Answer:
Period =
The Ferris wheel will complete one round in 40 seconds.
Step-by-step explanation:
We have the function representing the height of the passenger by,
, where t = time in minutes.
It is known that when a function f(x) has period P, then the function a×f(bx+c)+d will have the period .
Since, the function has period , so the function h will have period i.e. .
Thus, the period of the given function is .
Now, as the period is minutes i.e 40 seconds.
Hence, we get that the Ferris wheel will complete one round in 40 seconds.
<span>Answer: 6.5966889e+13</span>
The easiest ways is to use the quadratic formula that is:
x' = [-b+√(b² - 4ac)]/2a and x" = [-b -√(b² - 4ac)]/2a
Solving : 2x² + 5x - 11 = 0, gives:
x' = [-5+√(25 - 4(2)(-11)]/4 and x" = [-5-√(25 - 4(2)(-11)]/4
x' = (-5+√113)/4 & x" = (-5-√113)/4
Answer:
A
Step-by-step explanation:
Given the exponential function
f(t) = 228 ← where t is time in years
Substitute t = 20 into f(t), that is
f(20) = 228 × = 228 × 0.60268.... ≈ 137 → A
The given equation may be simplified as follows:
x² + 14xy + 49y² = 100
(x + 7y)(x + 7y) = 100
(x + 7y)² = 10²
x + 7y = 10
This is a straight line with the equation
y = -(1/7)x + 10/7
The minimum distance from the origin to this line is provided by a straight line that passes through the origin and which is perpendicular to the straight line.
The slope of the perpendicular line is 7 because the product of the two slopes should be -1.
The perpendicular line is of the form
y = 7x + c.
Because the line passes through (0,0), therefore c = 0.
The line y = 7x intercepts the original line when
y = 7x = -(1/7)x + 10/7
Therefore
7x = -(1/7)x + 10/7
Multiply through by 7.
49x = -x + 10
50x = 10
x = 1/5
y = 7x = 7/5
The minimum distance is
d = √(x² + y²)
= √[(1/5)² + (7/5)²]
= √2
The point is (1/5, 7/5).
Answer: (1/5, 7/5) or (0.2, 1.4)