ABJelly

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Algebra

Let $a$ and $b$ be complex numbers. If $a + b = 4$ and $a^2 + b^2 = 6,$ then what is $a^3 + b^3?$

ABJelly Apr 24, 2024

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Science

Make a cone out of a piece of paper, make some measurements and estimates. Remember that
Measure the mass of your cone.
Measure the cross-sectional area of your cone.
Measure the terminal velocity read more ..

ABJelly Apr 16, 2024

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Science

If we wanted to measure terminal velocity, we could see how far something falls, measure how long that takes, and divide to get the terminal velocity.
On the other hand, that method would fail if the object were still accelerating up to its terminal read more ..

ABJelly Apr 16, 2024

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Science

Stars, like the sun cannot run on chemical energy. If they did, we estimated that they would burn through all their fuel within a few thousand years.
Stars run on nuclear energy. In the sun, this is almost entirely the energy given off when hydrogen read more ..

ABJelly Apr 16, 2024

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Science

German physicist Max Planck built a theory of black body radiation and used it to help start the field of quantum mechanics.
Planck's theory predicted:
In this formula, is the peak frequency of radiation coming read more ..

ABJelly Apr 16, 2024

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Compute

ABJelly Apr 16, 2024

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Series

ABJelly Apr 16, 2024

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Fill in the blanks to make a true equation:

Fill in the blanks to make a true equation:

ABJelly Apr 16, 2024

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Geometric Series

Letbe an infinite geometric series. The sum of the series is 3 The sum of the squares of all the terms is 4 Find the common ratio.

ABJelly Apr 15, 2024

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Geometric Series

Compute the sum

ABJelly Apr 15, 2024

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Geometric Series

Fill in the blanks to make the statement true:
The infinite geometric series with first term and common ratio has a sum of .
4
10 read more ..

ABJelly Apr 15, 2024

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Geometric Series

Evaluate the infinite geometric series
Express your answer as a fraction with integer numerator and denominator.

ABJelly Apr 15, 2024

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Geometric Series

What is the tenth term in the geometric sequence 9, 3, 1, 1/3,...?

ABJelly Apr 15, 2024

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Arithmetic Sequences

Let be an arithmetic sequence. Let denote the sum of the first terms. If and then find

ABJelly Apr 9, 2024

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Arithmetic Sequences

Let be an arithmetic sequence. If and , then find .

ABJelly Apr 9, 2024

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Arithmetic Sequences

In a geometric sequence, the 23rd term is 16 and the 26th term is 12. What is the 32nd term?

ABJelly Apr 9, 2024

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Arithmetic sequences

When the same constant is added to the numbers 60, 100 and 165 a three-term geometric sequence arises. What is the common ratio of the resulting sequence?

ABJelly Apr 9, 2024