Alright, so the difference between tidal heights is 12.6 ft. right? For every integer cos(x) is multiplied, say a*cos(x) the amplitude doubles. So then, (1/2)=(n/12.6) will gives us a value for a that will match the differences in tidal height. a=6.3. Now let's say that 2pi will give us a full cycle from high to low back to high again. If 12:00 noon is our high, it takes 15.2hrs to complete a cycle back to high again. 2pi = 6.28 roughly, and we know that is less than our midpoint in a whole cycle, 7.6 hrs. Also, for every value k>1 in cos(kx), this increases the frequency of waves in a given period. So it seems that we need a value of k less than 1. So we can lower the frequency to match the cycle we are looking for, which is to come back to 17.7 ft by 15.2hrs. So to find our value k we divide 2pi by 15.2. This is 0.41. We do it that way based on the ratio for the standard period to what we need, which is a number that can get us to 15.2. So far we have f(t) = 6.3cos(0.41x). Now the problem we have now is that we are not at our height for max, nor our min, even though our wave matches the difference between them, we are between 6.3 and -6.3 so far. so for every value of c in cos(x)+c, this adds to the height cos starts on the y-axis. Since we are at 6.3 already, all we need to do is subtract 6.3 from 17.6 to get c. So C is 11.3 and our final equation is f(t)=6.3cos(0.41x)+11.3. This gives our tides in 15.2 hr periods, starting at 12 noon = x=0, with extremes at intervals of 7.6 hours. Let me know if you have any more questions about it, it's kind of rough to explain. We transformed by f(t)=a*cos(kx)+c altogether, but I thought it might help to separate each value independently.
Given system of inequalities: y > 2/5(x) - 2 and y < -3x + 1.
We are given greater than (>) inequality symbol in first inequality.
For "only greater than inequality symbol" we would draw only a "dotted line".
Also in second inequality we have less than (<) inequality symbol.
For "only greater than inequality symbol" we would draw only a "dotted line".
In the shared graph, both the lines plotted are solid lines.
Therefore, correct option is B) The lines graphed should be dashed.
Answer:
0.2π m
Step-by-step explanation:
Assuming your "x" is a multiplication symbol, form the product of the numerical constants.
= 0.2mπ
If m represents units of meters, it can be placed last:
= 0.2π m
If you want an approximate value, use an appropriate approximation of π.
≈ 0.628319 m
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Answer:</h2>
Option: C is the correct answer.
C.The domain is all real numbers 0 through 35.
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Step-by-step explanation:</h2>
We know that the domain of a function is the set of all those values or the x-values in which the function is well defined.
We are given a graph as a line segment that goes from ordered pair (0,25) to (35,10).
Hence, here the x-value denote the time and the y-value denote the temperature over the time 'x'.
Hence, we could check the temperature at any time between 0 to 35.
Hence, the domain will be:
The domain is all real numbers 0 through 35.
The Pythagorean theorem states:
where a and b are the lengths of the legs and c is the length of the hypotenuse of a right triangle.
Substituting with a = 80 and b = 39, we get:
![\begin{gathered} c^2=80^2+39^2 \\ c^2=6400+1521 \\ c^2=7921 \\ c=\sqrt[]{7921} \\ c=89 \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20c%5E2%3D80%5E2%2B39%5E2%20%5C%5C%20c%5E2%3D6400%2B1521%20%5C%5C%20c%5E2%3D7921%20%5C%5C%20c%3D%5Csqrt%5B%5D%7B7921%7D%20%5C%5C%20c%3D89%20%5Cend%7Bgathered%7D)
