The sum of two numbers is 3. Five times the larger number plus four times the smaller number is 29. Find the numbers
2 answers:
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Answer:
The answers to the question is
(a) Jamie is gaining altitude at 1.676 m/s
(b) Jamie rising most rapidly at t = 15 s
At a rate of 2.094 m/s.
Step-by-step explanation:
(a) The time to make one complete revolution = period T = 15 seconds
Here will be required to develop the periodic motion equation thus
One complete revolution = 2π,
therefore the we have T = 2π/k = 15
Therefore k = 2π/15
The diameter = radius of the wheel = (diameter of wheel)/2 = 5
also we note that the center of the wheel is 6 m above ground
We write our equation in the form
y =
When Jamie is 9 meters above the ground and rising we have
9 = or 3/5 =
= 0.6
which gives sin⁻¹(0.6) = 0.643 =
from where t = 1.536 s
Therefore Jamie is gaining altitude at
1.676 m/s.
(b) Jamie is rising most rapidly when the velocity curve is at the highest point, that is where the slope is zero
Therefore we differentiate the equation for the velocity again to get
=0, π, 2π
Therefore = 0 whereby t = 0 or
= π and t = 7.5 s, at 2·π t = 15 s
Plugging the value of t into the velocity equation we have
- 2/3π m/s which is decreasing
so we try at t = 15 s and we have m/s
Hence Jamie is rising most rapidly at t = 15 s
The maximum rate of Jamie's rise is 2/3π m/s or 2.094 m/s.
Answer:
36
Step-by-step explanation:
Objective: Find missing dimensions of the right triangle using the then subtract that area of the triangle from the rectangle's area.
Using the definition of a rectangle, the left vertical side measure is 7 and right vertical side is 6. So the missing legs of the triangle is 4 and 3.
Apply triangle formula, base x height divided by 2.
Area of rectangle is length x width so the area is
Subtract 6 from 42.
Since the problem is not telling us the height of Silvio, we are going to assume it is not relevant for our calculations.
Let
the altitude of the incoming plane. We know for our problem that the distance between Silvio and the tower is 3 miles, Also we know that the angle of elevation to the plane is 40°. With this information we can create a triangle as shown in the figure. We need a function that relates the angle of elevation with its opposite and adjacent sides, that function is tangent.
We can conclude that we should use the trig function tangent to model this situation; also, we can conclude that the equation that describes this situation is.
Let
We can conclude that we should use the trig function tangent to model this situation; also, we can conclude that the equation that describes this situation is