98. Avoiding a collision. A car is traveling on aroad that is perpendicular to a

Question

98. Avoiding a collision. A car is traveling on aroad that is perpendicular to a railroad track. When the car is 30meters from the crossing, the car’s new collision detectorwarns the driver that there is a train 50 meters from the car andheading toward the same crossing. How far is the train from thecrossing? 100. Winterwheat. While finding the amount of seed needed toplant his three square wheat fields, Hank observed that the side ofone field was 1 kilometer longer than the side of the smallestfield and that the side of the largest field was 3 kilometerslonger than the side of the smallest field. If the total area ofthe three fields is 38 square kilometers, then what is the area ofeach field?

Explanation / Answer

98. The train is 40 metres away. It doesn't matter which directionit is travelling in. This is an example of the famous 3-4-5 right angled triangle. The 3-4-5 triangle is famous because it is the smallest examplewith whole numbered sides that satisfies Pythagoras's Theorem. To check: 3^2 + 4^2 = 25 5^2 = 25 - It works. In the question, the road is perpendicular so it is at 90 degreesto the railtrack. This means we have a right-angled triangle withone length of 30 metres and a hypotenuse of 50 metres (thecollision detector measured the "diagonal" distance as 50m). The only right-angled triangle with one short side of 30m andhypotenuse of 50m is a version of the 3-4-5 triangle so the answeris 40m. Let's check: 50^2 - 30^2 = 1600 40^2 = 1600. - It works. Hope that is clear enough for you :) 100. Hi, Let L, M and S be the sides Largest, Medium and Smallest SquareFields therefore the side of the smallest field = S km the side of the medium field = M = S+1 km and the side of the largest field = L = S+3 km Total area = 38 km^2 Also Total Area = S^2 + M^2 + L^2 => 38 = S^2 + (S+1)^2 + (S+3)^2 => 38 = S^2 + [S^2 + 2S + 1] + [S^2 + 6S + 9] => 38 = S^2 + S^2 + 2S + 1 + S^2 + 6S + 9 .....(rearranging) => 38 = S^2 + S^2 + S^2 + 2S + 6S + 1 + 9 => 38 = 3S^2 + 8S + 10 => 0 = 3S^2 + 8S + 10 - 38 => 0 = 3S^2 + 8S - 28 Using quadratic solution => S = [-8 +/- {(8)^2 -4(3)(-28)}^(1/2)]/(2*3) => S = [-8 +/- {64 + 336}^(1/2)]/6 => S = [-8 +/- {400}^(1/2)]/6 => S = [-8 +/- 20]/6 => S = [-8+20]/6 or S = [-8 -20]/6 => S = 12/6 or S = -14/3 since a side can not be negative, therefore, S = 2 km S = 2 km M = 2+1 = 3 km L = 2+3 = 5 km and there area Smallest Field = S^2 = 2^2 = 4 km^2 Medium Field = M^2 = 3^2 = 9 km Largest Field = L^2 = 5^2 = 25 km also it can be varified that 4+9+25 = 38 hope to answer you well, keep smiling, bye. 104. Venture capital. Henry invested $12,000 in a new restaurant.When the resturant was sold two years later, he received $27,000.Find his average annual return by solving this equation12,000(1+r)^2=27,000 12,000(1+r)^2=27,000 (1+r)^2=27,000/12,000 1 + r = sqrt(9/4) r = 3/2 - 1 r = 1/2 Therefore, r = 0.5 or 50%

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