A piston rises to 5 cm and falls to 3 cm in such a way that it returns to the maximal height three times every two seconds. If we start observing the piston at its maximal height, find an equation modelling the height, h, t seconds from the initial observation.

Answers

Answer 1

Answer:

(1 cm)cos3πt

Step-by-step explanation:

Since the piston starts at its maximal height and returns to its maximal height three times evert 2 seconds, it is modelled by a cosine functions, since a cosine function starts at its maximum point. So, its height h = Acos2πft

where A = amplitude of the oscillation and f = frequency of oscillation and t = time of propagation of oscillation.

Now, since the piston rises in such a way that it returns to the maximal height three times every two seconds, its frequency, f = number of oscillations/time taken for oscillation where number of oscillations = 3 and time taken for oscillations  = 2 s

So, f = 3/2 s =1.5 /s = 1.5 Hz

Also, since the the piston moves between 3 cm and 5 cm, the distance between its maximum displacement(crest) of 5 cm and minimum displacement(trough) of 3 cm is H = 5 cm - 3 cm = 2 cm. So its amplitude, A = H/2 = 2 cm/2 = 1 cm

h = Acos2πft

= (1 cm)cos2π(1.5Hz)t

= (1 cm)cos3πt


Related Questions

can someone tell me the answer to this

Answers

Answer: W=12m

Step-by-step explanation:

Can someone pls help me ASAP I’ll give brainiest


Also show how u got the answer step by step pls

Answers

3^x+1=3^3
X+1=3
X=3-1
X=2

The median of 8 numbers is 4.5.Given that seven of the numbers are 9,2,3,4,12,13,1 find the eighth number

Answers

Answer:

5

Step-by-step explanation:

Answer:  5

Step-by-step explanation:

We rerange the number in 1,2,3,4,9,12,13

The median is 4, and a number x between 4 and 9.

We have 4.5 for median, which is the average of 4 and x.

(4 + x) /2 = 4.5

4 + x = 9

x = 5

Two angles are supplementary. The first angle is 3x degrees. The second angle is (2x + 25) degrees. Determine the measure of each angle.

Answers

Answer: a = 3x

b = 2x+25

180 = a + b

180 = 3x + 2x + 25

180 = 5x + 25

155 = 5x

x = 31

a = 3*31 = 93

b = 2*31 + 25 = 87

Step-by-step explanation: pls mark as branlyest

What is the probability that a randomly selected bottle is correctly placed and a Plastic #4 bottle?


A. 1/2

B. 1/3

C. 1/4

D. 1/6

Answers

Answer:

1/4

Step-by-step explanation:

The answer is C. 1/4

What’s the opposite of -5/8

Answers

The opposite of -5/8 is 5/8.
It’s 5/8, |-5/8| = 5/8

The design for the palladium window shown includes a semicircular shape at the top. The bottom is formed by squares of equal size. A shade for the window will extend 4 inches beyond the perimeter of the window, shown by the dashed line around the window. Each square in the window has an area of 169 in2. Round your answers to the nearest whole number.

Answers

Answer:

[tex](a)\ Area = 3765.32[/tex]

[tex](b)\ Area = 4773[/tex]

Step-by-step explanation:

Given

[tex]A_1 = 169in^2[/tex] --- area of each square

[tex]Shade = 4in[/tex]

See attachment for window

Solving (a): Area of the window

First, we calculate the dimension of each square

Let the length be L;

So:

[tex]L^2 = A_1[/tex]

[tex]L^2 = 169[/tex]

[tex]L = \sqrt{169[/tex]

[tex]L=13[/tex]

The length of two squares make up the radius of the semicircle.

So:

[tex]r = 2 * L[/tex]

[tex]r = 2*13[/tex]

[tex]r = 26[/tex]

The window is made up of a larger square and a semi-circle

Next, calculate the area of the larger square.

16 small squares made up the larger square.

So, the area is:

[tex]A_2 = 16 * 169[/tex]

[tex]A_2 = 2704[/tex]

The area of the semicircle is:

[tex]A_3 = \frac{\pi r^2}{2}[/tex]

[tex]A_3 = \frac{3.14 * 26^2}{2}[/tex]

[tex]A_3 = 1061.32[/tex]

So, the area of the window is:

[tex]Area = A_2 + A_3[/tex]

[tex]Area = 2704 + 1061.32[/tex]

[tex]Area = 3765.32[/tex]

Solving (b): Area of the shade

The shade extends 4 inches beyond the window.

This means that;

The bottom length is now; Initial length + 8

And the height is: Initial height + 4

In (a), the length of each square is calculated as: 13in

4 squares make up the length and the height.

