With a certain tailwind, an airplane reached its destination, 630 miles away, in 1 1/2 hours. flying
back against the same wind, the plane took 15 minutes longer to make the trip. find the wind speed and the airplanes airspeed.

V=390mph and W=30mph

Step-by-step explanation:

Let V be the speed of the airplane and W the speed of the wind.

We have two travels and the formula v=d/t:

V+W=630miles/1.5hr (With the wind)

V-W=630miles/1.75hr (agains the wind)

Clear V from the 1st equation. V=(630/1.5)-W

And replace it into the 2nd equation:

(630/1.5)-W-W=630/1.75

420-2W=360

420-360=2W

W = 60/2

W = 30mi/hr is the wind speed.

Now, we can find V using one equation:

V=(630/1.75)+30 = 360+30

V=390mi/hr is the speed of the airplane.

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).