 4 + 5 or x = 4 - 5
x = 9 or x = -1
Solution Set: {9, -1}
