Answer:
Distance between the observer and the red car is ![250 Sin \frac{\pi}{3}t](https://tex.z-dn.net/?f=250%20Sin%20%5Cfrac%7B%5Cpi%7D%7B3%7Dt)
Step-by-step explanation:
Diameter of field = 500 m
Radius of field =![\frac{Diameter}{2}=\frac{500}{2}=250 m](https://tex.z-dn.net/?f=%5Cfrac%7BDiameter%7D%7B2%7D%3D%5Cfrac%7B500%7D%7B2%7D%3D250%20m)
Let R be the radius and the speed at which the car completes race be w
So,![w=\frac{2\pi}{T}](https://tex.z-dn.net/?f=w%3D%5Cfrac%7B2%5Cpi%7D%7BT%7D)
Car finished 5 laps in minutes = 30
Car finished 1 lap in minutes = ![\frac{30}{5}=6](https://tex.z-dn.net/?f=%5Cfrac%7B30%7D%7B5%7D%3D6)
So, ![w=\frac{2\pi}{6}=\frac{\pi}{3}](https://tex.z-dn.net/?f=w%3D%5Cfrac%7B2%5Cpi%7D%7B6%7D%3D%5Cfrac%7B%5Cpi%7D%7B3%7D)
Refer the attached figure
Angle between car and observer = wt
So, Distance between the observer and the red car is give as A sin wt
So, Distance between the observer and the red car=![250 Sin \frac{\pi}{3}t](https://tex.z-dn.net/?f=250%20Sin%20%5Cfrac%7B%5Cpi%7D%7B3%7Dt)
Answer:
57
Step-by-step explanation:
Straight line value=180
Given Value=123
Value of ∆TKL
=180-123
=57(Ans)
Answer:
56.5 in^2
Step-by-step explanation:
The volume of a cone is π
h/3. The radius is d/2=6/2=3
V=(3.14 x
x 6)/3
=(3.14 x 54)/3
=169.56/3
=56.52
Answer:
Circumference = 62.8 cm
Step-by-step explanation:
Circumference =
![2 \: \pi \: r](https://tex.z-dn.net/?f=2%20%5C%3A%20%5Cpi%20%5C%3A%20r)
=》
![2 \times 3.14 \times 10](https://tex.z-dn.net/?f=2%20%5Ctimes%203.14%20%5Ctimes%2010)
=》
![6.28 \times 10](https://tex.z-dn.net/?f=6.28%20%5Ctimes%2010)
=》
![62.8](https://tex.z-dn.net/?f=62.8)
hence, the circumference = 62.8 cm
Step-by-step explanation:
it is really simple.
first of all, when 2 lines intersect (and we are talking straight lines, otherwise they are not lines in the mathematical sense), the angles created are the same in both sides of the lines (just left-right mirrored).
and secondly, the sum of all angles around a single point in one side of a line must be 180°, as the line can be considered the diameter of a circle, the point the center is the circle, and all the angles on one side are a half-circle.
so,
angle 3 = 37°
that means
angle 1 = 37° too
angle 2 is supplementary to e.g angle 3 (that means they both add up to 180° as explained above).
angle 2 = 180 - 37 = 143°
and angle 4 = 143° too