Tangent Θ = opposite / adjacent
AB = short leg = opposite = 12
AC = long leg = adjacent = 5
BC = hypotenuse = 13
tangent Θ = 12/5 ⇒⇒⇒ this is in ratio form
tanΘ = 2.4 ⇒⇒⇒ this is in decimal form
The length of the line joining the center of the circle and each coordinate is equal.
Let the center of the circle be (a, b), then
(a - 10)^2 + (b - 3)^2 = (a - 3)^2 + (b - 10)^2 = (a + 4)^2 + (b - 3)^2
a^2 - 20a + 100 + b^2 - 6b + 9 = a^2 - 6a + 9 + b^2 - 20b + 100 = a^2 + 8a + 16 + b^2 - 6b + 9
a^2 - 20a + 100 + b^2 - 6b + 9 = a^2 - 6a + 9 + b^2 - 20b + 100 . . . (1)
a^2 - 20a + 100 + b^2 - 6b + 9 = a^2 + 8a + 16 + b^2 - 6b + 9 . . . (2)
From (1): 14a - 14b = 0 => a = b
From (2): 28a = 84 => a = 84/28 = 3
Therefore, center = (a, b) = (3, 3)
Answer:
see below
Step-by-step explanation:
First line:
y = mx+b where m is the slope and b is the y intercept
y = 2x + 10
Second line
y = mx+b
y = 3x+0 since there are no barrels filled on this line when they flip the switch
Setting the two equations equal
2x+10 = 3x
Subtract 2x from each side
2x+10-2x= 3x-2x
10 = x
Each line will have filled 10 barrels when they numbers are equal.
1 Answer. Suryin =) . 96√3 cm. Explanation: Area of regular hexagon : A=3√32a2. a is the side which is 8 cm. A=3√32(82). A=3√32(64). A= 192√32.
