The depth of water in a tank oscillates sinusoidally once every

8 hours. If the smallest depth is 6. 6 feet and the largest

depth is 9. 4 feet, find a possible formula for the depth in terms

of time t in hours. Assume that at t=0 the water level is at

the average of the depth and is rising.
.

Answers

Answer 1

The possible formula for the depth of water in tank is , D = 2.8 + 8 sin(π t/4) where t is time in hours.

Sinusoidally function, is defined as one of triagnometric function with a smooth, repetitive oscillation. "Sinusoidal" comes from "sine", function. We can write its equation in the following form y = A·sin(B(x - C)) + D

where, A --> amplitude

B--> period in form of pi

C--> phase or horizontal shift

D --> vertical shift

We have, the depth of water in a tank oscillates sinusoidally.

The smallest depth of water in tank = 6.6 feet

The largest depth of water in tank = 9.4 feet

We have to determine the formula of depth of water in tank as a function of time in hours .

For sinusoidal function,

Amplitude , A = average depth

= ( largest depth + smallest depth)/2

= (6.6 + 9.4)/2

= 16.0/2 = 8

Now, The period of 8 hours so, B = 2π/8

=> B = 45° = π/4

Also, upward shift , D is 9.4 - 6.6 = 2.8

Horizontal shift, C = 0

So, required function is D = 2.8 + 8 sin(π t/4) .

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Related Questions

What is the relationship between the ratios of sin x° and cos y°?


The ratios are both identical (three fifths and three fifths).

b
The ratios are opposites (negative three fifths and three fifths).

c
The ratios are reciprocals (three fifths and five thirds).

d
The ratios are both negative (negative five thirds and negative three fifths).

Answers

Answer:

A. The ratios are both identical (three fifths and three fifths).

Step-by-step explanation:

ratio means fraction

ratio also means division

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"SOHCAHTOA"

sine equals opposite over hypotenuse cosine equals adjacent over hypotenuse tangent equals opposite over adjacent

mathworldwolframcom

sine equals opposite over hypotenuse

sine X equals 3 over 5

cosine equals adjacent over hypotenuse

cosine Y equals adjacent over hypotenuse

cosine Y equals 3 over 5

side thats 3 is adjacent for y but

side thats 3 is also opposite for x

both identical, aka C on their question is right

its the 1st option for flvs

Is Br2 equal to Avogadro's number?

Answers

Br₂ does not equal to Avogadro's number. Since bromine is a diatomic element.

What is a diatomic element?

Diatomic molecules—so named because they only contain two atoms of the same or different chemical elements—are molecules that are made up of two atoms. A diatomic molecule is considered to be homonuclear if it contains two atoms of the same element, such as oxygen (O₂) or hydrogen (H₂).

Each bromine molecule consists of 2 atoms of bromine. Br₂ consists of two moles. One mole of bromine consists of 6.02214076 × 10²³ atoms. Thus 2 moles of bromine consist of 2 × 6.02214076 × 10²³ = atoms. Thus Br₂ does not equal to Avogadro's number.

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Use the data in the table below to create a scatter plot. Based on your scatter plot, does the data
have a correlation? If so, what kind?

A. No - the data has no correlation
B. Yes - there is a negative correlation
C. Yes - there is a positive correlation
D. There is not enough information to answer

Answers

Answer:

C

Step-by-step explanation:

There is a positive correlation, as hours spent gets bigger the test score gets bigger with some outliers

WILL MARK BRAINLY IS RIGHT!!!!

Answers

Answer:

9

Step-by-step explanation:

Answer:

9

Step-by-step explanation:

Sara's mom takes the parkway to work. It takes her 30 minutes to travel from mile marker 88 where she enters to her exit at mile marker 121. What is her average speed

Answers

Sara's mom average speed is 66mph. The next step is to divide the distance by the time: 33/0.5 = 66 mph.

What is average speed ?

You may estimate the average pace at which an object will go a distance by looking at its average speed. Average speed is calculated by dividing a quantity by the time required to obtain that quantity.

