Answer:
Starts on Saturday, June 1
and ends on
Saturday, November 30
Explanation:
<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: c. Generally, metals are ductile.
Explanation:
From the options given in the question, the correct statement is that"Generally, metals are ductile.
Ductility of a metal simply means that a metal can be plastically deform before it is then fractured. It implies that metals can be drawn to thin wires. The only exception we have in this case is mercury.
Answer:
4.88 m/s
Explanation:
Vertical component would be 12 * sin 24 = 4.88 m/s
Horizontal is 12 * cos 24
Answer:
book speed is 3.99 m/s
Explanation:
given data
mass m = 490 g = 0.490 kg
compressing x = 7.10 cm = 0.0710 m
spring constant k = 1550 N/m
to find out
book speed
solution
we know energy is conserve so
we can say
loss in spring energy is equal to gain in kinetic energy
so
..................1
put here value
v = 3.99 m/s
so book speed is 3.99 m/s
