A company sells stellite, a cobalt-chromium-based alloy, at two different rates based on the location of the buyer. The total price of the alloy is determined by the ratio of cobalt and chromium in the alloy.
When sold locally they charge $9 for every gram of cobalt and $1 for every gram of chromium. The total price for one coin of stellite is $37.
The international price for just the metal without including transportation is $10 for every gram of cobalt and $3 for chromium and a single standard coin costs $43.
1 point
1
Question 2
2.
Simple and Familiar (1 - 2)
Define the variables in the situation given above.
1 point
1
Question 3
3.
Complex and Familiar (3 - 4)
Write an equation/equations expressing the situations mentioned above.
1 point
1
Question 4
4.
Challenging and Familiar (5 - 6)
Find the ratio of cobalt to chromium in a standard rod of stellite.
1 point
1
Question 5
5.
Challenging and Unfamiliar (7 - 8)
The RnD department of the company discover that by tweaking the ratio by reducing one portion of cobalt and adding one portion of a new ingredient, Carbon reduced the price and increases the strength of the alloy. If carbon only costs ¢10 then what would the cost of a single coin be, locally?
(1$ = 100¢)
When the brakes of a car are applied, the car does not come to a stop immediately, instead, it skids to a halt. The length, L, of the skid is given by,
where s is the speed of the car in km/hr at the time when the breaks were first applied.
A car involved in an accident leaves a skid mark of 50 m.
1 point
1
Question 6
6.
Simple and Familiar (1 - 2)
Write an equation expressing the situation.
1 point
1
Question 7
7.
Complex and Familar (3 - 4)
Determine the car's speed at the time of breaking.
1 point
1
Question 8
8.
Challenging and Unfamiliar (7 - 8)
Racers are familiar with taking sharp turns at high speeds. On a certain road, they can skid anywhere between 40 and 60 m safely. What is the range of speeds they can drive safely?
The apparent magnitude M of a star is a number that tells how bright that star appears at its distance from Earth. The scale is "backward" and logarithmic. Larger magnitudes correspond to fainter stars.
When comparing the magnitude of 2 stars, we use the formula:
Where B is the brightness ratio of the two stars,
Note that the ratio of brightness is the reverse of the difference in magnitude. This is why the higher the brightness the lower they are categorized on the magnitude scale.
1 point
1
Question 9
9.
Simple and Familiar (1 - 2)
The two brightest stars in the night sky are Sirius and Rigel. They have a brightness ratio of
Use this ratio to find the apparent magnitude of Sirius with respect to Rigel. Based on your data, which is brighter?
1 point
1
Question 10
10.
Complex and Familiar (3 - 4)
Our closest neighbours in the galaxy is a star binary that consists of the stars Alpha Centauri A and B; they have magnitudes of +4.38 and +5.71, respectively. Find the brightness ratio of the 2 stars.
1 point
1
Question 11
11.
Challenging and Unamiliar (7 - 8)
In a newly discovered star cluster, the most prominent star is a red-coloured star and scientists decided to use it as a reference to measure the apparent brightness of all other stars. The brightness of the reference star has been calculated to be 10.