# Tutor profile: Oren L.

## Questions

### Subject: Trigonometry

Write a sinusoidal function that oscillates between the values of 5 and -1 with a time period of T=2 seconds

The general structure of a sinusoidal function (without a phase shift) is: $$A\sin(\omega*t)+B=\sin((2*\pi)/T*t)+B$$ Where: A is the amplitude, $$\omega$$ the angular velocity (in Radians/sec) ,T the period (in seconds), t the time in seconds and B the vertical shift. Given that the required displacement is between 5 and -1 the corresponding amplitude would be 3 ($$(5-(-1))/2=6/2=3$$) with a vertical shift of 2 (a graph would best represent this part). Finally the period is given as 2 and therefore the resulting function is: $$3\sin((2*\pi)/2*t)+2=3\sin(\pi*t)+2$$

### Subject: Geometry

Sam's mother baked a round birthday cake with a diameter of 40cm for his birthday party. She cut the cake into 45 degrees equal sectors. What is the length of the arc of each piece and what is the area of each piece?

For this one we'll need to remember that the are of a circle is given by: $$A=\pi*r^2$$ and that the circle's circumference is given by: $$C=2*\pi*r=2*d$$ Now, since we know the circle's diameter 40cm and thus radius ($$r=d/2=20cm$$) we can use the corresponding formulas to calculate the cake's area and circumference $$A=\pi*20^2=1256.63 cm^2$$ and $$C=2*\pi*20=125.6cm$$ We now have to check into how many parts the cake was cut and we'll do that by calculating the ratio between the angle of each sector and 360 degrees (the number of degrees in a circle): $$Ratio=45/360=1/8$$ And therefore the area of each slice will be $$1256.63/8=157cm^2$$ and the circumference of each slice would be $$125.6/8=15.7cm$$

### Subject: Algebra

Today there are 100 sick people in a population. It is known that the number of affected people doubles every 3 days. Write a general formula that describes the number of sick people after t days and calculate how many sick people there will be after 21 days.

Let's try to find out how the number of sick people grows and then write a general formula: at t=0: 100 at t=3 days: $$100*2=200$$ at t=6 days:$$100*2*2=400$$ ..... at t days: $$ 100*2^{t/3}$$ Therefore after 21 days: $$100*2^{21/3}=12800$$ people will be sick

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