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 = 15 cosine (StartFraction pi Over 20 EndFraction t). How long does it take for the waterwheel to complete one turn? 5 seconds 10 seconds 20 seconds 40 seconds.

Answers

Answer 1

Solving the trigonometric equation, it is found that it takes 40 seconds to complete one turn.

The height is modeled by:

[tex]h(t) = 15\cos{\left(\frac{\pi}{20}t\right)}[/tex]

The initial height is [tex]h(0) = 15[/tex], hence, one turn is completed when h(t) = 15.

[tex]h(t) = 15\cos{\left(\frac{\pi}{20}t\right)}[/tex]

[tex]15 = 15\cos{\left(\frac{\pi}{20}t\right)}[/tex]

[tex]\cos{\left(\frac{\pi}{20}t\right)} = \frac{15}{15}[/tex]

[tex]\cos{\left(\frac{\pi}{20}t\right)} = 1[/tex]

The length of one turn is of [tex]2\pi[/tex], and [tex]\cos{(2\pi)} = 1[/tex], hence, the solution is found according to:

[tex]\frac{\pi}{20}t = 2\pi[/tex]

[tex]t = \frac{40\pi}{\pi}[/tex]

[tex]t = 40[/tex]

It takes 40 seconds to complete one turn.

You can learn more about trigonometric equations at https://brainly.com/question/24680641

Answer 2

Answer:

D. 40 seconds!! Props to guy above.


Related Questions

The supplement of the complement of an angle is 132 degrees. What is the supplement of that angle

Answers

Based on the information given, it should be noted that the supplement will be 48°.

It should be noted that two angles are called supplementary angles when the values that are added together will be equal to 180°.

In this case, we've been informed that one of the angles is 132°. Therefore, the value of the second angle will be:

= 180° - 132°

= 48°

The second angle is 48°.

Learn more about angles on:

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Hi, let me help you out!

- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

In this problem, we're trying to find the supplement of [tex]\tt{132\textdegree}[/tex].

Supplementary angles add up to [tex]\tt{180\textdegree}[/tex].

So, let's find its supplement:

[tex]\tt{\angle x+132=180}[/tex], where x is the unknown angle.

Subtract 132 from both sides of the equal sign:

[tex]\boxed{\tt{\angle x=48\textdegree}}[/tex] [tex]\longleftarrow\tt{We\:conclude\:that\:this\:is\:the\:answer.}[/tex]

I hope it helps you! Have an awesome day!

If you need any explanation or clarification, feel free to comment and ask me, and I'll respond asap and do my best to help you out! :D

- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -  - - - - -  - - - - - - - -

Type the expression that results from the following series of steps:
Start with 6 and subtract
z

Answers

6-z

Z-6 would be wrong because the question said start with 6

On a coordinate plane, triangle A B C is shown. Point A is at (negative 1, 1), point B is at (3, 2), and points C is at (negative 1, negative 1) If line segment BC is considered the base of triangle ABC, what is the corresponding height of the triangle? 0. 625 units 0. 8 units 1. 25 units 1. 6 units.

Answers

The corresponding height of the triangle is 1.6 units

The formula for calculating the area of a triangle is expressed as:

[tex]A=\frac{1}{2} bh[/tex]

b is the base of the triangleh is the height of the triangle

Given the coordinates of the base BC of the triangle given as B(3, 2), and C(-1,-1). Using the distance formula:

[tex]D=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\\BC= \sqrt{(-1-2)^2+(-1-3)^2}\\BC=\sqrt{3^2+4^2}\\BC=\sqrt{25}\\BC=5units[/tex]

The area of the triangle passing through the coordinate points A(-1, 1), B(3,2), and C(-1, -1) is expressed as:

[tex]A=\frac{1}{2}[x_1(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2)]\\[/tex]

Substituting the coordinate points:

[tex]A=\frac{1}{2}[(-1)(2-(-1))+3(-1-1)+-1(1-2)]\\A=\frac{1}{2}[(-1)(3)+3(-2)+-1(-1)]\\A=\frac{1}{2}[-3-6+1]\\A=\frac{1}{2} (-8)\\|A| =4 units^2[/tex]

Recall that:

[tex]A = 0.5bh\\h=\frac{A}{0.5b}\\h=\frac{4}{0.5(5)}\\h=\frac{4}{2.5}\\h= 1.6 units[/tex]

Hence the corresponding height of the triangle is 1.6 units

Learn more on area of triangles here: https://brainly.com/question/17335144

Select the correct answer.
A pencil costs $0.25 more than an eraser. If the cost of eight pencils is $6.80, what is the cost of one eraser?
A.
$1.80
B.
$0.85
C.
$0.60
D.
$0.40
E.
$0.30

Answers

Answer:

C.$0.60

hope this help!!!!!!!!!!!!!!!!!!!!!!

Solve each equation
6y-8-6-8y=4

Answers

Answer:

y = -9

Step-by-step explanation:

Combine like terms first; 6y-8y=-2y and -8-6=-14  

-2y-14=4.

Then add 14 to both sides.

