<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>
The type of reaction that occurred in the test tube is ACID BASE REACTION.
Acid base reaction is a type of chemical reaction in which an acid and a base react together to form salt and water molecules. It is also known as neutralization reaction. For the question given above, the applicable chemical reaction is as follows:
HF + NaOH = NaF + H2O
From this chemical reaction, it can be seen that, hydrogen fluoride, which is a weak acid react with sodium hydroxide which is a strong base to produce sodium fluoride, which is a salt and a molecule of water.
The northward components of the resultant displacement is 40.96 m and the westward components of the resultant displacement of the bird from its nest is 28.68 m.
<h3>
Displacement of the bird</h3>
The displacement of the bird is the change in the position of the bird.
<h3>Vertical component of the bird's displacement </h3>
Vy₁ = -25 m x sin(55)
Vy₁ = -20.48 m
Vy₂ = 75 m x sin(55)
Vy₂ = 61.44 m
Total vertical displacement = 61.44 m - 20.48 m = 40.96 m
<h3>Horizontal component of the bird's displacement </h3>
Vx₁ = -25 m x cos(55)
Vx₁ = -14.34 m
Vx₂ = 75 m x cos(55)
Vx₂ = 43.02 m
Total horizontal displacement = 43.02 m - 14.34 m = 28.68 m
Learn more about displacement here: brainly.com/question/2109763
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Axial Tilt and Sun Energy
This axial tilt means that during the Earth's journey around the sun the poles receive varying amounts of sunlight. The equator, however, receives relatively consistent sunlight all year. The consistency of energy means the equator's temperature stays relatively constant all year.
Answer:
P = F/S = 100/2 =50 (N/m2)
