Thread: Pre-Calc help?!?!?

If you read this before Wednesday I could really use your help. If you cannot answer this perhaps you know someone that could.

This is for my Pre-Calc.

#1.) The first row of a theater contains 50 seats, and each row there after contains an additional 8 seats. If the theater seats 938 people, find the number of rows in the theater. (I guess I have to use the Arithmetic Sum to find this answer)





#2.) The following statements about f(x) are true:
f(x) is a polynomial function
f(x) = 0 at exactly four different values of x
f(x) -> - infinity as x -> plus/minus infinity
For each of the following statements, write true if the statement must be true, false if the statement is never true, and sometimes true if it is sometimes true and sometimes false.
A.) f(x) is an odd function ____________
B.) f(x) is an even function ___________
C.) f(x) is a fourth degree polynomial ____________
D.) f(x) is a fifth degree polynomial ____________
E.) f(-x) -> - infinity as x -> plus/minus infinity _____________
F.) f(x) is invertible ______________









#3.) At Oceanside dock the first high tide today occurs at 2:00 AM with a depth of 6 meters and the first low occurs at 8:30 AM with depth of 2 meters.

A.) Assuming a sinusoidal function, sketch a graph of the depth of the water, d, at the dock as a function of the time t, after midnight.






B.) Write an equation of the graph showing the depth of the water d at the dock as a function of time t.





C.) Suppose a tanker that requires at least 4 meters of water depth is planning to dock after 9:00 AM. Using your graph in part "a," determine the earliest possible time that the tanker can dock and the longest period of time that the tanker can be docked before the water level becomes too low.




Thank you for your time!

Originally Posted by Wavikz

#1.) The first row of a theater contains 50 seats, and each row there after contains an additional 8 seats. If the theater seats 938 people, find the number of rows in the theater. (I guess I have to use the Arithmetic Sum to find this answer)
...

Hello,

the sequence which gives the number of seats per row is:

$\displaystyle s_r = 50 + 8(r-1)$

Using the arithmetic sum you get:

$\displaystyle N_s = \sum_{r=1}^n(50+8(r-1)) = 4n^2 + 46n$

That means you have to solve for n:

$\displaystyle 4n^2 + 46n = 938 \ \Longrightarrow n \approx 10.6...$
(There is a negative solution too but with your problem negative solutions are not very plausible)

Obviously 10 rows are not sufficient thus the theatre has 11 rows.

Originally Posted by Wavikz

[SIZE=2]...
3.) At Oceanside dock the first high tide today occurs at 2:00 AM with a depth of 6 meters and the first low occurs at 8:30 AM with depth of 2 meters.
A.) Assuming a sinusoidal function, sketch a graph of the depth of the water, d, at the dock as a function of the time t, after midnight.
B.) Write an equation of the graph showing the depth of the water d at the dock as a function of time t.
C.) Suppose a tanker that requires at least 4 meters of water depth is planning to dock after 9:00 AM. Using your graph in part "a," determine the earliest possible time that the tanker can dock and the longest period of time that the tanker can be docked before the water level becomes too low.

Hello,

to A.) I've attached a sketch of the graph.

to B.) Consider the following facts:

1. A half periode is 6.5 hours ==> length of period is 13 hours
2. The amplitude is 2
3. The lowest point is at +2 that means the complete graph must be shifted by +4
2. You are looking for a Sine function so you have to shift the sine function by a quarter period if the first peak is at midnight. Because the first peak is at 02:00 am you have to shift (the shifted graph) 2 units to the right

Finally you get:

$\displaystyle d(t)=4+2 \cdot \sin\left(\frac{2 \pi}{13} \cdot (t+3.25-2) \right) = 4+2 \cdot \sin\left(\frac{2 \pi}{13} \cdot (t+1.25) \right)$

to C.)

I've marked the time for the stay in harbour: From nearly 12:00 to 6.15 pm

Thank you! I also got 11 rows and the 11:45 to 6:15 for the time the boat can dock!