The tides around Cherokee Bay range between a low of 1 foot to a high of 5 feet. The tide is at its lowest point when time, t, is 0 and completes a full cycle over a 24 hour period. What is the amplitude, period, and midline of a function that would model this periodic phenomenon?
Answers
Low tide height = 1 ft
High tide height = 5 ft
Tide period, T = 24 houts
Let the height of the tide be modeled by the expression
h(t) = K + A cos(bt)
Because the period is 24, therefore
b = (2π)/24 = π/12
That is,
h(t) = K + Acos[(πt)/12]
When r=0, h = 1, therefore
K + A cos(0) = 1, ot
K + A = 1 (1)
When t = 12 (half cycle), h = 5, therefore
K + A cos(π) = 5, or
K - A = 5 (2)
Add (1) and (2):
2K = 6
K = 3
From(1), obtain
A = 1 - 3 = - 2
Answer:
The required function is h(t) = 3 - 2 cos[(πt)/12]
The amplitude is 2 feet
The period is 24 hours
The midline of the function is h = 3 feet
A graph of the function is shown below.
Answer:
C) Amplitude = 2 feet; period = 24 hours; midline: y = 3
Step-by-step explanation:
above
Related Questions
Three consecutive integers have a sum of 234. What are the three integers?
Answers
3x + 3 = 234
3x = 231
x = 77
so Three consecutive integers: 77,78,79
double check
77+78+79=234
The cosine of the angle is 4/5
Answers
The cotangent of the angle is [tex]\(\frac{4}{3}\).[/tex]
In triangle ABC, where angle ABC is a right angle (90 degrees) and sides AB, BC, and AC are given as 6, 8, and 10 units respectively, we can use the cosine and cotangent functions to find the cotangent of angle ABC.
The cosine of an angle in a right-angled triangle is defined as the ratio of the adjacent side to the hypotenuse.
In this case,[tex]\(\cos(\angle ABC) = \frac{BC}{AC} = \frac{8}{10} = \frac{4}{5}\).[/tex]
The cotangent [tex](\(\cot\))[/tex] of an angle is the reciprocal of the tangent (tan).
The tangent is the ratio of the opposite side to the adjacent side.
Therefore,[tex]\(\cot(\angle ABC) = \frac{1}{\tan(\angle ABC)}\).[/tex]
Since [tex]\(\tan(\angle ABC) = \frac{AB}{BC} = \frac{6}{8} = \frac{3}{4}\)[/tex], we can find the cotangent:
[tex]\[ \cot(\angle ABC) = \frac{1}{\tan(\angle ABC)} = \frac{1}{\frac{3}{4}} = \frac{4}{3} \][/tex]
Therefore, the cotangent of the angle is [tex]\(\frac{4}{3}\).[/tex]
The probable question may be:
The cosine of a certain angle is 4/5. What is the cotangent of the angle?
In triangle ABC , Angle ABC=90 degree, AB=6, BC=8 AC=10
Final answer:
The cosine of an angle being 4/5 means that the ratio of the adjacent side to the hypotenuse in a right triangle is 4/5.
Explanation:
The given question states that the cosine of an angle is 4/5. In trigonometry, the cosine function is defined as the ratio of the adjacent side to the hypotenuse in a right triangle. So, if we have a right triangle with an angle A, and the cosine of A is 4/5, it means that the ratio of the length of the adjacent side to the hypotenuse is 4/5.
Thus, we can say that if the length of the adjacent side is 4 units, then the length of the hypotenuse would be 5 units, assuming the units are consistent. This relationship holds true for any right triangle with an angle whose cosine is 4/5.
For example, if we have a right triangle with an adjacent side of 8 units, then the hypotenuse would be 10 units.
a number diminished by 2 is 6
Answers
n=8
x=8
hope that helps
A room measures 12 feet by 12 feet. A couch is 10 feet and 6 inches long. If you center the couch in the middle of the room, how far will each end of the couch be from the nearest wall?
Answers
72-63
9"
So the ends of the couch will be 9 inches away from the wall closest to that end.
Final answer:
To determine the distance from the ends of the couch to the nearest wall, convert all measurements to inches, find the difference between the room and couch lengths, and divide by two. The ends of the couch will be 0.75 feet or 9 inches from the nearest wall.
