1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
elena55 [62]
3 years ago
14

in a tidal river, the time between high and low tide is 7.6 hours. At high tide the depth of water is 17.2 feet, while at low ti

de the depth is 4.1 feet. Assume the water depth as a function of time can be expressed by a trigonometric function (sine or cosine). Write an equation of the tide, t after noon hours
Mathematics
2 answers:
Bogdan [553]3 years ago
8 0

Answer:

\texttt{Equation of the tide is f(t)= }4.1 + 13.1 sin\left (\frac{\pi t}{15.2} \right )

Step-by-step explanation:

Let us consider this as sine function,

Equation of this function can be represented as

          f(t) = a + b sin (ωt) ---------------eqn 1

Where a, and b are constants, we need to find values of a and b.

Let us consider at time time, t = 0 low tide occurs,

        f (0) = 4.1 feet

Substituting in eqn 1

              f(0) = a + b sin (ωx0)

                4.1 = a + b x 0

                 a = 4.1

              f(t) = 4.1 + bsin(ωt)  ---------------eqn 2

The maximum sine function is 1, so for high tide sinωt = 1

Substituting in eqn 2

              17.2 = 4.1 + b x 1

                 b = 17.2 -4.1 = 13.1 feet

             f(t) = 4.1 + 13.1 sinωt --------------------eqn 3

The maximum of sine occurs at 7.6 hours, sinωt value is 1 at t = 7.6 hours

                              1 =sin(ω x 7.6)

                           \omega \times 7.6=\frac{\pi}{2}\\\\\omega = \frac{\pi}{15.2}

\texttt{Equation of the tide is f(t)= }4.1 + 13.1 sin\left (\frac{\pi t}{15.2} \right )

Lady_Fox [76]3 years ago
4 0
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.
You might be interested in
What is the equation of the line that passes through the point (-5,5)and has a slope of -1
erastova [34]

Answer:

<h2>           y = - x  </h2>

Step-by-step explanation:

The point-slope form of the equation is y - y₀ = m(x - x₀), where (x₀, y₀) is any point the line passes through and m is the slope:

m = -1

(-5, 5)    ⇒   x₀ = -5,  y₀ = 5

The point-slope form of the equation:

y - 5 = -1(x + 5)

So:

y - 5 = -x - 5         {add 5 to both sides}

y = -x             ←  the slope-intercept form of the equation

3 0
3 years ago
A baby elephant that is 4 ft tall casts a
Kazeer [188]

Answer:

15 ft

Step-by-step explanation:

10/4

=2.5

6*2.5

=15 ft

PLS GIVE BRAINLIEST

7 0
3 years ago
Read 2 more answers
A survey was conducted to see what kinds of activities high school and college students liked best. The table shows the results
Alja [10]

Answer:

C & D

Step-by-step explanation:

Because A&B are wrong

7 0
3 years ago
Read 2 more answers
Chi è bravo in matematica?<br><br>​
solong [7]

Answer:

i cannot say that i am perfect or good in math but if there is any problem then i will try to solve.

Step-by-step explanation:

8 0
3 years ago
I'm not sure how to do these, slader is no assistance to me.
ki77a [65]

Answer:

Perimeter: 18 ft

Height: 7 ft

Base Area: 12

Surface Area: (7)*(8) + 2(47) = 150

Step-by-step explanation:

To find the perimeter add all the edges together.

5 + 5 + 8 = 18

To find the height look at the diagram. 7ft shows the height of the rectangle and thus is the height for the rest of the shape.

Base Area:

Multiply the length (8ft) of the base by the height of the base (3ft)

8 * 3 = 24

Then divide by 2 to get the total area of the triangle

24 / 2 = 12.

Surface Area:

To find the surface area you to need to find the specifics of each side.

The base area we already solved for which is 12. We'll get back to this in a minute. The other double sides are of 5 * 7. That equals 35. Add together 12 + 35 to get 47. That is what will go in the 2(___) box because both of those sides have 2. It is the same number when done this way versus just adding them up.

47 * 2 = 94

12 + 12 + 35 + 35 = 94

Then for the (___)(___) that would be 7ft * 8ft because it is the only side left and does not have a double so it must be separate.

7 * 8 = 56

56+94 = 150

5 0
3 years ago
Read 2 more answers
Other questions:
  • What is the equation of the inverse of g(x)=2/5x -1
    6·1 answer
  • What is -14 squared + 5675843
    15·1 answer
  • What is the solution to the equation 2(3)x = 3x + 1?
    13·2 answers
  • Please help me...<br><br> I think its the third graph or the last .<br> correct me if im wrong
    9·2 answers
  • A cylindrical tree trunk is 14 yards high from the ground up to the lowest branch, and it measures 4 yards around. What is the v
    9·1 answer
  • 15−x+y=14−(−x−y) help plz
    10·1 answer
  • Give good evidence to back it up and i will give brainliest. thnx to whoever helps.
    8·1 answer
  • Alexander reads 1/ 8<br> of a book each night. How long will it take him to read 3/ 4 of the book?
    10·1 answer
  • X+1&lt;-2x+11&lt;3x+5<br><br><br> A. -1/3 B. No solution<br> C.6/5 D.-2
    14·1 answer
  • 5+8-2x2 find all the possibilities for each problem by placing parenthesis in different places
    5·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!