This type of question makes a few assumptions. It assumes that tasks can be broken up into evenly divisible sub-tasks so that the more workers you have, the faster the task can be completed.  This is sort of an approximation.  Take this assumption to its extremes to say why it isn't going...

If you want to calculate the volume of a pyramid, you multiply the area of the base by the volume and also by another factor of one third.   So you tell me: How does what you get with the shortened base compare to what you get with the original base?

If all of the waves are the same frequency, you can use a phasor to represent each sine wave.   Phasor are vectors that represent the amplitude of the sine wave by their direction and the phase of each sine wave by their angle.  You can add up the phasors like vectors -- in a head...

What do we know (or should we know) about parabolas?   They are represented by quadratic equations, or in other words, polynomials of degree 2.  So we are looking for the coefficients of a second degree polynomial. We can assume the ground to be flat in this problem.  Let...

To achieve an overall average speed of 20m/s, the pilot realizes that it needs to take 30 seconds ( delta t = delta x / speed = 600 m / (20m/s)) to finish each 600 meter lap, so two laps should take precisely one minute.   But if the first lap is completed at 15m/sec, that would have...

Your answer seems to suggest a diagram showing that the distance between A and B is 9 m, the distance between B and C is 6m, from C to D is 5m, from D to E is 20 m, from E to F 7m, from F to G 11m, from G to H 10m, but then you put 8m.  I'll assume that last 8m goes from H to I.   If...

The question is poorly written.  A car in view between two obstacles is "in view" from the moment its front bumper comes out from behind the rearmost obstacle until its rear bumper disappears behind the foremost obstacle.  The other responders have assumed the distance traveled...

Can I take a look at your program?

Good work so far!   Now you just need to find another periodic function that does better, without doing too much better.     You could either adjust the average indoor temperature (the vertical offset), or the swing (the amplitude of the periodic indoor temperature),...

i) Looking at a typical phase diagram for H2O, with temperature plotted on the horizontal axis, increasing to the right, and pressure plotted on the vertical axis, increasing as you rise, you should see that if temperature is decreased, you are moving to the left into the region labelled "Ice"...

Dear Jack,    Yes, you are correct to infer a close relationship between heat energy, it is closely related to the velocity of its atoms in a sense.  The temperature of a gas is related to the root mean square velocity of its atoms.   What makes energy such a powerful...

No, I don't think so. Not a direct, or exact answer, at least. Not without using a graphical or recursive method, such as Newton's method or some other method.   What is the context of your question? If you are being tested on ways to find numerical solutions for algebraically "un-solvable"...

There is likely more than one geometry-based way to do this, but the way that seems most obvious and straight-forward to me would be to calculate the area of the sector of the circle subtended by arc AQ, subtract the area between chord AP and arc AP, and subtract the area of the triangle between...

Great answer Mark, but you forgot Yeast America. North America, South America, West America and Yeast America.                 (Just kidding)

Let me give you an example.  Then you take what you learn from my example, and apply it to your actual problem, ok?   Let's say there are ten houses with families who may have pets on a street. Four have them have only a dog, three have only a cat, and two have both a cat and a...

The product of three consecutive integers can be represented as three separate variables if you wish. Let's say m*n*o. But the fact that they are consecutive means n = m+1, and o = n + 1 or o = m+2. We'd be able to solve a single equation in terms of a single unknown, so...

1. Write the equation in std. form if it isn't already.  Yours is since the powers are in decreasing order. 1. Make a list of possible rational roots by listing all the factors of the last coefficient. 18 in this case. 1,2,3,6,9,18. Each of those can also be plus or minus. 2. Add to...

Draw yourself two circles, overlapping by about a third.Then draw a rectangle around both of them. The area rectangle represents all 30 families. Let's go with assigning meanings to the circles by alphabetical order from left to right (although this ordering doesn't really matter as long...

Matrix describing foods' content * vector describing quantities consumed = vector describing nutritional totals   Matrix [[500 50 80][80 2 0][0 5 15]]*[F M B]^T = [3100 260 275]^T where ^T indicates the vector should be transposed (a column vector instead of a row vector.   There...

Angular velocity is the rate at which the angle (in radians) changes. We know the moon takes 27.32 days to go around the earth. So we know the period of one orbit.   This can be thought of as a ratios question, or you can just use the formula.   Ratios: 2π is to...