Explanation:
The question involves determining the distance from the ends of a couch to the nearest wall when the couch is centered in a 12 feet by 12 feet room. The couch is 10 feet and 6 inches long.
To solve this, first convert the couch length to inches. 10 feet is 120 inches, and adding 6 inches gives us a total of 126 inches for the couch length. Since 1 foot equals 12 inches, the room's length in inches is 12 feet times 12 inches per foot, which equals 144 inches.
Now, to find the distance from each end of the couch to the nearest wall, we subtract the couch length from the room's length:
Room's length in inches: 144 inchesCouch length in inches: 126 inchesDifference: 144 inches - 126 inches = 18 inchesDivide the difference by 2 to get the distance from each end of the couch to the wall:
Distance from each end to the wall: 18 inches / 2 = 9 inchesFinally, convert this distance back to feet:
9 inches / 12 inches per foot = 0.75 feet, or 9 inchesTherefore, each end of the couch will be 0.75 feet, or 9 inches, from the nearest wall when the couch is centered in the room.
I NEED THIS ANSWER
Which linear inequality is represented by the graph?
y > 2x + 3
y < 2x + 3
y > −2x + 3
y < −2x + 3
Answers
y=mx+3, using any other point we can find the slope, m
-1=m(2)+3
-4=2m
-2=m
So the line is:
y=-2x+3
Since the shaded region is below the line:
y<-2x+3
There are 6 performers who will present their comedy acts this weekend at a comedy club. one of the performers insists on being the last? stand-up comic of the evening. if this? performer's request is? granted, how many different ways are there to schedule the? appearances
Answers
since the 6th comic will be last you need to know how many different ways to schedule 5 comics
5x4x3x2 = 120
there are 120 different ways.
Solve for x: 15x2 = x+2
x2 is x to the second power
Answers
15x² = x + 2
15x² - x -2= 0
Factor left side
(5x-2)(3x+1)=0
Set factors equal to 0
5x - 2 = 0 or 3x + 1 -0
x = 2/5 or x= -1/3
I hope that helps!
Brainlest answer :)
Find the coordinates of the circumcenter for ∆DEF with coordinates D(1,1) E (7,1) and F(1,5). Show your work
Answers
D, F have equal x coordinate, so DF is perpendicular to the x-axis.
D, E have equal x coordinate, so DE is perpendicular to the y-axis.
this means DF and DE are perpendicular, so DEF is a right triangle, with m(D)=90°.
Let A be the midpoint of DF. The x coordinate of A is 1 and the y coordinate can be found as follows:
subtract the y coordinate of D from the y coordinate of F, that is 5-1=4.
Divide by 2 and add to the y coordinate of D, that is 4/2+1=2+1=3 is the y coordinate of A.
Let B be the midpoint of DE, follow the previous procedure to find the coordinates of B.
A(1, 3) and B(4, 1).
draw the perpendicular through A and the perpendicular through B, thet meet at point C(4, 3), which is the circumcenter.
Answer: C(4, 3)
the volume of pyramid shown above is 147.97units and the height is is 9.6 units find the length of one edge of the square base
Answers
Volume = L * L * H / 3
L * L * 9.6 / 3 = 147.97
L * L = (3 * 147.97) / 9.6
L * L = 46.24
Let's take the square root of both sides.
L = sqrt(46.24) = 6.8
The length of one edge of the square base is 6.8 units.
Solve the equation.
12 + 0.35x = 20.05
A. 91.5
B. 57.3
C. 2.8175
D. 23
Answers
Peter bought an antique piece of furniture in 2000 for $10,000. Experts estimate that its value will increase by 12.12% each year. Identify the function that represents its value. Does the function represent growth or decay?
A) V(t) = 10000(1.1212)t; growth
B) V(t) = 10000(0.8788)t; decay
C) V(t) = 10000(1.1212)t; decay
D) V(t) = 10000(0.8788)t; growth
Answers
the exponent will be 1.1212
What is sum of the area under the standard normal curve to the left of z = -1 and to the right og z = 1.25?
