If r varies directly as p and inversely as q2, and r = 27 when p =3 and q = 2, find r when p = 2 and q= 3
k = r =

k = 36 and r = 8

Step-by-step explanation:

Given that r varies directly as p and inversely as q² then the equation relating them is

r = ← k is the constant of variation

To find k use the condition r = 27 when p  3 and q = 2, thus

27 = ( multiply both sides by 4 )

108 = 3k ( divide both sides by 3 )

k = 36

r = ← equation of variation

When p = 2 and q = 3, then

r = = = 8

175

step-by-step explanation:

2 inches x 10 miles = 200 miles - 3 inches = 175

the largest number of the four options is 1.8 x 10-2

you have it in scientific notation.

1.80 x 10-6   = 0.00000180

1.80 x 10-4   = 0.000180 (bigger, or "less small", than the former one)

so

1.8 x 10-2       = 0.0180. as you see. the "less small", or the biggest one of them all.

as you have negative exponent, it means you are dividing 1.8 by 100 (i.e. moving the dot towards left, two times).

if you had positive exponent for the scientific notation, power of tenths, you would be multiplying times 100 (moving the dot towards right) as below:

1.8 x (10)2 = 180

so. if you have negative exponent in scientific notation, move the dot toward left. if it is positive, toward right as many times the exponent tells you.