100 points! ap calculus ab related rates

#2. a circle of radius r has a square circumscribed about it as shown in the figure to the right. if the radius is increasing at the rate of 2 cm/sec, and the area of the shaded region is increasing at the rate of 8 cm^2/sec, what is the value of r in cm?

y -5 = (-1/4)(x + 8)

step-by-step explanation:

both triangles are similar because 2 is just smaller than the big one 1 is similar because they are facing different way's but are similar to each other

step-by-step explanation:

alright so i think for this one it would to draw it out. this may be hard for me to try and draw, but i will do my best on here:

        r

  /       |     \

notice how it forms 2 triangles inside one bigger triangle.

so if we know the angle spr is the same as psr that is saying the measure of angle p is the same as angle s. this means the big triangle psr is either isosceles or equilateral. in both cases, the triangle is perfectly symmetrical when split down the middle, which is in this case rq. because we know it is perfectly symmetrical on both sides, we know that the two triangles inside the bigger one are equal.

good luck on ur quiz test or homework. have a good day : )