Answers
A₁ = 0.1587
The area to the left of z = 1.25 is
A₂ = 0.8944
Therefore the area to the right of z = 1.25 is
1 - A₂ = 0.1056
The sum of the areas to the left of z = -1 and to the right of z = 1.25 is
0.1587 + 0.1056 = 0.2643
Answer: 0.2643
PLEASE HELP!! IMAGE ATTACHED find the measure of angle 2
Answers
the figure is an equilateral triangle, which all angles are 60 degrees
angle 3 divides a 60 degree angle in half so angle 3 = 30 degrees
the base is a right triangle which is 90 degrees
90+30 = 120
180-120 = 60
Angle 2 is 60 degrees
Given the declaration, where is the value 97 stored in the numbers array? int numbers[]={83, 62, 77, 97, 88};
Answers
Ok, so before I give you the answer, which is very simple, I will first show you how to answer questions like this in the future.
In the variable declaration, the array "numbers[]" has been declared as an integer. The values of the array "numbers[]" are: 83, 62, 77, 97, 88; respectively, the values are equivalent to: 0, 1, 2, 3, 4 which makes the range of array "numbers[]": 5.
To make it clearer:
numbers[0] = 83
numbers[1] = 62
numbers[2] = 77
numbers[3] = 97 <---- This is what we are looking for!
numbers[4] = 88
*** By the way, when counting the range, we don't start at 1, we start at 0. That's why even if the range is 5, the last value is 4.
Therefore, the answer is: 3 or numbers[3].
What is the cost of constructing a fence 6 and a half feet (6'6") high around a lot measuring 90 ft by 175 ft; if the cost of erecting the fence is $1.25 per linear ft and the cost of materials is $.825 per square ft?
Answers
Final answer:
To construct a fence around a 90 ft by 175 ft lot at $1.25 per linear foot and $.825 per square foot for materials, it would cost a total of $13,656.25.
Explanation:
To calculate the cost of constructing a fence for a lot that measures 90 ft by 175 ft with a fence height of 6'6" (6.5 ft), we need to determine both the perimeter of the lot for the linear feet cost and the total area for the material cost per square foot.
The perimeter of the lot is 2*(90 + 175) = 2*265 = 530 feet. So, the cost of erecting the fence at $1.25 per linear ft is 530 ft * $1.25/ft = $662.50.
The total area that needs to be fenced is 90 ft * 175 ft = 15,750 square feet. Thus, the cost of materials at $.825 per square ft is 15,750 sq ft * $0.825/sq ft = $12,993.75.
The total cost of constructing the fence is the sum of the cost of erecting the fence and the cost of materials, which adds up to $662.50 + $12,993.75 = $13,656.25.
Simplify completely quantity 6 x minus 12 over 10.
Answers
2(3x-6)/(2(5))
(3x-6)/5 and you can factor out 3 from the numerator too
3(x-2)/5 which can be expressed as:
0.6(x-2)
Answer:
3(x+12)
-----------
10
(three times x plus twelve OVER ten)
Step-by-step explanation:
Write log(x^2-9)-log(x+3) as a single logarithm.
Answers
So, log( x^2-9/(x+3))
Now x^2-9 = (x+3)*(x-3), and x^2-9/(x+3) = x-3,
so log(x^2-9)-log(x+3) = log(x-3),
Indeed for all x but for x = -3, but probably no one asks you about that detail?
Answer:
b edge
Step-by-step explanation:
if the trapezoid below is reflected across the x axis what are the coordinates of B
Answers
answer is B. (5,-9)
If the coordinate B is reflected over x-axis, the resulting coordinate will be (5, -9)
Reflection of imageIf an image is reflected over the x-axis, the resulting coordinate will be (x, -y). The reflections shows the mirror image of a figure.
Given the coordinate B before reflection as (5, 9)> If the coordinate is reflected over x-axis, the resulting coordinate will be (5, -9)
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In a zoo, there are 3 male penguins for every 4 female penguins. What is the ratio of females to the total number of penguins at the zoo? 4 to 7 3 to 7 4 to 3 4 to 1
Answers
Final answer:
The correct answer is a ratio of 4 to 7, representing the ratio of female penguins to the total number of penguins in the zoo.
Explanation:
We're given that there are 3 male penguins for every 4 female penguins in a zoo.
To find the ratio of females to the total number of penguins, we first have to add up the total number of penguins, which is 3 males + 4 females = 7 penguins in total.
Now, we can express the ratio of females to the total number of penguins. There are 4 females out of 7 total penguins, so the ratio is 4 females to 7 penguins in total.
Therefore, the correct answer to the student's question is 4 to 7.
Betty has 10 more dimes than quarters. If she has $3.45, how many coins does she have?
