5-6 Typhoon Phi, Dang, Emma, Angelina. Choose a random box you likeABCD 1 A1B1C1D12 A2B2C2D23 A3B3C3D34 A4B4C4D4.

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5-6 Typhoon Phi, Dang, Emma, Angelina

Choose a random box you likeABCD 1 A1B1C1D12 A2B2C2D23 A3B3C3D34 A4B4C4D4

A1 (30 points) Suppose a pig takes 24 mins to walk to from a farm to the farmer’s house at the rate of 4ft/min. How long will it take that pig to return to the farm at the speed of 2ft/min?

Solution to A1 time 1. speed 1 = time 2. speed = time = 2x 96 / 2 = x 48 = x BACK

A2 (10 points) Find the missing value: (x,55) and (5,77)

Solution to A2 x 1. y 1 = x 2. x 2 x = x = 385 x 1 = 385 / 55 x 1 = 7 BACK

A3 BACK TYPHOON!!!!

A4 (40 points) Your weight on Mars varies directly with your weight on Earth. A person weighing 125 lbs on Earth weighs lbs on Mars, since Mars has less gravity. If you weigh 155 lbs on Earth, how much will you weigh on Mars?

Solution to A4 e1 / e2 = m1 / m2 125 / 155 = / m2 125(m2) = 155(47.25) 125(m2) = m2 = / 125 m2 = lbs BACK

B1 TYPHOON!!!! BACK

B2 (30 points) A pump empties a swimming pool in 60 minutes at the rate of 1500 L/min. If the rate of pumping is 2500 L/min, how long does it take to empty the swimming pool?

Solution to B2 time 1. speed 2 = time 2. Speed = time = time / 2500 = time 2 36 = time 2 BACK

B3 TYPHOON!!!! BACK

B4 TYPHOON!!!! BACK

C1 (10 points) In an inverse variation, y = 3 when x = 8 Write an inverse variation equation that shows the relationship between x and y

Solution to C1 First find the constant of variation. Plug x = 8 and y = 3 into the inverse variation equation and then solve for k. x. y = k 8. 3 = k 24 = k

Solution to C1 (cont.) Now use k = 36 to write the inverse variation equation. y = k / x y = 24 / x  This is the inverse variation Can also be written as xy = 24 BACK

C2 (10 points) Find the missing value: (24,1.6) and (c,0.4)

Solution to C2 x 1. y 1 = x 2. x = x = x / 0.4 = x 2 96 = x 2 BACK

C3 (50 points) The time, T minutes,taken for a stadium to empty varies directly as the number of spectators, S, and inversely as the number of open exits, E. Write down a relationship connecting T,S and E. A. It takes 12 minutes for a stadium to empty when there are spectators and 20 open exits. B. How long does it take the stadium to empty when there are spectators and 24 open exits ?

Solution to C3 A.T= k(s )/ E B. K is the constant of variation. T = 12, S = 20,000 and E = / 1 = k(20,000) / 20 (20,000)K = K= 240 / 20,000 = 6 / 500

Solution to C3 (cont.) T= 6(S) / 500(E) Now S = and E = 24 T = 6(36,000) / 500(24) T= 18 (min) BACK

C4 (20 points) On the world map, the distance between the cities of Baconburp and Hamfat is 12 inches. Each inch on the map represents 400 miles. How far away are Baconburp and Hamfat actually?

Solution to C = 4800 BACK

D1 TYPHOON!!!! BACK

D2 (40 points) The volume V of a gas varies inversely as the pressure p on it. If the volume is 300 cm 3 under a pressure of 48 kg/cm 2, what is the volume under a pressure of 25 kg/cm 2 ?

Solution to D2 Volume 1. Pressure 1 = Volume 2. Pressure = Volume = Volume 2 (25) / 25 = Volume 2 (25) 576 = Volume 2 BACK

D3 TYPHOON!!!! BACK

D4 (10 points) In an inverse variation, y = 2 when x = 16 Write an inverse variation equation that shows the relationship between x and y

Solution to D4 First find the constant of variation. Plug x = 16 and y = 2 into the inverse variation equation and then solve for k. xy = k = k 32 = k

Solution to D4 (cont.) Now use k = 36 to write the inverse variation equation. y = k / x y = 32 / x  This is the inverse variation Can also be written as xy = 32 BACK