Apond is being dug according to plans that have a scale of 1 inch= 6.5 feet. the maximum distance across the pond is 9.75 inches on the plans. what will be the actual maximum distance across the pond?

We are given a scale that for every 1 in on the plan, the actual length will 6.5 ft. 

The maximum distance across the pond on the plan is 9.75 in. So that means we will need to take 6.5 ft 9.75 times. So our answer is 

6.5*9.75=63.375 ft. That's the answer. 

We can visualize this a different way

1 in = 6.5 ft

9.75 in = x ft

And from here it's a little more clear to see what needs to be done. 

Hope this helped! 

b.-4 units

all you   do is count how many times you move

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).