Finding the distance and the time is necessary to calculate speed.

In this situation, you must deduct mile marker 88 from 121 to determine the distance.

121 - 88 = 33mile

Even though the time is 30 minutes, you're probably interested in miles per hour. 30 minutes must be converted to 0.5 hours.

The next step is to divide the distance by the time: 33/0.5 = 66 mph.

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a pair of sunglasses originally priced at $50 are now on sale for $31. What is the discount percentages?

Answers

Answer:

They are discounted for 38% off.

What does ∠ ABC mean?

Answers

The measure of angle ABC means, vertex B lies in between A and C, whose value is to be obtained.

Explain the term angles?

Whenever two straight lines as well as rays intersect at a single endpoint, an angle is created. The vertex of the an angle is the location where two points come together.

Measure or "the measure of" are indicated by the "m." Consequently, m1 and m2 stand for "the measure for angle one" and "this same measure of angle two," respectively.The total of a triangle's three internal angles is 180 degrees, as stated by the angle sum feature of a triangle.A closed shape with both inner and exterior angles, a triangle is created by three line segments.When the values of the remaining two angles are known, then angle sum property is utilised to determine the measure of an uncertain interior angle.

Thus, the measure of angle ABC means, vertex B lies in between A and C, whose value is to be obtained.

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A packet of grass seed can be
used to cover 50m² of lawn.
A circular lawn has a diameter of 20 metres
How many packets of grass
seed must be bought so that the entire lawn can be covered?

Answers

Answer:

7 packets of grass seed

Step-by-step explanation:

First, find the area of the circular lawn using the formula, A = [tex]\pi[/tex]

If the diameter is 20 meters, the radius is 10 meters.

Plug in 10 as the radius and solve for the area:

A = [tex]\pi[/tex]r²

A = [tex]\pi[/tex](10²)

A = 100[tex]\pi[/tex]

So, the area of the lawn is 100[tex]\pi[/tex] m² or approximately 314.16 m²

Divide this by 50 to find how many packets of grass seed are needed:

314.16/50

= 6.28

Round this up to 7, since we need to have a whole number answer.

So, 7 packets of grass seed have to be bought.

7 packets
Ea y square m = 1/50 = 0.02 packets per square meter

Radius = 10
Area : 10 square x pi = 100 x pi. = 314.16.....

314.16....x 0.02 = 6.283....
More than 6 packets are needed
So 7 packets must be bought

I forgot how to do this- we are doing a review and I dont know how to do this-

Answers

Answer:

36.373 not rounded

Step-by-step explanation:

Using pythagoras theorem

a^2 =b^2 +c^2

a always is the hypotenuse (the opposite side to the 90 angle)

b and c are the other sides obviously

So here we have a = 38

let b =11

So for c =sqrt(38^2 - 11^2)=36.373

Which ordered pairs are solutions to this system of inequalities?

Answers

9514 1404 393

Answer:

  c, d, e

Step-by-step explanation:

The first two listed points are not in the solution set. The remaining three are.

__

Any point in the doubly-shaded area, or on the solid boundary line of that area is part of the solution set. Points (-1, -6), (0, -5), and (0.5, -2) are solutions to the given inequalities.

Find the area of the regular polygon. Round your answer to the nearest hundredth.
6.84
10
A
square units

Answers

Answer:

area = 289.24 units²

Step-by-step explanation:

divide the polygon into 9 equal triangles

the top angle of a triangle will be 360°/9 = 40°

the sides of a triangles are both 10 units

The base of a triangle is 6.84 units

the height of a triangle is:

cos 20° = height/10

0.9397 = height/10

height = 9.4 units

The area of a triangle = 1/2(6.84)(9.4) = 32.13 units²

the polygon is made from 9 of these triangles, so 9 x 32.13 = 289.24 units²

Determine whether quadrilateral EFGH is similar to quadrilateral QRST. If so, give the similarity statement. (ASAP PLS HELP!!)

A)
QRST ∼ EFGH

B)
QRST ∼ FEHG

C)
Impossible to determine.

