Answer:
Change in area=24
-48
Step-by-step explanation:
Let s will be the side of square and r will be the radius of circle.
Then two given conditions are
1)dr/dt=2 m/s
2)ds/dt=1 m/s
Area enclosed=(Area of square)-(Area of circle)
Area of square=
Area of circle=
Area enclosed=
dA/dt=2
r(dr/dt)-2s(ds/dt)
At s=24,and r=6
dA/dt=2(
)(6)(2)-2(24)(1)
Change in area=24
-48
length = 1/2 w+9
perimeter= 60 =2(l+w)
substitute in for length
60 = 2(1/2 w +9 +w)
60 = 2 (3/2 w +9)
distribute
60 = 3w + 18
subtract 18 from each side
42 = 3w
divide by 3 on each side
14 = w
length = 1/2 w + 9
length = 1/2 (14) +9
7 + 9
16cm
Answer:

Step-by-step explanation:
∵ The quadratic equation form is :
y = [1/2(b - k)] (x - a)² + (b + k)/2
Where (a , b) is the focus and directrix y = k
∵ The focus is (4 , -3) and directix is y = -6
∵ 
∴ 
∴ 
another way:
Assume that (x , y) is the general point on the parabola
∵ The distance between the directrix and (x , y) = the distance between the focus and (x , y)
By using the distance rule:
∵ (y - -6)² = (x - 4)² + (y - -3)² ⇒ (y + 6)² = (x - 4)² + (y + 3)
∴ y² + 12y + 36 = (x - 4)² + y² + 6y + 9
∴ 12y - 6y = (x - 4)² + 9 - 36
∴ 6y = (x - 4)² - 27 ⇒ ÷ 6
∴ y = 1/6 (x - 4)² - 9/2
Answer:
(x+3, y+2)
Step-by-step explanation:
choose a letter: let's use points A and A'
A: (-3, 3)
A': (0, 5)
the rule would be (x+3, y+2) because (-3+3, 3+2) = (0,5)
Try it on another point:
B: (-4, 0)
B': (-4+3, 0+2) = (-1, 2) which checks out!