Tides The length of time between consecutive high tides is 12 hours and 25 minutes. According to the National Oceanic and Atmospheric Administration, on Saturday, April 26, 2014, in Charleston, South Carolina, high tide occurred at 6:30 am (6.5 hours) and low tide occurred at 12:24 pm (12.4 hours). Water heights are measured as the amounts above or below the mean lower low water. The height of the water at high tide was 5.86 feet, and the height of the water at low tide was − 0.38 foot.
(a) Approximately when will the next high tide occur?
(b) Find a sinusoidal function of the form
y = A sin(ωx – ϕ) + B
that models the data.
(c) Use the function found in part (b) to predict the height of the water at 3 pm on April 26, 2014.

Answers

Answer 1

Answer:

(a) The next tide will occur at 6:55pm

(b) [tex]y = 3.12 \cos(\frac{24\pi}{149}(x - 6.5)) + 2.74[/tex]

(c) The height is: 2.904ft

Step-by-step explanation:

Given

[tex]T_1 = 12hr:25min[/tex] --- difference between high tides'

Solving (a): The next time a high tide will occur

From the question, we have that:

[tex]High =6:30am[/tex] --- The time a high tide occur

The next time it will occur is the sum of High and T1

i.e.

[tex]Next = High + T_1[/tex]

[tex]Next = 6:30am + 12hr : 25min[/tex]

Add the minutes

[tex]Next = 6:55am + 12hr[/tex]

Add the hours

[tex]Next = 6:55pm[/tex]

Solving (b): The sinusoidal function

Given

[tex]High\ Tide = 5.86[/tex]

[tex]Low\ Tide = -0.38[/tex]

[tex]T = 12hr:25min[/tex] -- difference between consecutive tides

[tex]Shift = 6.5hr[/tex]

The sinusoidal function is represented as:

[tex]y = A\cos(w(x - C)) + B[/tex]

Where

[tex]A = Amplitude[/tex]

[tex]A = \frac{1}{2}(High\ Tide - Low\ Tide)[/tex]

[tex]A = \frac{1}{2}(5.86 - -0.38)[/tex]

[tex]A = \frac{1}{2}(6.24)[/tex]

[tex]A = 3.12[/tex]

[tex]B = Mean[/tex]

[tex]B = \frac{1}{2}(High\ Tide + Low\ Tide)[/tex]

[tex]B = \frac{1}{2}(5.86 - 0.38)[/tex]

[tex]B = \frac{1}{2}(5.48)[/tex]

[tex]B = 2.74[/tex]

[tex]w = Period[/tex]

[tex]w = \frac{2\pi}{T}[/tex]

[tex]w = \frac{2\pi}{12:25}[/tex]

Convert to hours

[tex]w = \frac{2\pi}{12\frac{25}{60}}[/tex]

Simplify

[tex]w = \frac{2\pi}{12\frac{5}{12}}[/tex]

As improper fraction

[tex]w = \frac{2\pi}{\frac{149}{12}}[/tex]

Rewrite as:

[tex]w = \frac{2\pi*12}{149}[/tex]

[tex]w = \frac{24\pi}{149}[/tex]

[tex]C = shift[/tex]

[tex]C=6.5[/tex]

So, we have:

[tex]y = A\cos(w(x - C)) + B[/tex]

[tex]y = 3.12 \cos(\frac{24\pi}{149}(x - 6.5)) + 2.74[/tex]

Solving (c): The height at 3pm

At 3pm, the value of x is:

[tex]x=3:00pm - 6:30am[/tex]

[tex]x=9.5hrs[/tex]

So, we have:

[tex]y = 3.12 \cos(\frac{24\pi}{149}(x - 6.5)) + 2.74[/tex]

[tex]y = 3.12 \cos(\frac{24\pi}{149}(9.5 - 6.5)) + 2.74[/tex]

[tex]y = 3.12 \cos(\frac{24\pi}{149}(3)) + 2.74[/tex]

[tex]y = 3.12 \cos(\frac{72\pi}{149}) + 2.74[/tex]

[tex]y = 3.12 *0.0527 + 2.74[/tex]

[tex]y = 2.904ft[/tex]


Related Questions

Please help thank you

Answers

Answer:

The Angle-Side-Angle Postulate (ASA) states that if two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the two triangles are congruent.

