The height, h, in feet of a piece of cloth tied to a waterwheel in relation to sea level as a function of time, t, in seconds can be modeled by the equation h = 8 cosine (startfraction pi over 10 endfraction t). what is the period of the function? startfraction pi over 20 endfraction seconds startfraction pi over 10 endfraction seconds 8 seconds 20 seconds

Answers

Answer 1

Answer:

20 seconds

Step-by-step explanation:

I assume you mean [tex]h(t)=8\cos(\frac{\pi}{10}t)[/tex] for your function.

As the given function is in the form of [tex]f(t)=a\cos(bt+c)+d[/tex] (some textbooks may write this formula differently), the period is equal to [tex]\frac{2\pi}{|b|}[/tex]. Hence, the period of the given function is [tex]\frac{2\pi}{|\frac{\pi}{10}|}=\frac{2\pi}{1}*\frac{10}{\pi}=\frac{20\pi}{\pi}=20[/tex], or 20 seconds.

Answer 2

The period of the function that relates the sea level as the function of time is given by: Option D: 20 seconds.

What are some properties of a cosine function?

Suppose that we've got: [tex]f(x) = a\cos\left(\dfrac{2\pi x}{b}\right)[/tex]

Then, this function has:

Amplitude (the maximum distance of the graph from the middle line) = aPeriod = b

For this case, we're given that:

[tex]h = 8\cos\left(\dfrac{\pi x}{10}\right)[/tex]

We can rewrite it as:

[tex]h = 8\cos\left(\dfrac{2\pi x}{20}\right)[/tex]

Thus, we get a = amplitude = 8 units(distance), and b = period = 20 units(time in seconds).

Thus, the period of the function that relates the sea level as the function of time is given by: Option D: 20 seconds.

Learn more about amplitude and period of a cosine function here:

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The Height, H, In Feet Of A Piece Of Cloth Tied To A Waterwheel In Relation To Sea Level As A Function

Related Questions

Simplify.

2 × (3 – 1) + 3

Answers

Answer:

7

Step-by-step explanation:

do what is in the parenthesis first then multiply then add

What is the volume of a hemisphere with a radius of 2.3 m, rounded to the nearest tenth of a cubic meter?

Answers

Answer:

25.3m³

Step-by-step explanation:

The question is in the attachment.

Answers

Answer:

0.0816

Step-by-step explanation:

Given:

Total number of students = 5000Number of students taking an online class = 1200Number of students prefer watching baseball to football = 1700

Let O = Students taking an online class

Let B = Students prefer watching baseball to football

Therefore,

P(O) = 1200/5000 = 0.24

P(B) = 1700/5000 = 0.34

If events O and B are independent,

⇒ P(O ∩ B) = P(O) · P(B)

                   = 0.24 × 0.34

                   = 0.0816

ASAP GIVING 5 STARS AND A LIKE AND BRAINLIEST 412 ÷ 10¹

Answers

Answer:

Your answer would be:

41.2

10¹ = 10

412 / 10 = 41.2



Step-by-step explanation:

Have a great rest of your day
#TheWizzer

When you use a (______________), you pay for your purchases later.
A credit card
B checking account
C deposit
D credit score

Answers

Answer:

A. credit card

Step-by-step explanation:

When using a credit card, the bank is paying for you. Overtime through bills you will pay that amount back usually with interest.

Good evening! Can someone please answer this, ill give you brainliest and your earning 50 points. Would be very appreciated.

Answers

Answers:

1) [tex]\sf \boxed{1} \ x^2 + \boxed{2} \ x -24[/tex]

2) [tex]\sf \boxed{2} \ x^2+ \boxed{-1} \ x-15[/tex]

3) [tex]\sf \boxed{6} \ x^2+\boxed{19} \ x+10[/tex]

4) [tex]\sf \boxed{2} \ x^2+\boxed{-11} \ x+5[/tex]

solving step wise:

1)

(x+6)(x-4)x² + 6(x) -4(x) -24x² + 2(x) - 24

2)

(2(x)+5)(x-3)2(x)² - 6(x)+5(x)-152(x)² - x - 15

3)

