<span>f(x) = 5.05*sin(x*pi/12) + 5.15
First, you need to determine the period of the function. The period will be the time interval between identical points on the sinusoidal function. For this problem, the tide is rising and at 5.15 at midnight for two consecutive days. So the period is 24 hours. Over that 24 hour period, we want the parameter passed to sine to range from 0 to 2*pi. So the scale factor for x will be 2*pi/24 = pi/12 which is approximately 0.261799388. The next thing to note is the magnitude of the wave. That will simply be the difference between the maximum and minimum values. So 10.2 ft - 0.1 ft = 10.1 ft. And since the value of sine ranges from -1 to 1, we need to divide that magnitude by 2, so 10.1 ft / 2 = 5.05 ft.
So our function at this point looks like
f(x) = 5.05*sin(x*pi/12)
But the above function ranges in value from -5.05 to 5.05. So we need to add a bias to it in order to make the low value equal to 0.1. So 0.1 = X - 5.05, 0.1 + 5.05 = X, 5.15 = X. So our function now looks like:
f(x) = 5.05*sin(x*pi/12) + 5.15
The final thing that might have been needed would have been a phase correction. With this problem, we don't need a phase correction since at X = 0 (midnight), the value of X*pi/12 = 0, and the sine of 0 is 0, so the value of the equation is 5.15 which matches the given value of 5.15. But if the problem had been slightly different and the height of the tide at midnight has been something like 7 feet, then we would have had to calculate a phase shift value for the function and add that constant to the parameter being passed into sine, making the function look like:
f(x) = 5.05*sin(x*pi/12 + C) + 5.15
where
C = Phase correction offset.
But we don't need it for this problem, so the answer is:
f(x) = 5.05*sin(x*pi/12) + 5.15
Note: The above solution assumes that angles are being measured in radians. If you're using degrees, then instead of multiplying x by 2*pi/24 = pi/12, you need to multiply by 360/24 = 15 instead, giving f(x) = 5.05*sin(x*15) + 5.15</span>
Answer:
1- The acceleration of the object is larger in magnitude the smaller the radius of the circle.
Explanation:
The acceleration of an object in a circular path is
As can be seen from the equation, if the radius of the circle is decreases, the magnitude of the acceleration increases.
As for the direction of the acceleration, it is always towards the center, and it is always perpendicular to the direction of the velocity.
Explanation:
Expression to calculate thermal resistance for iron (
) is as follows.
where, 
= length of the iron bar
= thermal conductivity of iron
= Area of cross-section for the iron bar
Thermal resistance for copper (
) = \frac{L_{c}}{k_{c} \times A_{c}}[/tex]
where, 
= length of copper bar
= thermal conductivity of copper
= Area of cross-section for the copper bar
Now, expression for the transfer of heat per unit cell is as follows.
Q = 
Putting the given values into the above formula as follows.
Q = 
= 
= 2.92 Joule
It is known that heat transfer per unit time is equal to the power conducted through the rod. Hence,
P = 
Here, T is 1 second so, power conducted is equal to heat transferred.
So, P = 2.92 watt
Thus, we can conclude that 2.92 watt power will be conducted through the rod when it reaches steady state.
For a reaction to occur, energy must be absorbed to break chemical bonds
<u>Explanation:</u>
Reactions can be classified as chemical reaction, nuclear reaction, thermal reaction. So in these three reaction types, the nature of energy will only be varying.
But in order to execute a reaction, there should be breaking of existing bonds and then formation of new bonds. So for breaking of the bonds of reactants, energy should be absorbed from the surrounding.
Then the extra energy will be released after forming the products. Thus, the process of absorption of energy will lead to endothermic process and the process of releasing of energy will lead to exothermic reaction. So for a reaction to occur, energy must be absorbed to break the chemical bonds.