Step-by-step explanation:

What is the point-slope equation of a line with slope -4 that contains the point
(-2,7)?
A. Y+7 = -4(x-2)
B. y-7 = -4(x - 2)
c. y+ 7 = -4(x + 2)
D. Y-7 = -4(x + 2)

Answers

Answer:

y -7 = -4(x + 2)   (Answer D)

Step-by-step explanation:

The general point-slope equation is y - k = m(x - h)

If the slope, m, is -4, and the point is (h, k) with h = -2 and k = 7), then we have in this case

y -7 = -4(x + 2)   (Answer D)

I’ll give brainiest whoever answers this

Answers

Answer:

about 75.36

Step-by-step explanation:

we know the radius of the base (circle) is 2 since 4/2 is 2.

Area of cylinder is height times area of base

6*4π=24π

You round π as 3.14

so 3.14*24= 75.36

Answer:

[tex] 75.4 \: {cm}^{3} [/tex]

Step-by-step explanation:

Height of the cylinder h = 6 cm

Diameter d = 4 cm

Radius r = 4/2 = 2 cm

[tex]V_{cylinder} = \pi {r}^{2} h \\ \\ = 3.14 \times {(2)}^{2} \times 6 \\ \\ = 3.14 \times 4 \times 6 \\ \\ = 3.14 \times 24 \\ \\ = 75.36 \\ \\ = 75.4 \: {cm}^{3} [/tex]

I REALLY NEED HELP!!!! ASAP!!! WORTH 50 POINTS!!!!!!

Answers

Because one tablet is 1/40 grams, half a tablet is 1/80 grams, together that adds up to 3/80 grams of vitamin C

ANSWER ASAP PLS <3
20 points !
Which expression matches the graph?

Answers

Answer: the answer is b?

hope this helps

calculate the area of a circle with a diameter of 0, 8m​

Answers

Answer:

50.24=4squared times pie

Step-by-step explanation:

Answer:

The area of a circle with a diameter of 0.8 meters is approximately 0.50 [tex]m^2[/tex].

Step-by-step explanation:

Since the diameter of the circle is 0.8 meters, that means the radius of the circle would be 0.4 meters. The area of a circle can be found by the formula [tex]\pi r^2[/tex], where [tex]r[/tex] represents the radius of the circle. In this case, the area would be [tex]0.4^2*\pi[/tex] = [tex]0.16 * \pi[/tex] ≈ 0.50 [tex]m^2[/tex].


Does anyone know the answer to this one ?

A: (-0.25,0),(4.25,0)

B: (1,4),(4,-1)

C: (0,-5), (5,0)

D: (0,-1), (2,-5)

Answers

Answer:

(1, -4), (4, -1)

Step-by-step explanation:

A solution to a system of equations is when the two lines intersect. In this case, we have two intersections, which means two solutions.

From left to right, we first see an intersection at (1, -4).

Continuing to the right, we see another intersection at (4, -1)

These are our two solutions.

(1, -4), (4, -1)

Hope this helps!

Solve the system by substitution

-8x+y=-9
y=7

Answers

In point for (2,7) and in Equation form x=2 y=7

What's the inches equivalent of 63.5 millimeters? A. 2.5, B. 24, C. 3.2. D 31

Answers

Answer: A

Step-by-step explanation: 2.5 inches = 63.5 millimeters

The average basketball has a diameter of 9.5 inches. What is the volume of an average basketball?

Answers

the formula for volume of sphere is 4/3||r^3

diameter=2radius

in the formula we need to have radius but we have been given diameter so we convert diameter to radius

d=2r

r=d/2

9.5÷2

4.75

An algebraic expression 2x² + 2xy is trinomial algebraic expression true or false​

Answers

Answer:

False

Step-by-step explanation:

right!!

A line has a slope of 3/8 and passes through the point (15.2,-7)

The equation of the line in point-slope form is???
ANSWERS↓↓

Answers

Considering the definition of a line, the correct answer is option A: the equation of the line in point-slope form is y + 7= 3/8(x- 15.2)

Linear equation

A linear equation o line can be expressed in the form y = mx + b

where

x and y are coordinates of a point.m is the slope.b is the ordinate to the origin and represents the coordinate of the point where the line crosses the y axis.

The point-slope form of an equation of a line is written as y-y₁=m(x-x₁)

where:

m is the slope.(x₁, y₁) are the coordinates of the point.Equation of a line in this case

In this case, you know:

A line has a slope of 3/8.The line passes through the point (15.2,-7).

The point-slope form of the line is written as:

y- (-7)= 3/8(x- 15.2)

y + 7= 3/8(x- 15.2)

Learn more about equation of the line in point-slope form:

brainly.com/question/29761173

brainly.com/question/18617367

brainly.com/question/28764237

#SPJ1

What does this statement mean? The probability of drawing a brown sock from a drawer of
socks is 0.

