8. a kayaker spends 2 hours paddling up a
stream from point a to point b, quickly turns
her kayak around, and immediately heads
back downstream. it takes her only 1 hour to
float back down the stream from point b to
point a. if points a and b are 6 miles apart,
what was the kayaker's average rate of
speed in miles per hour?
a. 12 mph
b. 6 mph
c. 4 mph
d. 2 mph

.

D. 2 mph

Step-by-step explanation:

You would add up her total time going upstream and down stream, so 2+1 hours = 3 hours. Then, since speed = distance divided by time, you would divide 6 by 3 to get 2 mph.

p ÷ r = tan(x)

step-by-step explanation:

given that there is a figure below shows a right triangle: a right triangle is shown with hypotenuse equal to q units and the length of the legs equal to p units and r units.

graph is missing so i will create the graph as per given information.

the angle between the legs having lengths p units and q units is y degrees. the angle between the legs having lengths r units and q units is x degrees.

now we need to find about what is p ÷ r equal to.

so we can use trigonometric ratio tan(x)=[altitude]/[base] to find the value of p ÷ r, because p is the altitude and r is the base.

p ÷ r=tan(x)

hence final answer is p ÷ r=tan(x).