The tide removes sand from Sandy Point Beach at a rate modeled by the function R, given by

A pumping station adds sand to the beach at a rate modeled by the function S, given by

Both R(t) and S(t) have units of cubic yards per hour and t is measured in hours for . At time t=0, the beach contains 2500 cubic yards of sand.

(a) How much sand will the tide remove from the beach during this 6-hour period? Indicate units of measure.

First plug integrate the function at with the x values fnInt(2+5sin(4pi t/25),x,0,6)

shoul get =31.816^3 yds

(b) Write an espression for Y(t), total number of cubic yards of sand on the beach at time t.

y(t)= fnInt(s(t)-fnIntR(t)) dt +2500

(c) Find the rate at which the total amount of sand on the beach is changing at time t=4.

y'(4)= { (15t/1+3t) dt - { (2+5sin(4pi t/25 dt + 2500

=

plug in 4 and integrate result=-1.908 yd/hr

(d) For

, at what time t is the amount of sand on the beach a minimum? What is the minimum value? Justify your answers.

find where the y1-y2 gives you 0 or undefined. (critical points)

at that x value plug in to the funvtion integrate and final result will give you the minimum value.

The function f(x) from the graph f '(x)

1. f(x) is increasing at the intervals (-2,0)U(2,0)


f(x) is decreasing at the intervals (-infinti, -2)U(2, infinti)

where f '(x)>0 f is increasing & f '(x)<0function is decreasing


2. at x= +/- 1.25 local max. the slope increases then decreases so they have to be max's.


3.concave up at (-infinti, 2) concave down (2, infinti)

we know where f is increasing up and then decreasing down determining the concavities.


4.quadratic maybe end behavior of x to the power of 5.

My Mindset?

1. When it comes to intelligence i understand yes i am who i am but i too know it deosnt end there i understand that my intelligence can change. the same a baby into a teen and a teen into an adult. I belive it just takes some time and patience for example the more stress you apply to a muscle yeah it hurts but it becomes stronger. another example would be ways of life you may not live a certain lifestyle but as you apply it into yours you get stronger, lifestyle wise of course. According to the reading i hope i am growth mindset and if others see me as fixed then i can also change my mentality.

2. This has hurt me in math due to the fact that i fully understand that my intelligence can change and i could learn more... this means more work. however more work means that eventually the subject should get easier. i just have to pace myself and try to stay onboard during whatever climate. Help from the captain and the instructions last but not least my fellow crew.

3. When i read the news i immedialtey thought of a fighting style example muay thai and the muscles you train. first the start off normal then you build and develop better skill.

4.The future looks brighter, iHope on. i just cant stop here there is more to accomplish.