D)
The quadrilaterals are not similar.

Answers

Answer:

qrst similar to fehg

Step-by-step explanation:

opposite angles are equal in parallelogram so 70 is equal to 70 on both and similarly other angles also are equal that we can find using co interior property as well

plz marks me brainliest plz plz

Answer:

the quads are NOT similar is the right answer!!!

Step-by-step explanation:

I got it right:)

Jesse from Boston goes to his grandpa Isaac in New York by bus at an average speed of 35 mph and it takes him 6 hours. In a while, Jesse and Isaac go back from New York to Boston in Isaac's car at an average speed of 42 mph. How long does Jesse's trip from New York to Boston take?

Answers

Answer:

The Average Speed is 48mph

Step-by-step explanation:

I've done this problem before, I wish A+'s upon all that read this answer. take care man!

The time it takes for Jesse to complete his trip from New York to Boston is 5 hours.

How long does Jesse's trip from New York to Boston take?

To calculate the time it takes for Jesse's trip from New York to Boston, we need to use the formula: time = distance / speed.

Given that Jesse traveled from Boston to his grandpa Isaac in New York at an average speed of 35 mph, and the trip took him 6 hours, we can determine the distance using the formula: distance = speed × time.

Distance = 35 mph × 6 hours = 210 miles.

Now, for the return trip from New York to Boston, Jesse and Isaac travel at an average speed of 42 mph. To find the time it takes, we divide the distance by the speed:

Time = 210 miles / 42 mph = 5 hours.

Therefore, Jesse's trip from New York to Boston takes 5 hours time.

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12x+105=55x+0 solve for x

12y=155 sovle for y

Answers

Answer:

Step-by-step explanation:

12x + 105 = 55x + 0
=> 12x + 105 = 55x
=> 55x - 12x = 105
=> 43x = 105
=> x = 105/43
12y = 155
=> y = 155/12

A triangle has an angle that measures 126°. The other two angles are in a ratio of 11:16. What are the measures of those two angles?

Answers

Therefore, the measures of those two angles are 33° and 24°.

Define angles.

An angle is a figure in plane geometry that is created by two rays or lines that have a shared endpoint. The Latin word "angulus," which means "corner," is the source of the English term "angle."

Define geometry.

Geometry is a branch of mathematics that studies the sizes, shapes, positions, angles, and dimensions of things.

We know, the sum of the angles in a triangle is always 180 degrees.

126 + x + y = 180

x + y = 54

Given that the two angles are in a ratio of 11:16, the proportion:

x/y = 11/16

Solving for x and y, we get:

x = 11y/16

We substitute this equation into the equation x + y = 54 and we get:

11y/16 + y = 54

Solving for y we get y = 24. Then we can use the proportion to find x:

x = 11 * 24 / 16 = 33.

So the two angles are 33° and 24°.

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the sides of a triangle are 7,10,12 cm long. Classify the triangle

Answers

Answer:340 cm long

Step-by-step explanation: multiply 7 x 10 then 70 x 12

Help me out with this question please

Answers

Answer: 3

The answer is three, do you need me to show you how I solved it?

If θ is an angle in standard position and its terminal side passes through the point (12,-5), find the exact value of \sec\thetasecθ in simplest radical form.

Answers

The exact value of secθ in simplest radical for is 1.083

What are trigonometric identities?

Trigonometric identities are the functions that include trigonometric functions such as sine, cosine, tangents, secant, and, cot.

We are Given θ is an angle in standard position.

Its terminal side passes through the point (12, -5).

To find the exact value of secθ in simplest radical form.

When θ is an angle in standard position and its terminal side passes through the point (x,y), then the exact value of secθ is:

So, we have x = 12 and y = -5 which is in the first quadrant.

