The number of hours, h, it takes for a block of ice to melt varies inversely as the temperature, t. If it takes 3 hours for a square inch of ice to melt at 60 degrees, find the constant of proportionality
a. 150
c. 210
b. 180
d. 200

180

Step-by-step explanation:

hours = constant / temperature     hours varies inversely as the temperature

3 = c / 60

c (constant) = 3 * 60 = 180

we have three similar triangles, because each has a right angle and shares an angle.   let's write the angles in order: opposite to short leg, long leg, hypotenuse.

cab similar to bad similar to cbd

or as ratios,

ca: ab: cb = ba: ad: bd = cb: bd: cd

we also know

ac = ad + cd

(ad+cd): ab: cb = ba: ad: bd = cb: bd: cd

(ad+cd)/cb=cb/cd

we have cb=6, ad=5 and seek x=cd.

we reject the negative root and conclude x=4

answer: 4

step-by-step explanation :

we know that

the measurement of the outer angle is the semi-difference of the arcs which comprises

in this problem

m< xzy is the outer angle

substitute the values

the measure of angle xoy is equal to

> by central angle

substitute the value