King Curry

23 May

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This is LaBron Gems and he is considered one of the best basketball player of all time. Lebron James has a 50.10% field goal percentage, which means out of the total shots he tried, he made 50% of them. In order for Bron to increase his ratio to 55%, he would not be able to reach it. As you can see there is an horizontal asymptote. The number of additional shots would be higher than 10,000,000 which is impossible for his lifetime.

Which player in the NBA do you think has a better field goal percentage than bron bron?

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Reflection

8 Apr

In this semester we’ve learned several topics such as linear functions, average rates of change and polynomial in the short-run and the long-run, exponential function, and quadratic functions. I don’t think pre-calculus has been much different than the math I learned in high school. Calculating the average rate of change was surprising to me because it was something new that I never learned. The most interesting idea was finding the roots. However the topic I had most trouble with was piecewise functions.

I think the idea Ill use the most is calculating the average rate of change. It is the change in the value of a quantity divided by the elapsed time. For a function, this is the change in the y-value divided by the change in the x-value for two distinct points on the graph. Something I would like to go differently moving forward is having the professor teach more using the white board instead of desmos.

What do you want to do differently going forward?

Imagine All The Numbers

5 Apr

Complex does not mean complicated. A complex number is a combination of a real number and an imaginary number. Real numbers are basically any number you can think of and imaginary numbers when squared give you a negative result.

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Ex) Add 3+5i and 4-3i

(3 + 5i) + (4 − 3i)
= 3 + 4 + (5 − 3)i
= 7 + 2i

An electromagnetic field, for example, requires imaginary numbers to measure because the strength of the field is determined by both electrical and magnetic components that must be combined into a single complex imaginary number to get an accurate measurement. Is my example helpful?

 

Fancy Factoring

3 Apr

x^3 – 5x +3x -15 – Factoring by group

In order to factor by grouping this polynomial we have to see if the terms have any GCF (Greatest Common Factor). In this case there is 1 GCF. Then we create smaller groups by grouping the first two terms together and the last two terms together which will be x^3 – 5x^2 + 3x – 15, then we factor out the GCF from each of the two groups and in this problem the signs in front of the 5x^2 and the 15 are different so you need to factor out a positive 3 which then you will get x^2(x – 5) + 3(x – 5), the thing that the groups have in common are the (x – 5) so you can factor that out which gives you (x – 5)(x^2+3), then see if any of the remaining factors can be factored which they cannot so that is the final answer

18x^2 – 98y^2  – Factoring the difference of squares

the two terms have 2 in common and gives us 2(9x^2 – 49^2), To factor this problem into the form (a + b)(a – b), you need to determine what squares will equal 9x2and what squared will equal 49y2. In this case the choices are 3x and 7y because (3x)(3x) = 9x2 and (7y)(7y) =49y^2 which gives us 2(3x + 7y)(3x – 7y)

Was this helpful?

 

In the Long Run…

3 Apr

A polynomial is an expression consisting of variables and coefficients, that involves only the operations of addition, subtraction, multiplication, and non-negative integer exponents. The degree of the polynomial is the largest exponent on the variable. The leading coefficient in a polynomial is the highest degree term. The polynomial I created is x(1+3x^9), when zoomed out it looks like the function u(x) =5x^2 and when zoomed in it looks like the function q(x)=0.5x. Below the blue line represents u(x) =5x^2 and the red line is x(1+3x^9).

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Below the blue line is x(1+3x^9) and the red line is q(x)=0.5x.

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Any feedback on my polynomials?

Fiddler Crabs and Babies

28 Mar

Allometry is the study of the relative change in proportion of an attribute compared to another one during organismal growth. Basically when a body part grow bigger and another grows smaller over time. Allometric growth can be seen in nonhuman primates. For example the jaw and other facial structures of baboons have a growth rate about four and one-quarter times that of the skull. As the baboon matures, the jaw protrudes further and further until it dominates the facial features. A power function that depicts allometry is F(x) = Kx^P. I had trouble finding examples of positive and negative allometry formulas, if anyone know please share.

Graphs that Bend

27 Mar

When a graph is concave up it means that the average rate of change is increasing if you move from left to right and when the graph is concave down it means that the average rate of change is decreasing as you move from left to right. For a graph to concave up, it means that the slope is increasing which means the second derivative over an interval must be greater than zero and for it to concave down it means that the slope is decreasing and the second derivative is negative. What else do you know about concavity?