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Catherine Q.

Studying Applied Math & Statistics at Johns Hopkins

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Environmental Science

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Question:

Explain the concept of a carbon sink

Catherine Q.

Answer:

Through the carbon cycle carbon is moved around within the atmosphere, hydropshere (all the water on Earth) , lithosphere (crust and upper mantle of Earth) , and land biosphere (plants and animals). Carbon moves between these 4 reservoirs of carbon through carbon fluxes, which are methods of releasing or capturing carbon A carbon sink is a carbon flux which pulls carbon out of the atmosphere These are especially important now as we look to slow global warming by restricting the amount of carbon in the atmosphere An example of a carbon sink is photosynthesis, plants take in carbon from the atmosphere

Calculus

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Question:

Find the derivative of the equation 3x^2

Catherine Q.

Answer:

The derivative of an equation is the rate of change of an equation at any point it can be found by calculating the change in y over the change in x as the change in x gets smaller and smaller approaching 0 formally the derivative of a function y = f(x) can be found by taking the limit of the slope formula (the change in y over the change in x) as the change in x goes to 0 the change in y is f(x + delta x ) - f(x) and the change in x is delta x change in y / change in x = f(x + delta x ) - f(x) / delta x in this instance f(x) = 3x^2 so change in y / change in x =( 3(x + delta x)^2 - 3x^2) / delta x when you expand out 3(x +delta x)^2 it becomes 3(x^2 + 2x(delta x) + (delta x )^2) -> 3x^2 + 6x (delta x ) + 3(delta x )^2 change in y / change in x = (3x^2 + 6x (delta x ) + 3(delta x )^2 - 3x^2) / delta x the 3x^2 cancel (6x (delta x ) + 3(delta x )^2) / delta x since both terms in the numerator contain a delta x it can be factored out so the numerator becomes delta x (6x + 3 delta x) the factored out delta x in the numerator cancels with the delta x in the denominator change in y / change in x = 6x + 3 delta x as the change in x goes to 0 delta x goes to 0 so the derivative of 3x^2 is 6x

Algebra

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Question:

How to find the y intercept and slope of the graph equation 2x - 4y = 9

Catherine Q.

Answer:

First you should manipulate the equation into y = mx + b with m being the slope of the line and b being the y intercept 2x - 4y = 9 -> move the 4y to the other side of the equal sign but adding 4y to each side by adding to both sides of the equal sign it does not change the slope or the intercept of the graph equation 2x - 4y + 4y = 9 + 4y -> 2x = 9 + 4y next subtract 9 by both sides -> 2x - 9 = 4y the last step in putting the equation into y = mx + b format is to divide both sides of the equation by 4 (2/4)x - 9/4 = (4/4)y -> (1/2)x - 9/4 = y So the slope of the line is 1/2 and the intercept is 9/4

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