Answers

Answer:

there are no brown socks

Step-by-step explanation:

there is zero possibility of pulling a brown sock from the drawer fro this to be possible there would have to be no brown socks

The residual value of the car is estimated to be $13,650. The lease has no termination fees or charges. If you decide to purchase, your bank requires a down payment of $3,800 and will finance the balance with a 10.25% APR loan for 36 months. The sales tax in your state is 6.5%, and the tag and title charges are $75. The opportunity cost is the interest your down payment could have earned if you didn’t purchase the vehicle. Currently, your money earns 4.5% in a savings account.

Answers

I dont know but i do know that two plus two is fish

. How many four letter patterns can be formed using the letters A, B, and C if letters may be repeated?

Answers

Answer:

24 patterns

Step-by-step explanation:

Given that four lettered patterns are to be formed using the three alphabets. Since letters may be repeated, then;

4[tex]P_{3}[/tex] = [tex]\frac{4!}{(4 - 3)!}[/tex]

      = [tex]\frac{4 x 3 x 2!}{1!}[/tex]

     = 4 x 3 x 2

     = 24

4[tex]P_{3}[/tex] = 24

Therefore, 24 four letter patterns can be formed when the given letters are repeated.

N is an integer -1 < n < 4 list the possible values of n

Answers

Answer:

0 1 2 3

Step-by-step explanation:

Since n is an integer

We have n = { 0 1 2 3 }

Find the value of x that will make A||B

Answers

Answer:

the value of x that will make A||B is 4

1. What property could you use to show that these two triangles are congruent? QRP XWY​

Answers

The property that could be used to determine that the triangles are congruent is the SSA congruent theorem

How to determine the congruent property

From the question, we have the following parameters that can be used in our computation:

Triangles = QRP and XWY​

On the triangles, we can see that:

Two corresponding sides on both triangles are marked with I and IIThe triangles have a pair of corresponding angles

This means that we make use of the SSA congruent theorem

The SSA congruent theorem implies that  if two sides and an angle not included between them are respectively equal to two sides and an angle of the other than the two triangles are equal.

In this case, we have

Congruent sides: RQ and HG & PR and HF

Congruent angles: Angles Q and G

Hence, the additional information on the congruency of the triangles is the SSA theorem

Read more about congruent triangles at

brainly.com/question/1675117

#SPJ1

help pls no li is I'll give you briliantest pls help pls pls pls pls pls pls pls pls pls pls​

Answers

Answer:

40.5

I hope u get a good mark glll

Step-by-step explanation:

Evaluate the expressions 56 with a variable of -1

Answers

Answer:

The expression 56 with a variable of -1 is not well defined. The term 56 is a constant number, and the variable of -1 is also a constant. Therefore there is nothing to evaluate.

Step-by-step explanation:

If you want to evaluate the expression 56*(-1) it would give -56 as output because -1 is a scalar and multiplying with a scalar will change the sign of the constant 56 but it won't change its value.

In other words, to evaluate an expression, it needs to have a mathematical operation or function, operands, and/or variables that can be replaced with values or expressions. Without any operation, there's nothing to evaluate.

Determine the value of mAB in the following diagram

is it 110 or 20????
please please don't tell me to click a link I will report you

Answers

The answer to this question is 110

The points obtained by students of a class in a test are normally distributed with a mean of 60 points and a standard
deviation of 5 points.

About what percent of students have scored less than 45 points?

0.15
2.5
15.5
34

Answers

Answer:

0.135%

Step-by-step explanation:

Given :

Mean, m = 60

Standard deviation, σ = 5

x = 45

The Zscore = (x - m) / σ

Z = (45 - 60) / 5 = - 15 / 5 = - 3

P(Z < - 3) = 0.0013499

0.0013499 * 100%

= 0.13499%

Only about 0.135% scored below 45

Compute the MIRR statistic for project I if the appropriate cost of capital is 11 percent.
Cash flow -12,000, 5830, 4680, 2,500

Answers

The MIRR statistic for the project I given the cost of capital and the reinvestment rate, is 7. 43 %.

How to find the MIRR statistic ?

A monetary indicator of an investment's allure is the modified internal rate of return or MIRR. Ranking equivalent alternative investments is done in capital budgeting.

You can use a spreadsheet to find the MIRR by first ordering the cash flows as shown in the attached image. Then use the = MIRR function.

The cost of capital is the finance charge which is 11 %. The reivestment rate will be the same as the finance charge if not given so it will be 11 % as well.

