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Answers by Isaak B.

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...

Minimum Speed (answer)

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...

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),...

Define Energy (answer)

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"...

Circular Measure (answer)

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...

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...

If the inflation rate of something is 0.9% per month, that means after one month, original price P0 has increased by 0.9% or in effect, been multiplied by one factor of 100%+0.9% = 100.9% = 1.009   Therefore after one month P1= 1.009P0   After another month, the...