-2y=18

Lastly, divide both sides by -2

y=-9

Answer: = -9

Step-by-step explanation:

1. subtract -8-6 which equals -14

2. Combine like terms which are -8y and 6y and you should get -2y

3. Add 14 on both sides eliminate the -14 on one side. it should be -2y = 18

4. Now you want to get y all on its own so you divide -2 on both sides -2y/2 = 18/-2

5. and you should be able to cancel out -2y and get y= -9

Pls answer these two questions

Answers

Answer:

1. C

2. C

Hope This Helps!!!

if the discriminant is negative how many solutions are there

Answers

Answer:

  no real solutions

Step-by-step explanation:

If it is a quadratic equation, there are always two solutions, regardless of the value of the discriminant.

When the discriminant is negative there are no real solutions, but there are two complex solutions.

What is the slope of the line?

Answers

The slope of the line is 4/5

"a deposit plus $8 per hour"

Answers

Answer:

d + 8/hr

Step-by-step explanation:

14b = −56
i need help figuring out what this is i'm doing it but i keep getting it wrong please help

Answers

Answer:

-4

Step-by-step explanation:

14b = -56

divide by 14

-56 ÷ 14 = -4

b = -4

I hope this helps!

Answer:

b = -4

Step-by-step explanation:

[tex]14b = -56\\\\rule{150}{0.5}\\\frac{14b=-56}{14}\\\\ \boxed{b = -4}[/tex]

Hope this helps.

Please help me with this

Answers

Step-by-step explanation:

the only reason you would need help with this is, if you don't understand what exponents are and how they work.

because once you understand that, you can do the whole question in 30 seconds yourself. way faster than the posting here and then copying answers back into your system.

so, let me explain this important element :

when you have something like 5³, then this 3 is the exponent, and the 5 is the base.

when we talk about such a thing we typically say "5 to the power of 3".

now what did it mean ?

well, it is a multiplication. a multiplication of the base by itself (like when we square a number).

and the exponent tells is how often the base is multiplied by itself.

so, back to my example :

5³ = 5×5×5

3² = 3×3

13⁴ = 13×13×13×13

once you understand that, you can solve the question yourself in seconds.

e.g. the first is looking for the equivalent of 7⁴.

we need to find the answer option that dissolves this like the examples above to 7×7×7×7.

and we find B to be the right answer.

for 3⁶ = 3×3×3×3×3×3

and E is right. and so on.

A rectangular lawn 80 m x 60 m has two roads each 10m wide running in the middle of it, one parallel to the length and the other parallel to the breadth. Find the cost of gravelling them at ₹ 1.20 per sq meter.​

Answers

Answer:

₹1680

Step-by-step explanation:

Road  Length (m)  Width (m)   Area ([tex]m^{2}[/tex])

  1            80              10              800

  2           60              10               600

(800+600) = 1400 ([tex]m^{2}[/tex])

1400 ([tex]m^{2}[/tex])*(₹ 1.20/m) = ₹1680

Pls help I'm falling behind

Answers

this would be 2.7•10^5

a rectangular parking lot has a perimiter of 500 feet and a width of 100 feet. find the lenght of the parking lot be sure to show all four steps

Answers

Answer:

50,0

Step-by-step explanation:

So we know 500×100=50,000

So it's 50,000

I’ll give 100 points

Answers

Answer:

2055 is the answer.

Step-by-step explanation:

If x represents the number of minutes and y represents the hiker elevation in feet.

y = 8.19x + 663

y = 8.19(170) + 663

y = 1392.3 + 663

y = 2055.3

Hope it helps:)

Answer:

:)

Step-by-step explanation:

what is 400X600+1200=

Answers

Answer: 241,200

just multiply and add hope this helps

Answer:

24,1200

Step-by-step explanation:

400x600=24,000

Then let's add 24,000+1,200 which is 24,1200.

Dress:$35.99 tax:6.75%

Answers

Answer:

38.14 but if rounded up it becomes 38.15

MY HEAD IS HURTING I BEG FOR YOUR HELP. I WILL MARK BRAINLIST!!

Answers

Answer: No association

Step-by-step explanation:

There is absolutely no pattern going on. This means that the miles ran per week are not really affecting the standing heartbeat. Therefore, I'd say there is no association.

Emma and her 3 friends were thirsty so she shared 1/2 gallon of lemonade equally among 4 people. How much did each purdon get


1/8
1/4
1/2
4

Answers

Answer:

1/4

Step-by-step explanation:

its kinda hard to

explain

Find the product -1.2(0.04)

Answers

Answer:

-0.048

Step-by-step explanation:

-1.2 * 0.04 = -1.2 * 4 / 100 = -4.8 / 100 = -).048

A tree cast a shadow 21 meters long
The angle of elevation for the sun is 51 degrees
What is the height of the tree?

Answers

Step-by-step explanation:

I do not understand .____.

Which expression can be used to approximate the expression below, for all positive numbers a, b, and x, where a Not-equals 1 and b Not-equals 1? log Subscript x Baseline x StartFraction log Subscript b Baseline x Over log Subscript b Baseline a EndFraction StartFraction log Subscript b Baseline a Over log Subscript b Baseline x EndFraction StartFraction log Subscript a Baseline b Over log Subscript x Baseline b EndFraction StartFraction log Subscript a Baseline x Over log Subscript b Baseline x EndFraction.