Therefore,

r² = x² + y²

r² = ( 12 )² + ( -5 )²

r² = 144 + 25

r² = 169

r = 13

Then,

sec θ = 1/cosθ

sec θ = [ 1/(x/r) ]

sec θ = r/x

sec θ = 13/12

sec θ = 1.083

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Give the most precise classification for each figure

Answers

Answer:

D

Step-by-step explanation:

Answer:

A. Quadrilateral

Step-by-step explanation:

quardrilateral Shapes have 4 corners. and That is the Most Precise classification of this Shape

Write four different expressions for the perimeter of a square whose sides are all s 2 2 units long.

Answers

Mathematical statements are called expressions if they have at least two words that are related by an operator and contain either numbers, variables, or both.

What are expressions in maths?Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation. An expression's structure is as follows: Expression: (Math Operator, Number/Variable, Math Operator)An expression, often known as a mathematical expression, is a finite collection of symbols that are well-formed in accordance with context-dependent principles.An expression in mathematics is made up of numbers, variables, and functions (such as addition, subtraction, multiplication or division etc.) You may think of expressions as being comparable to phrases. A phrase in language may contain an action on its own, but it does not constitute a whole sentence.

For a square whose side are 2 units long is :

= 2 + 2 x 2 + 2

= ( 2 + 2 ) x 2

= 2 x 4

= 2 x 3 + 2 = 8

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Match the solution to its expression.

Answers

Answer:

1/3 + 1/3 = (1+1)/3 = 2/3

1) 2/3

5/7 - 2/7 = (5-2)/7 = 3/7

2) 3/7

so all you have to do is add or sub the fractions together.

1/3 + 1/3 = 2/3

5/7 - 2/7 = 3/7


for the first box is 2/3

Second box is 3/7


GOODLUCK

Student tickets cost $2.00 and everyone else
is $4.00. If $500 was made by selling 175
tickets, how many student tickets were sold?

Answers

Answer:

Student =100

Step-by-step explanation:

which of the following is a linear function

Answers

Answer:

f(x)=5x-6

Step-by-step explanation:

When I entered this in Desmos it crossed through the line crossed  through the x and y axis which makes this equation a linear function.

Answer:

f(x) = 5x - 6

Step-by-step explanation:

The first function is a Linear Function

The second function is a Exponential Function

The third is an Inverse Function

The forth is a Quadratic Function

Hope this helps!

Find the flux of F across S,
F. N dS
where N is the upward unit normal vector to S.
F(x, y, z) = xi + yj + zk
S: z = 1 − x^2 − y^2, z ≥ 0

Answers

The flux of F across S will be [tex]\frac{3\Pi}{2}[/tex]

A vector of magnitude 1 that is at some point perpendicular to a two-dimensional curve is referred to as the unit normal vector. Normally, you search for a function that returns not just one vector but all potential unit normal vectors of a given curve.

A vector that is perpendicular to a surface at a certain location is known as the normal vector, also referred to as the "normal" to a surface. The inward-pointing normal (pointing toward the interior of the surface) and outward-pointing normal are often distinguished when normals are taken into consideration on closed surfaces.

[tex]$Z_x=-2 x: \quad Z_y=-2 y$[/tex]

[tex]$N=\langle 2 x, 2 y, 1\rangle \quad: f=\langle x, y, z\rangle$[/tex]

[tex]f. $N=2 x^2+2 y^2+z=2 x^2+2 y^2+1-x^2-y^2$[/tex]

=1+x^2+y^2

[tex]x^2+y^2=1\\ \Rightarrow \quad x=r \cos \theta\\ \Rightarrow \quad y=r \sin \theta \\ \Rightarrow x^2+y^2=r^2 \\ 0 < r < 1: \quad 0 < \theta < 2 \pi[/tex]

[tex]$R \cdot v=\int_0^{2 \pi} \int_0^1\left(1+r^2\right)(r) dr d \theta$[/tex]

[tex]$=2 \pi \int_0^1 r+r^3 d r$[/tex]

[tex]$2 \pi\left[\frac{r^2}{2}+\frac{r^4}{4}\right]_0^1$[/tex]

[tex]$=(2 \pi)\left(\frac{1}{2}+\frac{1}{4}\right)$[/tex]

[tex]$=\frac{(2 \pi)(3)}{42}=\frac{3 \pi}{2}$[/tex]

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A line that includes the point (4,1) has a slope of 1 7 . What is its equation in point-slope form?

