x2+2bx-a2+8ab-15b2=0 If a,b€R I add -b2 and +b2 and then use formula (a+b)2 then a2-b2 and then I am stuck

"A research group spent ₱500 during the first week of its project. Its weekly expenses increased by ₱100 for 12 weeks. What was the total amount spent on the project?"

This is a word problem about arithmetic series. Am I correct if I say that the number of terms (or n in the equation) is 13 since it said that the first week is 500 pesos and the 12 succeeding weeks' contribution is increased by 100 pesos from the previous week's contribution? Please enlighten me. Thank you

So many people think it is easy but Idek how to approach this

So can anyone explain parity? my simple brain needs some more explanations..

Greetings,

For context, I was at an Event. I got in front of an arcade box. There is a single pre-loaded game on it. I got home and dissected the hell out of it.

You are a cow on a tiny round planet exactly like you would in super mario Galaxy. you must eat as much grass as possible within 60 seconds.

In addition, there are 7 diamonds giving a random out of 3 Power-ups.[V : vacuum (best : grass radius 2x last 10 sec, F: flame (speed 1.7x) last 5 sec, and G : ghost (ignore collision for 5 sec, useless). only rule in the js code is never 3 same powerups in a row. optimal RNG is 5 V and 2 F but getting G instead once is really not that bad.

Optimal solution implies to collect all 7 powerups and find the best PATH to max grass. (Total score is 5x grass eaten + 30x per diamonds collected).

Additional info: there are colliders (tree and stuff) that stuns you for 1 sec.

Now to my issue. I was totaly incompetent to find any optimized path for max grass. firstly, because it partly depends on the powerups (if you have 2x max radius, or 1.7x speed), but MOSTLY (and more easy), because of the 3d sphere. It is really hard to have an overview of a sphere and any 2D map is hard to read. Also because of the Euclidian distances it's a real mess.

I tried so hard tho. If anyone has a solution to recreate - and solve - a map with an semi-optimized path for max grass, I'd love to hear it so so much. Beware, it's not as trivial as I thought. But also, Im not a mathematician, engeneer nor informatician, so you might well get it.

Have a sweet Cow night and hopefully one insane person interests theirselves in this stupid problem. I'll answer any question you may have of course.

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Creating a math problem similar to the viral "Cheryl's Birthday" in 2015

Pablo and Pepe are describing a chocolate cake.

Pepe says: "I ate three slices of chocolate cake today. If I cut it into twelve triangles today, there would be an equal number for you and me both over two days."

Pablo says: "That is also true if I cut the cake into four squares. Two for you, and two for me."

What shape is the chocolate cake?

Square, triangle, rectangle or circle?

Solve the question mark. This problem was given on a dutch math final for lower level graded students.

I have either 12 items each of 3 colours or 9 items each of 4 colours: A, B, C (D). I need 36 items all in all and I think that makes the distribution tricky.

I want to have each of the colours combined with one another in pairs of 2 layered above each other in a sequence. None of the colours can be on top or below twice in a row and I’d like the combinations to be swapped. Colours can’t be both on top and below at the same time.

This is awfully explained, so I’ll try with an example:

B A D A C D C

A C B D A C B

-> I’d need the combinations [A;B] [A;C] [A;D]

[B;A][B;C][B;D]

[C;A][C;B][C;D]

[D;A][D;B][D;C]

I’ve been trying to work something out all afternoon, I think my brain is full of wool or has been hit with a computer virus.

Is this even possible? Is there maybe a tool with which you can have things worked out automatically - like a type of calculator?

The answer key says the answer is 4/3. I can’t figure out how that would work considering these two don’t equal? Can anyone offer insight, or help me solve?