lots of questions from UILB 2008

[sinkokuyou]

that was a hard test, I only got a 247 and missed 5punchins...
anyway,
18-The Toyota Prius hybrid automobile costs $23070 and gets 50 mi/gal. It uses both gasoline and a battery that is charged when braking. What is the break-even dricing distance for a Prius compared to a $18000 car that gets 30 min/gal if gasoline costs $3.03 gal? ANS:125000 mi
28-A line 150 units long spans from the origin to a point (a,b) on the parabola y=4x^2. What is (pos) a? ANS: 6.12
37-5 oz of dye is needed to make 1 gallon of dye stock. How much dye is needed to convert 15 gallons of water to dye stock? ANS:9.76 cups
and 70: ANS:466

[AuSmith]

[sinkokuyou]

a problem from the study list
07A-38 On a Texas ranch, a pond is 285ft in diameter and the land slopes at [unparseable or potentially dangerous latex formula] (from horizontal) away from the pond. What is the pond diameter after a 1.5 in rain if 40% of the rain ruins into the pond, and the rain gathering area is 3 acres? ANS: 288 ft^2
(what is a TX ranch?)

[AuSmith]

08B-70.PNG (119.21 KiB) Viewed 1183 times

08B-70) Note that the radius of the quarter circle is not exactly the same length as the distance from the center of the circle to the intersection of the stray line segment and the top side of the square. Though, we can find the latter:

You can use the "Alternating interior angles are congruent" jazz from geometry to get another angle equal to [unparseable or potentially dangerous latex formula], then use right triangle geometry. Eventually, if we name the lengths [unparseable or potentially dangerous latex formula] and [unparseable or potentially dangerous latex formula] as in the diagram, we get

[unparseable or potentially dangerous latex formula]

Now, we want to use the midpoint part.

[unparseable or potentially dangerous latex formula]

substituting for [unparseable or potentially dangerous latex formula],

[unparseable or potentially dangerous latex formula]

Multiply by the downstairs and solve the linear equation.

[unparseable or potentially dangerous latex formula]

[AuSmith]