(3(x)+2)(2(x)+5)6(x)²+15(x)+4(x)+106(x)² + 19(x)+10

4)

(2(x)-1)(x-5)2(x)² -10(x)-x+52(x)² -11(x)+5

#1

(x+6)(x-4)x(x-4)+6(x-4)x^2-4x+6x-24x^2+2x-24

#2

(2x+5)(x-3)2x(x-3)+5(x-3)2x^2-6x+5x-152x^2-x-15

#3

(3x+2)(2x+5)3x(2x+5)+2(2x+5)6x^2+15x+4x+106x^2+19x+10

#4

(2x-1)(x-5)2x(x-5)-1(x-5)2x^2-10x-x+52x^2-11x+5

simplify (3a^2-6a+3)/(a^2-1) if a is not 1

Answers

[tex]\dfrac{3a^2-6a+3}{a^2-1}\\\\=\dfrac{3(a^2 -2a+1)}{(a+1)(a-1)}\\\\=\dfrac{3(a-1)^2}{(a+1)(a-1)}\\\\=\dfrac{3(a-1)}{a+1}\\\\=\dfrac{3a-3}{a+1} ~~~\text{for}~ a\neq 1[/tex]

Select the expression equivalent to (4.5x + 3.1) - (-3x - 5).
a
7.5x + 1.9
b
7.5x - 1.9
7.5x + 8.1
d.
7.7x - 1.9

Answers

Answer:

Option C :- 7.5x + 8.1

Step-by-step explanation:

Let's simplify step-by-step.

4.5x+3.1−(−3x−5)

Distribute the Negative Sign:

=4.5x+3.1+−1(−3x−5)

=4.5x+3.1+−1(−3x)+(−1)(−5)

=4.5x+3.1+3x+5

Combine Like Terms:

=4.5x+3.1+3x+5

=(4.5x+3x)+(3.1+5)

=7.5x+8.1

Answer:

=7.5x+8.1

How may you rethink the way you choose people in a group? No links please or I will report you. The best explanation gets Brainliest!

Answers

Step-by-step explanation:

How to rethink the way you choose people in a group is to figure out if they like you or not. Don't chose people that do not like you because they will not work well with you. Pick the people you feel will help you succeed in the group. And sometimes the people you pick in your group aren't even your friend, but they can help you succeed by staying on task and focusing on the task at hand.

Write an expression equivalent to 6 — 2.2 +5+ 4. that only has two
terms.

Answers

Answer:

3.8 + 9?

Step-by-step explanation:

2. Jada fills her aquarium with water.

The graph shows the height of the water, in cm, in the aquarium as a function of time in minutes. Invent a story of how Jada fills the aquarium that fits the graph.

Answers

Answer:

Jada fills her aquarium with water at a constant rate of 5cm/minute for 2 minutes. She then stops the water from running for 1 minute. After that, she started to fill the aquarium at a constant rate of 10cm/minute for another 2 minutes. After 5 minutes, she reduces the water running at a rate of 5cm for 2 minutes. After 7 minutes, she turns off the water and the water is at 25cm.

The lengths of all sides are different in which type of triangle?.

Answers

Answer: Scalene Triangle

Step-by-step explanation:

Answer:

Scalene Triangle

Step-by-step explanation:

Scalene Triangle: All sides are different


Isosceles Triangle: 2 sides are the same

Equilateral Triangle: All sides are the same.

can you help me pls? i need it

Answers

Answer:

$168.75

Step-by-step explanation:

In the morning you'll have a time of about 4 hours.

In the afternoon you'll have 8.5 hours.

You take these and add them together 4 + 8.5 = 12.5

Then you take your sum and multiply it by the wage you make per hour 13.50 x 12.5 = $168.75

Find+the+z-scores+that+separate+the+middle+69%+of+the+distribution+from+the+area+in+the+tails+of+the+standard+normal+distribution

Answers

Answer and Explanation:

1 - 0.69/ 2 = 0.155

0.155 = -1.02

(-1.02, 1.02) = z

The z -score separates the middle 69% of the distribution from the area in the tails of the standard normal distribution is  (-1.02, 1.02).

What is a z- score?

Z- score refers to how much a given value differs from the standard deviation.

