actually, it is relatively simple. since you are given the equation and the height of the pole, we just need to find 't'. Since the question just states that the water height has to be 80cm to solve, using the equation, the water depth 'd' must equal 80cm. So, that would make the equation, 80cm=40+60cos((pi/6)*t). Now, we have to seperate 't' from the rest of the equation. So, (80cm-40)/(60)=cos((pi/6)*t). ((80cm-40)/(60)) equals (2/3). Therefore, (2/3)=cos((pi/6)*t). To get rid of the cosine ('cos' in the equation) we have to take the inverse of it. (This is the cos^(-1) key on your calculator.) And using basic algebra, you know that what you do to one side of the equal to sign, you also have to do to the other side. So, now the equation looks like (cos^(-1)[(2/3)])= (cos^(-1)[cos((pi/6)*t)]. wow, that is a lot of explaining. Anyways, Type (cos^(-1)[(2/3)]) into your calculator (you can do this on a scientific calculator.) and you will get something like: 48.18968511. (*Be sure that your calculator is in DEGREE mode unless you can directly convert radians*) 48.18968511= ((pi/6)*t) [cos^-1 and cos cancel on the right hand side]
now convert 48.189..... to radians (because (pi/6) is a radian angle) in order to convert degrees to radians, you have to multiply the degree measure by (pi/180) (that's just how it is done, dunno why) and you will get 48.189...*(pi/180)=.841066... now the equation reads 0.841066=((pi/6)*t). Therefore, t=0.841066/((pi/6)). that give the value of 't'. Now the value of t='A'. Type ln(A) into your calculator, and obtain the value of the tenths digit of the answer. THAT, my friends is your answer LOL!!!!! since none of you could answer, i think you should increase my rep. bar. If you can give me a problem that i can't solve, then i will increase your rep. bar. :chris: :nuke:
-majin3
two4one said:
majin3 said:
interesting question, I have another one though:
On a beach in Hawaii, there sits a small post sticking up out of the ground. The top of the pole is 80 cm from the ground. The water depth on this beach increases and decreases in a sinusoidal motion. The water depth is denoted by the equation d=40+60cos((pi/6)*t), where 't' is the number of hours after midnight. Let 'A' be the first value of t, t>0, to the nearest thousandth at which the water level just at the top of the post. Find the tenths digit of ln(A).
:nuke:
this is somewhat tough one for normal science students... unless he is familiar with physics and maths .....
i tried but failed.. i think in solving this we adopt sine wave functions and trigonometric equations in solving this mystery