Answers
d = dimes
q = quarters
d=10+q
0.25q +0.10d = 3.45
0.25q + 0.10(10+q) = 3.45
0.25q + 1 +0.10q =3.45
0.35q=2.45
q = 2.45/0.35 = 7
d = 10+7 =17
0.25*7=1.75, 17*0.10 = 1.70, 1.75+1.70 = 3.45
she has 7 quarters and 17 dimes for a total of 24 coins
At a particular music store, CDs are on sale at $13.00 for the first one purchased and $10.00 for each additional disc purchased. Maria spends $83.00 on CDs. How many CDs has Maria purchased
Answers
13+10d=83
10d=83-13
10d=70
D=70/10
D=7
7+1=8
Maria purchased 8 CDs. Hope this helps!
Answer:
Maria purchased total 8 CDs.
Step-by-step explanation:
At a particular music store, CDs are on sale at $13.00 for the first one purchased and $10.00 for each additional disc purchased.
Maria spends = $83.00
She purchased her first CD for = $13.00
Now balance of her charge = 83.00 - 13.00 = $70.00
other CDs are purchased for $10.00
Therefore, 70.00 ÷ 10.00 = 7 CDs
Total CDs = 7 + 1 = 8 CDs
Maria purchased total 8 CDs.
The area of the rectangular playground enclosure at Happy Times Nursery School is 600 meters. The length of the playground is 25 meters longer than the width. Find the dimensions of the playground. Use an algebraic solution.
Answers
The solution would be like this for this specific problem:
Area = L * W = 600
Length = W + 25
Substitute and solve for "W":
(W + 25)W = 600
w^2 + 25w - 500 = 0
(w - 15) (w + 40) = 0
Positive solution:
Width = 15 meters
Length = 15 + 25 = 40 meters
So, the dimensions of the playground using an algebraic solution is 15 meters by 40 meters.
To add, the minimum number of coordinates needed to specify any point within it is the informal definition of the dimension of a mathematical space.
Select the assumption necessary to start an indirect proof of the statement. If 3a+7 < 28, then a<7.
Answers
In our case we assume a is not smaller than 7, that is we assume a≥7.
a≥7 then, multiplying both sides by 3:
3a≥21, then, adding both sides 7:
3a+7≥28,
which is a contradiction because 3a+7 is smaller than 28.
So our assumption is wrong, which means the opposite of it is correct.
Answer: assume a≥7
A woman entering an outside glass elevator on the ground floor of a hotel glances up to the top of the building across the street and notices that the angle of elevation is 51°. she rides the elevator up three floors (60 feet) and finds that the angle of elevation to the top of the building across the street is 34°. how tall is the building across the street? (round to the nearest foot.)
Answers
Using trigonometric functions, specifically the tangent function, we create two equations corresponding to two right triangles formed by the lines of sight from the ground floor and from 60 feet high in the elevator. Solving those equations simultaneously, we can calculate that the height of the building across the street is approximately 149 feet.
Explanation:This is a trigonometry problem where we're going to establish two right triangles with the elevator as one side, the building across the street as another (the one we're trying to find), and the line of sight as the hypotenuse. From the ground, we form a triangle with the angle of elevation of 51 degrees. Then from 60 feet above the ground, we form another triangle with an angle of elevation of 34 degrees.
Here, we apply tangent of an angle which equals the opposite over adjacent sides in a right triangle. So, we get tan(51) = h/x and tan(34) = (h-60)/x. We have two unknowns here: 'h' which is the height of the building and 'x' the distance from the elevator to the building. Solving these equations simultaneously, we can find 'h'.
If we solve these equations, we'll get 'h' equals approximately 149 feet (rounding to the nearest foot). So, the building across the street is around 149 feet tall.
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Given a soda can with a volume of 21 and a diameter of 6, what is the volume of a cone that fits perfectly inside the soda can? (Hint: only enter numerals in the answer blank).
Answers
it looks like
6.688=r^2h
that means we must find 3^2
that basically means 3x3 which is 9
then you have to divide that from 6.688
then you get 0.743
that is your height.
now we must find the volume of the cone. The formula for that is
V=пr^2(h/3)
now lets plug in our info
V=(3.14)(9)(0.743/3)
you get 6.999
Answer:
Volume of the cone = 7 unit³
Step-by-step explanation:
Soda can has the shape of a cylinder.
