On January 1, 2017, the City of Hastings created a solid waste landfill that it expects to reach capacity gradually over the next 20 years. If the landfill were to be closed at the current time, closure costs would be approximately $1.60 million plus an additional $920,000 for postclosure work. Of these totals, the city must pay $57,000 on December 31 of each year for preliminary closure work. At the end of 2017, the landfill reached 3 percent of capacity. At the end of 2018, the landfill reached 13 percent of capacity. Also at the end of 2018, a reassessment is made; total closure costs are determined to be $1.80 million rather than $1.60 million.

advanced placement tests

bd = 9 cm

step-by-step explanation:

in a 30°-60°-90° triangle, the ratio of side lengths is 1 : √3 : 2. that is, the longest side (hypotenuse) is twice the length of the shortest side.

all of the triangles in your geometry are 30°-60°-90° triangles. ac is the hypotenuse of δacd, and the short side of δabc.

the short side ad of δacd will be half the length of ac, so 3 cm. the hypotenuse ab of δabc will be twice the length of ac, so 12 cm. segment bd is the difference of the lengths ab and ad, so is

bd = ab -ad

bd = 12 cm - 3 cm = 9 cm

comment on side length ratios

you can figure the ratios of side lengths in a 30°-60°-90° triangle by considering the trig ratios of the angles. or you can figure the length of the altitude of an equilateral triangle of side length 2 using the pythagorean theorem.

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