9514 1404 393
Answer:
- base: 2.18 m
- height: 7.35 m
Step-by-step explanation:
Let b represent the base of the triangle in meters. Then the height is ...
h = 3 +2b
and the area is ...
A = 1/2bh
8 = 1/2(b)(3 +2b)
16 = 3b +2b^2 . . . . . . . multiply by 2 and eliminate parentheses
2(b^2 +3/2b + (9/16)) = 16 + 9/8 . . . . . . complete the square
2(b +3/4)^2 = 17.125
(b +3/4)^2 = 8.5625 . . . . . divide by 2
b + 0.75 = √8.5625 ≈ 2.9262
b = -0.75 +2.9262 = 2.1762
h = 3 +2b = 7.3523
The base is about 2.18 meters and the height is about 7.35 meters.
The answer to the problem is x=6
Answer:
t = sqrt((2 z)/h + ((q_1)^2)/(h^2)) - q_1/h or t = -q_1/h - sqrt((2 z)/h + ((q_1)^2)/(h^2))
Step-by-step explanation:
Solve for t:
z = (h t^2)/2 + t q_1
z = (h t^2)/2 + t q_1 is equivalent to (h t^2)/2 + t q_1 = z:
(h t^2)/2 + t q_1 = z
Divide both sides by h/2:
t^2 + (2 t q_1)/h = (2 z)/h
Add q_1^2/h^2 to both sides:
t^2 + (2 t q_1)/h + q_1^2/h^2 = (2 z)/h + q_1^2/h^2
Write the left hand side as a square:
(t + q_1/h)^2 = (2 z)/h + q_1^2/h^2
Take the square root of both sides:
t + q_1/h = sqrt((2 z)/h + q_1^2/h^2) or t + q_1/h = -sqrt((2 z)/h + q_1^2/h^2)
Subtract q_1/h from both sides:
t = sqrt((2 z)/h + ((q_1)^2)/(h^2)) - q_1/h or t + q_1/h = -sqrt((2 z)/h + q_1^2/h^2)
Subtract q_1/h from both sides:
Answer: t = sqrt((2 z)/h + ((q_1)^2)/(h^2)) - q_1/h or t = -q_1/h - sqrt((2 z)/h + ((q_1)^2)/(h^2))