Volume of soda can = πr²h
where r = [tex]\frac{6}{2}=3[/tex] units
and volume = 21 unit³
We put the values in the formula to get the value of h.
21 = πr²h
[tex]h=\frac{21}{\pi r^{2} }[/tex]
Now If we fit a cone inside the can, radius of the cone will be equal to the radius of the cylinder and height of the cylinder will be equal to the height of the cone fit inside.
By the formula of volume of cone
Volume = [tex]\frac{1}{3}\pi r^{2}h[/tex]
= [tex]\frac{1}{3}\pi r^{2}( \frac{21}{\pi r^{2} })[/tex]
= [tex]\frac{21}{3}=7[/tex] units³
Volume of the cone is 7 unit³
Find the missing terms in the following geometric sequence.
a.48, 162c.96, 192b.116, 220d.36, 108
Answers
We flip three coins and obtain more tails than heads. Write the event as a set of outcomes.
Answers
Sample space of all outcomes
= {HHH,THH, HTH, HHT, TTT, HTT, THT, TTH} = 8 =All possible outcomes
Sample space of all favorable outcomes (more tails than heads)
= {TTT, HTT, THT, TTH} = 4 = All favorable outcome
The set of outcomes is {HHH, THH, HTH, HHT, TTT, HTT, THT, TTH}. The total number is 8.
What is probability?Probability is defined as the ratio of the number of favorable outcomes to the total number of outcomes in other words the probability is the number that shows the happening of the event.
Probability = Number of favorable outcomes / Number of sample
All outcomes in flipping 3 coins then the number of samples will be:-
Sample space of all outcomes
Sample space = {HHH,THH, HTH, HHT, TTT, HTT, THT, TTH} = 8 =All possible outcomes.
Sample space of all favorable outcomes (more tails than heads)
Favourable outcomes= {TTT, HTT, THT, TTH} = 4 = All favorable outcome.
Therefore, the set of outcomes is {HHH, THH, HTH, HHT, TTT, HTT, THT, TTH}. The total number is 8.
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Are the lines parallel, perpendicular, or neither?
5x + 2y = 10
15x + 4y = -4
Answers
15x+4y=-4, 4y=-15x-4, y=-3.75x-1
-2.5 != -3.75
And -2.5m=-1, m=0.4, 0.4 !=-3.75
So the slopes are not equal and they are also not negative reciprocals of one another.
Thus the lines are neither parallel nor perpendicular.
7+2[3(x+1) -2 (3x-1)]
Answers
= 7 + 2(3x + 3 - 6x + 2) ...expand by using distributive property
= 7 + 2(-3x + 5) .....combine like terms
= 7 - 6x + 10...expand by using distributive property
= -6x + 17 ...simplify
hope it helps
A carnival ride is in the shape of a wheel with a radius of 20 feet. The wheel has 16 cars attached to the center of the wheel. What is the central angle, arc length, and area of a sector between any two cars? Round answers to the nearest hundredth if applicable. You must show all work and calculations to receive credit.
Answers
The total central angle around the wheel is 2π.
Therefore the central angle between two cars is
(2π)/16 = π/8 = 0.39 radians (nearest hundredth)
The arc length between two cars is
s = (20 ft)*(π/8 radians) = 2.5π = 7.85 ft (nearest hundredth)
The area of a sector formed by two cars is
(1/16)*(π*20²) = 78.54 ft² (nearest hundredth)
Answers: (to the nearest hundredth)
Between two cars,
Central angle = 0.39 radians (or 71.4°)
Arc length = 7.85 ft
Area of a sector = 78.54 ft²
Refer to the diagram shown below, which shows two of 16 equally-spaced cars attached to the center of the wheel.
The total central angle around the wheel is 2π.
Therefore the central angle between two cars is
(2π)/16 = π/8 = 0.39 radians (nearest hundredth)
The arc length between two cars is
s = (20 ft)*(π/8 radians) = 2.5π = 7.85 ft (nearest hundredth)
The area of a sector formed by two cars is
(1/16)*(π*20²) = 78.54 ft² (nearest hundredth)
Answers: (to the nearest hundredth)
Between two cars,
Central angle = 0.39 radians (or 71.4°)
Arc length = 7.85 ft
Area of a sector = 78.54 ft²