The z -score separates the middle 69% of the distribution from the area in the tails of the standard normal distribution.

α = 1 - 0.69/ 2

α =  0.155

0.155 = -1.02

z = (-1.02, 1.02)

Learn more about standard deviation:

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#SPJ4

pls help with this Its on ixl

Answers

Answer:

142 cm squared

Step-by-step explanation:

the formula used was 2(lw + wh +lh)

where l is length

w is width

and h is height

Answer:

142

Step-by-step explanation:

5 x 3 = 15 Times by 2 = 30

7 x 5 = 35 Times by 2 = 70

7 x 3 = 21 Times by 2 = 42

what is a pair lines that are parallel​

Answers

Answer:

The pairs of lines that do not intersect or meet at any point are called parallel lines. These lines lie on the same plane but do not intersect. The line segments or rays that lie on the same plane but do not intersect are also parallel.

Step-by-step explanation:

Answer

A parallel line is a position of two lines on a plane that does not have a point of intersection even though the two lines are extended.Geometrically, parallel lines will never meet each other because they have the same slope (gradient). Parallel lines do not have to be the same length

x + y = 5 2x - y = 1 substitution method

Answers

[tex]x+y = 5~~...(i)\\\\2x-y = 1~~...(ii)\\\\\text{From (i):}\\\\x+y = 5\\\\\implies x = 5-y~~~.....(iii)\\\\\text{Substitute equation (iii) in equation (ii):}\\ \\2(5-y)-y = 1\\\\\implies 10 - 2y -y = 1\\\\\implies 3y = 9\\\\\implies y = \dfrac 93 = 3\\\\\text{Substitute y= 3 in equation (iii):}\\\\x= 5-3 = 2\\\\\text{Hence,}~ (x,y) = (2,3)[/tex]

Answer:

Solve for the first variable in one of the equations, then substitute the result into the other equation.

Point Form:

(2,3)

Equation Form:

x = 2, y = 3

Step-by-step explanation:

You have decided to purchase a car for $25,625. the credit union requires a 10% down payment and will finance the balance with a 9% annual interest loan for 36 months. the sales tax in your city is 7.5%, and the license and title charges are $175.13. what is the total purchase price of the car including tax, license, and title? round your answer to the nearest cent. a. $24,949.80 c. $27,722.01 b. $24,967.32 d. $27,735.14

Answers

The total purchase price of the car including tax, license, and title $27,722.01.

The purchase price of a car is $25,625 the credit union requires a 10% down payment and an annual interest 9% loan for 36 months. The sales tax is given 7.5%, and the license and title charges are $175.13.

What is the total sale?

The total sale is the product of the selling price and one plus the sales tax rates.

Total sale = selling price × (1 + sales tax rate)

The price of the car including tax

= $25,625 × (1 +7.5%)

= $27,546.88

By adding license and title charges to the amount, we get

= $27,546.88 +175.13

= $27,722.01

Hence, The total purchase price of the car including tax, license, and title $27,722.01.

Learn more about the total sale here:

https://brainly.com/question/2777438

There are 63 female performers in a dance recital. the ratio of men to women is 5:9. how many men are in the dance recital?

Answers

In d ratio 5:9 which equals 5+9=14
the total female performers is 63
For men = 5/14*63=5/2*9
=45/2 =22.5
The men would be about 22.5 in the dance recital

Tony is working on an arithmetic sequence where t(1) =4 and t(8) =67 Write the explicit equation and recursive equation for this sequence. Is 500 a term of the sequence? Explain why or why not.

Answers

Assuming t(1) is our first term, we can say:

t(2)=t(1)+dt(3)=t(2)+dt(4)=t(3)+d

This can go on forever, we can then establish the recursive formula which states:

t(n+1)=t(n)+dort(n)=t(n-1)+d

Explicit formula:

t(2)=t(1)+d

t(3)=t(2)+d, but t(2)=t(1)+d

t(3)=t(1)+d+d

t(3)=t(1)+2d

t(4)=t(1)+3d

t(n)=t(1)+(n-1)d

We can calculate d for these equations:

t(8)=t(1)+7d67=4+7d7d=63d=9

Explicit relation:t(n)=4+9(n-1)t(n)=9n-5

Recursive relation:

t(n)=t(n-1)+9

t(500)=9(500)-5=4500-5=4495

2x = 37 find solve of x

Answers

Answer:

18.5

Step-by-step explanation:

37 divided by 2 is 18.5

Find base of triangle on coodinate plane 8,2 and 6,2

Answers

Answer:

The base of this triangle is 2 units wide

Step-by-step explanation:

Your explanation is in the picture shown below!!!