Answers

Answer:

y = 17x-67

Step-by-step explanation:

The one point form of line also called slope point form is given by

[tex](y-y_1)=m(x-x_1)[/tex]

where (x1, y1) is the point and m is slope

Given: (x1, y1) = (4,1) and m= 17

Substituting these values in above equation to find equation in point-slope form

(y-1)=17(x-4)

y-1 = 17x-68

y = 17x-67

the point -slope form of equation y = 17x-67

help help help help help

Answers

y-1=2/3(x-14)

y-1=2/3x-28/3

+1 +1

y=2/3x-25/3
hope that makes sense :)

An's backpack weighs as much as Lin's backpack. Clare's backpack weighs as much as Lin's backpack. Whose backpack weighs the most? Whose backpack weighs the least? Explain or show your reasoning.

Answers

Answer:

All 3 backpacks are equal in weight, there is none that is heavier or lighter than the others. That is, the 3 backpacks have the same weight.

Step-by-step explanation:

Given that An's backpack weighs as much as Lin's backpack, and Clare's backpack weighs as much as Lin's backpack, to determine whose backpack weighs the most and whose backpack weighs the least the following mathematical reasoning must be considered:

A = L

C = L

Therefore, A = C.

Since all 3 backpacks are equal in weight, there is none that is heavier or lighter than the others. That is, the 3 backpacks have the same weight.

What is reflex angle class 9?

Answers

A reflex angle is an angle which measures more than 180 degrees and less than 360 degrees.

There are different types of angles in geometry, such as obtuse, acute and right angles, which all are under 180 degrees.

Assume, z is an acute or obtuse angle, and r is the reflex angle, then:

z + r = 360

r = 360 - z

Therefore, we can find the related reflex angle(r), if we know the value of the acute or obtuse angle(z).

A reflex angle equals the summation of 180 degrees and any of the primary angles (acute, right and obtuse angles). Therefore,

Reflex angle = 180° + Acute angle

Reflex angle = 180° + Right angle

Reflex angle = 180° + Obtuse angle

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Two people stand on opposite ends of a bridge that crosses a river. Both can see an island located in the river. The angle
formed at the location of the first person is 37' and the angle formed at the second person is 55'. If the bridge is 5280 feet
long, how far is the first person from the island?

Answers

Answer:

The first person is about 4327.76 feet away from the island.

Step-by-step explanation:

We can draw a diagram to represent the situation. This is attached below.

Essentially, we want to find the value of x.

We are given that ∠A is 37° and ∠B is 55°.

The interior angles of a triangle must total 180°. Hence:

[tex]m\angle A+m\angle B+m\angle C=180[/tex]

Substitute:

[tex](37)+(55)+m\angle C=180[/tex]

Thus:

[tex]\displaystyle m\angle C=88^\circ[/tex]

We are also given that the length of the bridge is 5,280 feet. Since we want to find x, we can use the Law of Sines:

[tex]\displaystyle \frac{\sin(A)}{a}=\frac{\sin(B)}{b}=\frac{\sin(C)}{c}[/tex]

The variables do not really matter. It is more important that we align the angles with their respective (i.e. opposite) sides.

The respective side to ∠C is AB which measures 5280.

The respective angle to x is ∠B, which is 55°.

Hence:

[tex]\displaystyle \frac{\sin(55)}{x}=\frac{\sin(88)}{5280}[/tex]

Solve for x. Cross-multiply:

[tex]x\sin(88)=5280\sin(55)[/tex]

Thus:

[tex]\displaystyle x=\frac{5280\sin(55)}{\sin(88)}[/tex]

Use a calculator:

[tex]\displaystyle x\approx 4327.76\text{ feet}[/tex]

The first person is about 4327.76 feet away from the island.

I literally need help with this question-

It’s ASA congruence btw

Answers

Answer:

AB and DE

Step-by-step explanation:

Look closely and you can notice whats the difference.

OK

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