The MIRR is therefore 7 .43 %.

Find out more on MIRR at https://brainly.com/question/25296684

#SPJ1

HELPPP ASPPO!!
4x -y=6
-4x +y =8
which statement correctly describes the system of equations

Answers

The equation system is appropriately described by the formula 4x - y=6.A mathematical formula known as an equation combines two assertions .

what is equations ?

A mathematical formula known as an equation combines two assertions using the equal sign (=) to denote equivalence. The terms 3x + 5 and 14 are separated by an equal sign in the equation 3x + 5 = 14, for example. Mathematical equations are used to express the relationship between two phrases on either side of a letter. In most cases, the symbol serves as the sole variable. a good example is 2x - 4 = 2.

given

Graphing, substitution, and elimination are the three techniques used to solve systems of equations.

By graphing the given equations, you can easily solve a system by finding the point(s) where they all cross.

The values of the variables you are solving for will be provided by the coordinate of this point.

The equation system is appropriately described by the formula 4x - y=6.

To know more about equation visit:

https://brainly.com/question/649785

#SPJ1


Write an equation and solve for x using the diagram
below. Also give the angle measure. YOU MUST
WRITE THE EQUATION IN ORDER TO GET

Answers

Answer:

x = 45

Step-by-step explanation:

2x + 6 and 96 are vertically opposite angles and are congruent , then equation is

2x + 6 = 96 ( subtract 6 from both sides )

2x = 90 ( divide both sides by 2 )

x = 45

Can someone help with this? Please be right

Answers

Answer:

  See attached

Step-by-step explanation:

You want various combinations of the functions g(a) = -3a+1 and h(a) = 3a³ +4a.

g/h

The functions have no common factors, so their ratio leaves the function expressions unchanged:

  [tex]\dfrac{g(a)}{h(a)}=\boxed{\dfrac{-3a+1}{3a^3+4a}}[/tex]

h+g

The like terms are combined when the functions are added.

  [tex]h(a)+g(a)=(3a^3+4a)+(-3a+1)=3a^3+(4-3)a+1\\\\=\boxed{3a^3+a+1}[/tex]

g-h

Similarly, the like terms are combined when the functions are subtracted.

  [tex]g(a)-h(a)=(-3a+1)-(3a^3+4a)=-3a^3+(-3-4)a+1\\\\=\boxed{-3a^3-7a+1}[/tex]

g·h

The product is found the way products are usually found. Each term of one of the factors is multiplied by each term of the other factor, and these products are summed. You can think of it as repeated application of the distributive property.

  [tex]g(a)\cdot h(a)=(-3a+1)(3a^3+4a)=-3a(3a^3+4a)+1(3a^3+4a)\\\\=-9a^4-12a^2+3a^3+4a\\\\=\boxed{-9a^4+3a^3-12a^2+4a}[/tex]

Write each fraction as the sum of a whole number and a fraction less than 1

6/5

11/7

21/4

Answers

Given:

The fractions are:

[tex]\dfrac{6}{5},\dfrac{11}{7},\dfrac{21}{4}[/tex]

To find:

The each fraction as the sum of a whole number and a fraction less than 1.

Solution:

The given fraction is [tex]\dfrac{6}{5}[/tex].

[tex]\dfrac{6}{5}=\dfrac{5+1}{5}[/tex]

[tex]\dfrac{6}{5}=\dfrac{5}{5}+\dfrac{1}{5}[/tex]

[tex]\dfrac{6}{5}=1+\dfrac{1}{5}[/tex]

Therefore, the given fraction [tex]\dfrac{6}{5}[/tex] can be written as [tex]1+\dfrac{1}{5}[/tex].

The given fraction is [tex]\dfrac{11}{7}[/tex].

[tex]\dfrac{11}{7}=\dfrac{7+4}{7}[/tex]

[tex]\dfrac{11}{7}=\dfrac{7}{7}+\dfrac{4}{7}[/tex]

[tex]\dfrac{11}{7}=1+\dfrac{4}{7}[/tex]

Therefore, the given fraction [tex]\dfrac{11}{7}[/tex] can be written as [tex]1+\dfrac{4}{7}[/tex].

The given fraction is [tex]\dfrac{21}{4}[/tex].

[tex]\dfrac{21}{4}=\dfrac{20+1}{4}[/tex]

[tex]\dfrac{21}{4}=\dfrac{20}{4}+\dfrac{1}{4}[/tex]

[tex]\dfrac{21}{4}=5+\dfrac{1}{4}[/tex]

Therefore, the given fraction [tex]\dfrac{21}{4}[/tex] can be written as [tex]5+\dfrac{1}{4}[/tex].