Find the volume of the solid. Use 3.14 for π.​

Answers

Answer:

vol= 10366.3175in²

Step-by-step explanation:

So this is a cylinder

formula: π r²h

R= 8.75in

h=43.12in

So it will be = 3.14x8.75²x43.12

=> 3.14x76.5625x43.12

3.14x 3301.375

10366.3175in²

i think it is correct

.

stay safe

.

have a nice TIME

What value of c makes the polynomial below a perfect square?

Answers

Answer:

B

Step-by-step explanation:

x² + 9x

to complete the square

add ( half the coefficient of the x- term )² to x² + 9x

= x² + 2([tex]\frac{9}{2}[/tex] )x + ([tex]\frac{9}{2}[/tex] )²

= x² + 9x + [tex]\frac{81}{4}[/tex] ← the value of c

= (x + [tex]\frac{9}{2}[/tex] )² ← a perfect square

81/4
Because I found the answer by using a Calculator I found online

Solve for X. Leave your answer in the simplest radical form.
Image down below!
Someone please help me with this, I’ll give you brainlist and points!

Answers

Apply Pythagorean theorem

P²=10²-4²P²=100-16P²=84p=2√21

Again

x²=84-8²x²=84-64x²=20x≈√20=√4×5=2√5

Answer:

2√5

Step-by-step explanation:

The given pyramid is composed of two right angle triangles. Notice the triangles of the pyramid share a common side. With the help of it, we can figure out x

recall Pythagoras theorem

[tex] {a}^{2} + { b }^{2} = {c}^{2} [/tex]

Case-1: Finding the opposite side

here,

a=4c=10

To find:

b

now plug in the value of a and c in the formula respectively:

[tex] {4}^{2} + { b }^{2} = {10}^{2} \\ \implies {b}^{2} = {10}^{2} - {4}^{2} \\ \implies {b}^{2} = 84 \\ \implies \boxed{ b_{1} = 2\sqrt{21}}[/tex]

Case-2: Finding x

here,

[tex]b_1 \implies c=2\sqrt{21}[/tex]b=8a[tex]\implies[/tex] x

Utilizing Pythagoras theorem yields:

[tex] {x}^{2} + { 8}^{2} = {(2\sqrt{21})}^{2} \\ \implies {x}^{2} = {(2\sqrt{21})}^{2} - {8}^{2} \\ \implies {x}^{2} = 20\\ \implies \boxed{ x= 2\sqrt{5}}[/tex]

and we're done!

change 1.77 tones to kilograms

Answers

Answer:

1.77 Tones = 1770 Kilograms

Step-by-step explanation:

Multiply the value of the tone by 1000 to get KG

1.77 x 1000 = 1770

1770 kilograms
Multiply the mass value by 1000

A babysitter charges an hourly rate. The equation y = 12x represents the relationship between hours of babysitting, x, and total pay, y, in
dollars.
What is the salary per hour for the babysitter?

Answers

salary : $12 per hour

A bank is offering 2.5% simple interest on a savings account. if you deposit $5000,how much interest will you earn in one year?​

Answers

Answer:

$125 you will end up w/ $5125

Step-by-step explanation:

The number of calories consumed in an oreo cookie is directly proportional

Answers

Yes this isn’t really a question but every Oreo has the same number of calories making it proportional

The radius of a circle is 14 feet. What is the area of the circle?

87.92 ft 2
615.44 ft 2
153.86 ft 2
1,230.44 ft 2

Answers

Answer:

615.44 ft 2

Step-by-step explanation:

radius times radius times 3.14(pie)

Answer:

Area of circle = pie r²

22/7×14²

616,,

According to me

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