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# Tutor profile: Jesse M.

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Jesse M.
Experienced Science and Math Tutor and Graduate Student in Evolution, Ecology, and Behavior
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## Questions

### Subject:Environmental Science

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Question:

Based on the understanding of how energy moves up the tropic trophic pyramid, what change can humans make to conserve large amounts of energy on a global scale?

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Jesse M.

It is a basic rule that only 10% of the energy is conserved by consumers from what they eat. The rest of the energy is lost in the form of heat. What this means that the way energy transfers from one organism to another is not very efficient and that most of the energy that hits the earth is lost. Of all the solar energy from sun that hits the earth, plants only are able to use around 10% in the process of photosynthesis. Of the energy available in all producers (plants), only 10% of the energy consumed will be transferred to the next trophic level. This next level would be made up of herbivores like cows. The 10% pattern would continue to the next level to any organism eating the cow and so on. When thinking about conserving this energy we need to consider how this energy moves up this trophic cascade and where humans fall in the trophic pyramid. When a human eats a cow, they are really getting 1/100th the amount of energy in terms of the sun compared to what they get from eating just eating plants. So a switch to a plant only diet would conserve large amounts of energy based on a understanding the trophic cascade.

### Subject:Biology

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Question:

What is the Red Queen Hypothesis and how does it inform our understanding of the evolution of sexual reproduction?

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Jesse M.

### Subject:Calculus

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Question:

Find the derivative of the following: \$\$2(5x^{2}+3x+10)^{4}e^{x^{3}+2x^{2}}\$\$

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Jesse M.

Just looking at this you can tell it will be a monster of a problem but do not give up now because this is far from impossible. We see there is a polynomial raised to an exponent so that should yell chain rule but also there are two functions being multiplied so that tells us to be thinking product rule and lastly there is the dreaded e. Instead of trying to attack this all in one go lets take a step back and see if we chip away at the problem one piece at a time. In this case, nothing can be started until we address the product rule because we cannot take any derivatives while there is a multiplication between the functions. A brief reminder: the product rule states when [f(x)g(x)]'= f(x)g'(x) + f'(x)g(x). Applying the product rule to our really big and complex problem, we get \$\$2(5x^{2}+3x+10)^{4}(e^{x^{3}+2x^{2}})'\$\$+\$\$(2(5x^{2}+3x+10)^{4})'e^{x^{3}+2x^{2}}\$\$. Now that we have applied the product rule, we can just focus on where we need to apply the chain rule. We can see that \$\$(2(5x^{2}+3x+10)^{4})'\$\$ will have to be solved by the chain rule because it is a polynomial raised to an exponent. So let us solve this portion. First, the chain rule states that the exponent is multiplied to the coefficient and subtracted by 1. Then, the polynomial is left alone but the whole function is multiplied by the derivative of the polynomial. What this looks like in our problem is we go from \$\$(2(5x^{2}+3x+10)^{4})'\$\$ to \$\$8(5x^{2}+3x+10)^{3}(10x+3)\$\$. Derivatives of \$\$e^x\$\$ are a slightly different story but we can still apply the chain rule. When dealing with an "e" raised to anything, the derivative will be the "e" and its exponent left alone then multiplied the derivative of the exponent. So in the case of \$\$e^{x^{3}+2x^{2}}\$\$, the derivative would be \$\$e^{x^{3}+2x^{2}}(3x^{2}+4x)\$\$. With all of the derivatives in hand, we can pull all the pieces together and get one more step closer to solving this problem. After applying the product rule then chain rule to the problem we now have: \$\$2(5x^{2}+3x+10)^{4}e^{x^{3}+2x^{2}}(3x^{2}+4x)+8(5x^{2}+3x+10)^{3}(10x+3)e^{x^{3}+2x^{2}}\$\$. Now, you could do some condensing to make this look a little nicer but this is the derivative and we were able to take an impossible looking problem and solve it by taking it one step at a time.

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