Math help grade 11 functions

[chaosrunner]

Part A


1) marcus and his family decide to go to niagara falls to enjoy the ride of the niagra sky wheel,the sky wheel is risen 53.3 m above the ground, giveing the riders a spectacular view
of the falls and its souroundings the skywheel has a diameter of 50.5 m and rotates at the rate of one revolution every 120 seconds

marcus and his family bought 4 tickets at a total price of 49.67 including taxes thier ride started at the bottom of the ride which is 2.8 m above the ground

a) sketch the height, h meters of marcus and his family above the ground during one complete revolution at time, t seconds

b) determine a sine/cos function that will model height (h t), of marcus and his family above the ground t seconds

c) determine the height of marcus and his family after 45 seconds round to nearest meter

d) determine speed of skywheel express answer to two decimal places


Part B

1) fatima drops a ball from the height of 16m each time the ball touches the ground it bounces 5/8 of maximum height of previous bounce
determine total vertical distance the ball has traveld when it touches the ground on the seventh bounce

2) 10 years ago raj deposited $5000 into an investment account with intrest compound quarterly. for the first 5 years the intrest rate was 6%
and for the next 5 years the interest rate changed to 4.5% how much money is in the account now


Part C

2) lee wants to make semi anual deposits into an account at 6% a compound semi-anually. he would like to have $4500 in the account at the end of 25 years

a) how much should he deposit at the end of each 6 months

b) how much intrest does he accumilate

 

[Dorimori]

seven

 

[FAST6191]

Why are you posting this in the EOF? Usual policy of not giving full answers is in effect.

a) rather depends upon how you reference the start. "at one full revolution" you are back at the bottom if you start there. Unless you mean you need a graph showing the height during the course of the revolution. Classically it is a sine wave function (the one I was taught was imagine a cotton bobbin on a record player, which was old even then) as b) appears to say so yeah I guess it is asking for that. I also assume they are not trying to be cute and used the same reference point for the height at all points.

b) If 1 revolution is 120 seconds then t/120 gives you the ratio of a full turn.
Set your calculator into radians if you like (being a ratio based thing it makes sense to go down that path for me), you could still use degrees if you want though.
(2*pi*t)/120 is the radians value of the angle between the mid point of the circle and the start point (which I will fix to the lowest point). Both lengths are the radius as you are in a circle.
I kind of just woke up (stayed up for the Sony conference, even if I only saw the IRC reactions) and I am really not thinking elegantly right now, sketching it out did not help either. To that end I want to make an equation that changes between periods in the trip (between 0 and pi/2 radius-(cos (angle) * radius), between pi/2 and pi (((cos(angle-pi/2))*radius)+radius as you are a radius height up), between pi and 1.5pi, and a final one for between 1.5pi and 2pi.
It is however what I would do if asked for a singular value without an equation needed.
I don't know if this approach is what you might learn in the 11th grade though -- I just do maths these days and probably would not even be able to tell you if it is year 11 in the UK/GCSE suitable. There is probably some basic way staring me right in the face though, either way once you have the angle it is a fairly basic application of trig and geometry).

In any case makes a triangle with the hypotenuse as the radius and the height being related to that and the angle.
All this plus the height above the ground the thing is to begin with. Round at this point.

As a check your value at t=60 should be 2*r+initial off the ground height. At quarter and three quarters it should be radius plus initial and at 0 and full turn it should be just initial off the ground height.
c) you have the equation.

d) Speed = distance travelled / time, and it did ask for speed rather than velocity. Anyway distance travelled is the circumference of the circle (pi x diameter) and the time is t which you know. You are told the diameter so need to calculate there from height and height above the ground, though if you wanted to use it as a check then by all means.

2)
a) Yay compound.
16*5/8*5/8*5/8*5/8*5/8*5/8*5/8 = 16* (5/8)^7

b) 5 years of quarterly is what 20 periods, or is it 19 depending upon how you want to view things?
5000*1.06... I am not going to do all the brackets. ((1.06)^20)*5000
Another 5 years or 20 periods quarterly with the sum from the first period as the initial investment
(((1.06)^20)*5000)*((1.045)^20)= sum total.

C
Semi annually means twice a year I take it.
50 deposits then (helps to think of it that way if you are using an online calculator which does not do semi annually). It does not say identical deposits but I assume that is what it is going for. I am not sure if there is a fudge with opening payments (one does not tend to open an account and get 6% on the day, also if the last payment is accounted for even if he then withdraws it before the interest for the next cycle is paid), interest and such if one of those wants to be one less or more so I will assume it is basic. It would not be terribly hard to jig a couple of things anyway.
Three periods then would be
(((X*1.06)+X)*1.06)+X)*1.06=whatever
To expand that to 50 would be annoying, much less solving for X using that.

Anyway answer is between 14 and 15 dollars I think. http://www.ajdesigner.com/phpinterest/interest_regular_deposits_p.php#ajscroll might also help but I have to leave now.
I would probably use a spreadsheet for this in real life, bonus being it would also easily tell me what is there at each stage. Alternatively it is the inverse version of a loan in which you only pay on your remaining amount of the initial borrowing.

 

[BurningDesire]

@MarcusD How was the trip

 

[Sono]

@MarcusD How was the trip

My headache got stronger after reading thru' this thread

But otherwise if I wouldn't have a headache, I would be probably able to fully calculate part A on my own.

marcus and his family

It only says "Marcus", not "MarcusD", so it's not me

 

[BurningDesire]

My headache got stronger after reading thru' this thread

But otherwise if I wouldn't have a headache, I would be probably able to fully calculate part A on my own.



It only says "Marcus", not "MarcusD", so it's not me

You're the only marcus I know on the site lmao

 

[EarlAB]

Marcus likes the D.

 

[Sono]

Marcus likes the D.

Yes, I like Diana

 

[EarlAB]

All I saw was this:
Spiritus menthae cum sale.