Topic: Equations

##### Equations

What is the approximate density of a mineral with a mass of 262.2 grams that displaces 46 cubic centimeters of water?

(1) 1.8 g/cm^{3}

(2) 5.7 g/cm^{3}

(3) 6.1 g/cm^{3}

(4) 12.2 g/cm^{3}

What is the approximate gradient from point A to point B on the map?

(1) 25 feet per mile

(2) 50 feet per mile

(3) 75 feet per mile

(4) 100 feet per mile

The gradient between location A and location B is approximately

(1) 0.04 ft/mi

(2) 25 ft/mi

(3) 40 ft/mi

(4) 50 ft/mi

Which equation is used to determine the approximate rate of Earth’s revolution?

(1)

(2)

(3)

(4)

Gold Mining

A sluice box is used to remove gold pieces from other sediments in a stream. The box is placed in the stream to channel some of the water flow. Gold-bearing sediment is placed at the upper end of the box. The riffles in the bottom of the box are designed and positioned to create disruptions in the water flow. These disruptions cause dead zones in the current that allow the more dense gold to drop out of suspension and be deposited behind the riffles. Lighter material flows out of the box as tailings. Typically, particles of the mineral pyrite, which shares characteristics with gold, are deposited with gold particles in the sluice box. Since miners were fooled into thinking the nuggets of pyrite were gold, the name “fool’s gold” is often applied to pyrite.

A gold nugget with a volume of 0.8 cubic centimeter (cm^{3}) was found in the sluice box. Calculate the mass of this gold nugget. [1]

______________ g

Allow 1 credit for 15.44 g or 15.4 g or 15 g.

Calculate the snow depth gradient between point A and point B, in inches per mile. [1]

in/mi

Allow 1 credit for any response from 0.75 in/mi to 0.85 in/mi.

• Note: Do not allow credit for 20/25 because this does not show a complete calculation.

Calculate the gradient along line XY. Label your answer with the correct units. [1]

Allow 1 credit for any value from 38 to 42 with acceptable units. Acceptable units include, but are not limited to:

• — ft/mi

• — feet/mi

• — feet/mile

Determine the rate at which the ball traveled, in centimeters per second, from location A to location B. [1]

cm/s

Allow 1 credit for 50 cm/s.

Calculate the gradient along the reference line from A to B, in meters per kilometer. [1]

Gradient =

Allow 1 credit for any value from 22 m/km to 29 m/km.

Cowlesville, New York, received a total of 88 inches of snow in 85 hours. Calculate the average rate of snowfall in inches per hour (in/h) for Cowlesville. [1]

______________ in/h

Allow 1 credit for any value from 1.0 in/h to 1.1 in/h.

From 12 noon Thursday until 8 p.m. Thursday, the total amount of snowfall was 12 inches. Calculate the snowfall rate, in inches per hour. [1]

Snowfall rate =

Allow 1 credit for 1.5 in/h or 1 ^{1__}2 in/h.

• Note: Do not allow credit for ^{12__}8 or ^{3__}2 in/h because these do not show a complete calculation.

Calculate the air pressure gradient between locations A and B in millibars per kilometer. [1]

______________ mb/km

Allow 1 credit for any value from 0.016 to 0.027 mb/km.

• Note: Do not allow credit for 4/200 or 1/50 because this does not show a complete calculation.

Calculate the gradient along Kris Creek between locations X and Y. Label your answer with the correct units. [1]

Allow 1 credit for any value from 37 to 43 with correct units. Acceptable units include, but are not limited to:

• — ft/mi

• — feet/mi

• — feet per mile

How long will it take a person to hike along the trail from point C to point D at a rate of 3 miles per hour? [1]

__________ h

Allow 1 credit for any value from 1.8 h to 2.2 h.

Calculate the gradient of Otter Creek, in meters per kilometer, between points Y and Z. [1]

______________ m/km

Allow 1 credit for any value from 38 m/km to 42 m/km.