Answer: 18.66 miles per hour.
Step-by-step explanation:
The velocity of the Kayak can be written as the velocity of the kayak in still water plus the rate of the current.
If K is the velocity of the kajak, and C the velocity of the current, we have that:
When the kajak moves along with the current, for a given time T.
(K + C)*T = 10mi
when the kajak move against the current:
(K - C)*T = 4mi
now we can replace C by 8mph, and take the quotient of both equations:
((K + 8mph)*T)/(K - 8mph)*T)) = 10mi/4mi
(K + 8)/(K-8) = 10/4
K + 8 = (K- 8)*10/4
K + 8 = K*10/4 - 20
K*10/4 - K = K*6/4 = 20 + 8 = 28
K = 28*4/6 = 18.66
So the rate of the kajak is 18.66 miles per hour.
Answer:
diameter = 16cm, circumference ≈ 50.27
Step-by-step explanation:
The radius is 8 centimeters, so the diameter should be twice of that because the radius is the distance from the middle of the circle to the edge while the diameter is from edge to edge passing through the middle of the circle. Therefore,
8 · 2 = 16cm
The equation for the circumference of a circle is 2πr. In this case, because nothing else is specified about π, we use 3.14. So,
2 · 3.14 · 8 ≈ 50.27
Hope this helped! Have a great day. ^^
Answer:
The anchor should be located at the midpoint between the 20m high and 60m high antennas.
Step-by-step explanation:
Let the length of cable for 20m high antenna be represented by x, and that for 60m high antenna be y.
The single length of cable required = x + y.
From the principle of geometry, if the cable is anchored at 200m from the 20m high antenna, it forms a right angled triangle. Applying the Pythagoras theorem,
x =
= 199
Applying the same principle to the 60m high antenna gives,
y =
= 191
The single length of cable required = 199+ 191
= 390m
Varying the point of location of the anchor between the two antennas causes an increase in the length of cable required.
The anchor should be located at the midpoint between the two antennas to achieve a minimum amount of cable.