Answer:
A) down
B) x intercept (5, 0)
y intercept (0, 80)
C) 144 ft
Step-by-step explanation:
y = Ax² + Bx + C
y = -16x² + 64x + 80
A)
Parabola opens down because A is negative
B)
x intercept (5, 0)
x = (-64 ±√(64² - 4(-16)(80))) / (2(-16))
x = -1 which means if the profile is continuous, the balloon launched one hour ago.
or
x = 5 which means the balloon will be on the ground in 5 hours.
(assuming level ground or no wind at all.
y intercept
y = -16(0)² + 64(0) + 80
y = 80 ft
meaning the balloon is already 80 feet above the ground when we start looking at t = 0
C)
Maximum altitude will occur when the vertical velocity is zero. Velocity is the derivative of position.
x' = -32x + 64
0 = -32x + 64
32x = 64
x = 2 hrs
y = -16(2)² + 64(2) + 80
y = 144 ft
Total cost = 62 + (6% of 62) + (20% of 62)
- Find 6% of 62:
1% = 62 / 100 = 0.62
0.62 x 6 = 3.72
- Find 20% of 62:
10% = 6.2
6.2 x 2 = 12.4
Add everything together:
62 + 12.4 + 3.72 = 78.12
The total cost was $78.12
Answer:
The three given points are the vertices of a right triangle.
Step-by-step explanation:
To determine that the three points are the vertices of a right triangle let us find the distance between each two points
The formula of the distance is 
∵ 
= 6 and 
= -6
∵ 
= 9 and 
= -6
∴ 
= 
∴ = 3
∵ = 6 and = -6
∵ = 9 and = 1
∴ 
= 
∴ = 
∵ = 9 and = 1
∵ = 9 and = -6
∴ 
= 
∴ = 7
<em>Let us use the fact that if the square of the longest side of a triangle is equal to the sum of the squares of the other two sides, then the triangle is a right triangle at the vertex which opposite to the longest side</em>
∵ The longest side is
∵ The other two sides are 3 and 7
∵ ( )² = 58
∵ (3)² + (7)² = 9 + 49 = 58
∴ ( )² = (3)² + (7)²
- By using the fact above
∴ The triangle is a right triangle
The three given points are the vertices of a right triangle.