Answers

The expression that can be used to approximate the expression below is[tex]log_a x = \frac{log_{b}a}{log_{b}x}[/tex]

Given the logarithmic function expressed as [tex]log_a x[/tex], we need the log expression that is equivalent to the given expression.

To do this, we will write the logarithm as a quotient to the same base. Using the base of 10, the expression can be written as;

[tex]log_a x = \frac{log_{10}a}{log_{10}x}[/tex]

This is similar to the option c where the base of "b" was used as [tex]log_a x = \frac{log_{b}a}{log_{b}x}[/tex]

Learn more on law of logarithms here: https://brainly.com/question/11587706

Answer: C

Step-by-step explanation:

If you don't want to read it all

A motorcycle can travel 60 miles per gallon. Approximately how many gallons of fuel will the motorcycle need to travel 40 km? [1 mile = 1. 6 km] 0. 04 0. 08 0. 20 0. 42.

Answers

The motorcycle needs to travel 40 km, 0.42 gallons of fuel.

Given that,

A motorcycle can travel 60 miles per gallon.

We have to find,

How many gallons of fuel will the motorcycle need to travel 40 km?

According to the question,

The motorcycle travel 60 miles per gallon,

The motorcycle travels 40 km,

To convert it into kilometers 60 miles per gallon.

[tex]\rm 1 \ mile = 1.6\ k.m.\\\\60 \ miles \times 1.6 \ k.m. = 96 \ k.m.[/tex]

Therefore,

The gallons of fuel will the motorcycle need to travel 40 km is,

[tex]= \dfrac{96}{40}\\\\= 0.42[/tex]

Hence, The motorcycle needs to travel 40 km, 0.42 gallons of fuel.

For more details refer to the link given below.

https://brainly.com/question/13108874

You sell tickets for admission to your school play and collect a
total of $156. Admission prices are $8 for adults and $4 for
children, you sold 24 tickets. How many adult tickets and how
many children tickets did you sell?

Answers

Answer:

adults 15 and children 9

Step-by-step explanation:

Jenny's great grandmother is 95 years old.
Jenny is 12 years old.
What percent of Jenny's great grandmother's age is Jenny's age?

Hurry! Worth a lot of points!

Answers

Think of it as 12/95. 12.63

will give brainliest!

Answers

Answer 4/5 now give brainliest

brainlyest, plus 5 points
PLEASE STEP BY STEP
Evaluate x/2+5y-1.5 when x = 10 and y = 8

Answers

Answer:

43.5

Step-by-step explanation:

x/2+5y-1.5

10/2+5×8-1.5

5+40-1.5

5+38.5

=43.5

Answer:

43.5

Step-by-step explanation:

x ÷ 2 + 5y - 1.5

Start by replacing the x's and y's

10 ÷ 2 + (5 · 8) - 1.5

Start with parenthesis

10 ÷ 2 + 40 - 1.5

Then do the division

5 + 40 - 1.5

Then go left to right

45 - 1.5

43.5

I hope this helps!!!

Add.
(4+4n)+(7+2a)

Thanks!

Answers

Answer:

[tex](4+4n)+(7+2a) = 11+4n+2a[/tex]

Step-by-step explanation:

Please solve this problem please ASAP !

Answers

Answer:

3/x+2 = 4/y

then y equals

3y = 4(x+2)

y = 4x + 8 / 3

Elsa is selling bracelets at craft shows to raise money for an animal shelter. She is also accepting additional cash donations. She plans to give 75% of the money from all bracelet sales and donations to the shelter. She will use the remaining money to buy more supplies. Bracelet sales and donations from the first craft show are represented by the expression 24n+32 , where n represents the amount Elsa charges for each bracelet. The second craft show sales and donations is represented by the expression 40n+56 . If Elsa charges $4 for each bracelet, how much money will she donate to the animal shelter?

Answers

Answer:

22-1n-3

Step-by-step explanation:

The percentage is calculated by dividing the required value by the total value and multiplying by 100.

The amount donated to the animal shelter is $258

What is a percentage?

The percentage is calculated by dividing the required value by the total value and multiplying by 100.

Example:

Required percentage value = a

total value = b

Percentage = a/b x 100

We have,

Percentage to donate to the shelter = 75%

The expression that shows the amount from the first and second craft shows.

24n + 32 _____(1)

40n + 56 ______(2)

Where n is the amount of each bracelet.

Now,

Cost of each bracelet = $4.

From (1) and (2) we get,

24 x 4 + 32 = 96 + 32 = 128

40 x 4 + 56 = 160 + 56 = 216

Now,

The total amount collected from both the craft shows.

= 128 + 216

= $344

The amount donated to the animal shelter.

= 75% of $344

= 75/100 x 344

= $258

Thus,

The amount donated to the animal shelter is $258

Learn more about percentages here:

https://brainly.com/question/11403063

#SPJ2

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