Answer:
109.9 ft
Step-by-step explanation:
The length of an arc that is 1/4 of a circle of radius 70 ft is ...
s = rθ
s = (70 ft)(π/2) = 35π ft ≈ 109.9557 ft
The best answer choice appears to be 109.9 feet.
Answer: Time t = 33.0 seconds
Step-by-step explanation:
Given that the vertical distance H between the dock and the top of the boat's mast t seconds after its first peak is modeled by the function
H(t) = 5cos( 2π/3 t) − 35.5H
Where the maximum vertical distance = 5
At the down position, H(t) = 0
5cos( 2π/3 t) − (35.5/100)H = 0
5cos( 2π/3 t) − 0.355 × 5 =0
5cos( 2π/3 t) − 0.1775 = 0
5cos( 2π/3 t) = 0.1775
cos( 2π/3 t) = 0.1775/5
cos( 2π/3 t) = 0.355
2π/3 t = cos^-1 (0.355)
2π/3 t = 69.2
2πt = 69.2 × 3
2πt = 207.6
t = 207.6/2π
t = 33.0 seconds
Answer:
4,2,7
Step-by-step explanation
they are the ones repeating at the end
Answer: f(x) = (x + 3)(x – 7)
Step-by-step explanation: Use "standard form" of the function and insert values given: vertex (2,-25) intercept point (7,0)
f(x) = a(x-h)² + k from vertex, h is 2 y is -25 from intercept, x is 7 f(x) is 0
to find a, 0 = a(7-2)² +(-25) 0 = a(7-2)² -25 add 25 to both sides
25 = a(5)² 25 = 25a 25/25 = a 1=a (seems useless but verifies implied "a"coefficient is 1)
f(x) = a(x-h)² + k solve to get the quadratic form
f(x) = (x-2)² -25 (x - 2)² is x² -4x +4
f(x) = x² -4x +4 -25 simplify
f(x) = x² -4x - 21 then factor
f(x) = (x + 3)(x - 7)
