When they form conical piles, granular materials such as salt, gravel, and sand settle at different "angles of repose," depending on the shapes of the grains. One particular 13-foot tall cone of dry sand has a base diameter of 38.6 fee To the nearest tenth of a degree, what is the angle of repose of this type of dry sand?

A different conical pile of the same type of sand is 10 feet tall. What is the diameter of the cone's base?

Henley Landscaping Supply sells a type of sand with a 30° angle of repose for $32 per cubic yard. Find the cost of an 11-foot-tall cone of this type of sand. Show your work. 40 points

x =-.20752

step-by-step explanation:

4^(x+2)=12

4^(x+2)=12

take the log base 4 on each side

log 4 (4^(x+2) = log 4(12)

we know log b(a^y) = y log b (a)

(x+2) log 4(4) = log 4 (12)

x+2 = log 4 (12)

we know   logb c = loga c/loga b

we want to convert to base 10   so a = 10

by default, we do not write the 10   c = 4   and b = 10

log4 10 = log 12/log 4

log4 10 = log 12/ log 4

x+2 = log 12/ log 4

subtract 2 from each side

x +2 -2 = log 12/ log 4 -2

x = 1.79248125 -2

x =-.20752

this is a direct variation proportion. y = kx

y is the total amount due, k is the constant of variation, and x is the number of texts sent.

plug in the 3.20 and the 16 to solve for the "k". this is the constant of proportionality. it is the value that will not change.

3.20 = k(16). solving you get $.20 per text.

the equation would then be y = .20x