Challenges cover a variety of topics
Today’s challenge requires the concept of Algebra.
5 glasses contain amounts of various liquids. The glasses are numbered 1 to 5. Non-prime glasses contain liquid A, and prime glasses contain liquid B. Odd glasses contain 750mL, and even ones contain 500mL. When you mix 2 glasses they then contain the same quantity of liquid in the same proportions. The challenge is to find the minimum number of mixes to ensure that each glass contains the same quantity of liquid A.
Graph theory and algebra are required to solve this challenge.
Our challenge begins with a set of points. There are points of red, orange, yellow, green, blue, and purple. These points are all interconnected as follows. Every red point connects to 1 red point, 2 orange points, and 3 green points. Each orange point connects to 1 red point, 2 orange points, 2 yellow points, and 1 blue point. All yellow points connects to 1 orange point, 1 other yellow point, 3 green points, and 1 purple point. Green points all connect to 1 red point, 4 yellow points, and 1 blue point. All of the blue points connect to 2 orange points, 3 green points, and 1 purple point. And finally, purple points connect to 4 yellow points, 1 blue point, and 1 purple point. The question is this: what is the minimum number of points for each colour?
Calculus is required to solve today’s challenge.
let:f(x)=1/g(x),h(x)=-g(x)Today’s challenge is to find the antiderivative of f(x), given that the derivative of h(x) is 0.5. Remember that both functions are related to g(x).
This challenge challenges your algebra skills.
Joanne is doing a science experiment. She is trying to purify water so that there are no isotopes. This means that there will be only normal H₂O molecules. If Joanne has 9kg of water after all of this, how many kilograms of hydrogen atoms does she have?
Solving this challenge requires an understanding of geometry, trigonometry, and angle theorems.
In today’s challenge, we face two triangles who are not congruent. This is surprising because they appear identical, and we are told they share two sides. We can find that they also share and angle. However, because the angle isn’t between the sides, it’s only SSA. SSA is not a valid congruency theorem, because in some cases it gives two possible solutions. In this case, we have both of them, directly connected. The question is this: what is the length of the line that is cut unevenly? That is, the one whose length equals the sum of the sides that the triangles do not share.
In today’s challenge, you will have to use your pathmaking and graph theory skills.
The challenge is to make as many connections as you can. However, your connections must follow these rules: 1. All connections must be on a dotted line, and 2. That path must start at A and end at B.
In today’s challenge, you will need to use trigonometry, angle theorems, and geometry.
The challenge for today is to find the area of the entire figure. We are given 3 lengths, 2 angles, 1 length equality, an angle equality, and finally, 1 set of parallel lines. Remember the units!
Today’s challenge utilizes the concept of algebra.
let: a+5=2-b, ab+3=a-74This time, the challenge is to see if you find all solutions to the above system of equations.
Today’s challenge features the concepts of geometry, angle theorems, and trigonometry. No calculator required, though.
The challenge for today is to find the area of △ABD, given that the area of △ACD is √2, that AB is 3, DC is 4, ∠BAD = 30°, and ∠ADC = 45°.
In today’s challenge, you will need the concept of path-making.
In today’s challenge, we have 5 connected points. Can you find the number of possible paths, starting and ending at intersections, that never use the same intersection twice?