A book claims that more hockey players are born in January through March than in October through December. The following data show the number of players selected in a draft of new players for a hockey league according to their birth month. Is there evidence to suggest that hockey​ players' birthdates are not uniformly distributed throughout the​ year? Use the level of significance .

Answers

Complete question :

Birth Month Frequency

January-March 67

April-June 56

July-September 30

October-December 37

Answer:

Yes, There is significant evidence to conclude that hockey​ players' birthdates are not uniformly distributed throughout the​ year.

Step-by-step explanation:

Observed value, O

Mean value, E

The test statistic :

χ² = (O - E)² / E

E = Σx / n = (67+56+30+37)/4 = 47.5

χ² = ((67-47.5)^2 /47.5) + ((56-47.5)^2 /47.5) + ((30-47.5)^2/47.5) + ((37-47.5)^2/47.5) = 18.295

Degree of freedom = (Number of categories - 1) = 4 - 1 = 3

Using the Pvalue from Chisquare calculator :

χ² (18.295 ; df = 3) = 0.00038

Since the obtained Pvalue is so small ;

P < α ; We reject H0 and conclude that there is significant evidence to suggest that hockey​ players' birthdates are not uniformly distributed throughout the​ year.

two angles add up to 180 if and only if they are supplementary

Answers

Answer:

  True

Step-by-step explanation:

You want to know if it is true or false that "two angles add up to 180° if and only if they are supplementary."

Supplementary angles

Two supplementary angles have a sum of 180°. That is the definition of supplementary angles. The offered statement is True.

What is the volume of the rectangular prism shown below?





A. 476 in³
B. 4,760 in³
C. 1,700 in³
D. 340 in³

Answers

Answer:

B. 4760 in³

Step-by-step explanation:

V= l×w×h

=34×10×14

=4760 in³

Other Questions
Employees who keep themselves up to date on company news and continually learn new aspects of their job show _____. What were some of the laws that were passed under the Napoleonic Code? If a device is stolen, how can you set it to the factory defaults, disable it, or clear any personal data that is on it remotely Identify the sequence that lists sides of STU in order from shortest to longestST, UT, SUUT, SU, STSU, ST, UTSU, UT, ST g(x) = (2 (x+3))^3 + 4 simplify cos^2 A/1+sin A HELP NOW PLEASE PLEASE PLEASE!!!! What does it mean to "evangelize" people? Like, does it mean converting them, or does it mean persuading them to pursue evangelism? I really need some help here!!!! A type of mortgage which allows the lender to increase the outstanding balance of a loan up to the original amount of the loan in order to advance additional funds is called an I loved her against reason, against promise, against peace, against hope, against happiness, against all discouragement that could be. Is this a simple, complex, or compound sentence? a successful defense releases the defendant from partial or full liability for a tortious act.a. trueb. false What are the coordinates of the point on the directed line segment from3. 2) to (77) that nartitions the segment into a ratio of 3 to 2? The function f(x) = StartRoot negative x EndRoot is shown on the graph. Which statement is correct? 13. Solve for x. (show work) Delta bought equipment on 1/1/15 at a cost of $525. The equipment has a useful life of 7 years and no salvage value. The full cost of the equipment was mistakenly expensed immediately as repairs and maintenance expense. a) Assume the error was discovered on 1/1/17. Because of the error, is net income for 2015 correct or incorrect (if incorrect, is it too high or too low and by what amount?)b) Assume the error was discovered on 1/1/17. Because of the error, is net income for 2016 correct or incorrect (if incorrect, is it too high or too low and by what amount?)c) Now assume, instead, that the error was caught on 1/1/18. Because of the error, are total assets on 1/1/18 correct or incorrect? (if incorrect, are they too high or too low and by what amount?)d) Now assume that the error is not discovered until 1/1/24, are R.E. and total assets correct or incorrect on 1/1/24? (if incorrect, are they too high or too low and by what amount?) During a fireworks display, one rocket went up and came down without exploding. The height of the rocket was described by the function, h(t)= 16 t 2 + 88 t , where t = time in seconds and h(t) = height in feet. What was the maximum height reached by the rocket? Please please please help ASAP!! Circle C has radius 8 ft with an arc AB intercepted by a central angle of pi/4 radians. What is the length of arc AB expressed interms of pi? Find the measure of forty children from an after-school club went to the field trip . this is 25% of the children in the club. how many children are in the club? What is the formula of law of lever?