So, the new dimension is:

[tex]Length = 4 * 13 + 8[/tex]

[tex]Length = 60[/tex]

[tex]Height = 4*13 + 4[/tex]

[tex]Height = 56[/tex]

The area is:

[tex]A_1 = 60 * 56 = 3360[/tex]

The radius of the semicircle becomes initial radius + 4

[tex]r = 26 + 4 = 30[/tex]

The area is:

[tex]A_2 = \frac{3.14 * 30^2}{2} = 1413[/tex]

The area of the shade is:

[tex]Area = A_1 + A_2[/tex]

[tex]Area = 3360 + 1413[/tex]

[tex]Area = 4773[/tex]

Lollipops cost 12p each, but I get 3 for 30p. What is the maximum number of lollipops I can buy if I have £2 to spend?

Answers

Answer:

18 lolly pops

Step-by-step explanation:

3 = 30p

3x6 = 1.80

= 18

Which system of inequalities has this graph as its solution?
y 10
-10
- म
5
10
-10
OA. y < 21 - 3
y OB.y > 2 - 3
y> : +4
Ocy > 21 - 3
y < = + 4

Answers

Is this real math?!

price marked at R85 with VAT included​

Answers

Answer: No image? Incomplete question? FREE POINTS!

Step-by-step explanation:

BRAINLIEST PLEASE!

The volume of a square pyramid is 48 in^3 with a height of 4 inches. Find the length of one of the side of the base.

Answers

Answer:

6 inches

Step-by-step explanation:

area of square = 48 x 3 / 4 = 36 in^2

side = 6 in

Answer:

6 in

Step-by-step explanation:

The volume formula for a square-base pyramid of side length x and height h is V = (1/3)x²h.  We want to solve this for the base side length x:

Multiplying both sides by (3/h) results in:

3V

----- = x²       and so the side length, x, is √(3V/h).

 h

Substituting 4 in for h and 48 in³ for V, we get:  x = √(144 in³/4 in) = 6 in

Check:  Does the volume formula given above result in 48 in³ when x = 6 in and h = 4 in?

     

V = (1/3)x²h  = (1/3)(6 in)²(4 in) = 48 in³        YES:  x =  6 in is correct.

A square underwent a dilation using a scale factor of 1:4. Find the missing side length, x, of the smaller square

Answers

Answer:

[tex]x= 3.5[/tex]

Step-by-step explanation:

Given

[tex]k =1:4[/tex] --- scale factor

See attachment for squares

Required

Find x

The corresponding side of length x on the bigger square is 14.

So, we have:

[tex]k = x : 14[/tex]

Equate both values of k

[tex]x : 14 = 1 : 4[/tex]

Express as fractions

[tex]\frac{x }{ 14 }= \frac{1 }{ 4}[/tex]

Solve for x

[tex]x= \frac{1 }{ 4} * 14[/tex]

[tex]x= \frac{14}{4}[/tex]

[tex]x= 3.5[/tex]

PLEASE HELP ME PUT THEM IN ORDER

Answers

Answer

picture below of order. Not entirely

Step-by-step explanation:

Question in pic plz help! ~

Answers

Im gonna label the long side of a rectangle a and the smaller side b.

For the perimeter, 2a + 2b = 34

For the area, a x b = 66

if a is 11 and b is 6, the equation for perimeter would be 22 + 12 = 34.

So a = 11 and  b = 6

Answer:

Longer side = 11

Shorter side = 6

Step-by-step explanation:

L x W = 66,  then W = 66/L

2L + 2W = 34

substitute for W:

2L + 2(66/L) = 34

2L + 132/L = 34

multiply both sides of the equation by L:

2L² + 132 = 34L

divide both sides by 2:

L² + 66 = 17L

L² - 17L + 66 = 0

factor:

(L - 11)(L - 6) = 0

L = 11 or L = 6

if L = 11, then W = 6

if L = 6 then W = 11

Compare each set of rational numbers.

Answers

hey.. don’t click on that link or any links on here !!! but i jus wanna say you didn’t attach an image of your question :).

find the area of this polygon

Answers

Answer:

answer is 65 in²

hope this helps

There were two times as many pepperoni pizzas as cheese pizzas, plus one pizza they ordered 13 pizzas altogether how many pepperoni pizzas were there? How many cheese pizzas were there

Answers

Answer:

pepperoni pizzas = 8

cheese pizzas = 4

Step-by-step explanation:

let x = cheese pizza

2x + x + 1 = 13

3x = 13 -1

3x = 12

x = 4

pepperoni = 2x4 = 8

28) (-5ưyA +9u) + (-5ư v4 - 8u + 8u²v2)+(-8u*v + 8uº4)=

Answers

Answer: good luck

Step-by-step explanation:

1. A psychologist was interested in the effect of Vitamin A deficiency on maze learning rats. A group of nine rats learned a simple maze. Next, these same rats were deprived of Vitamin A for six weeks and were then tested again on their ability to learn a second maze equal in difficulty to the first. The scores represent the number of maze errors made under the two treatment conditions. Perform an appropriate two-tailed test of the significance of the mean difference.

Answers

Answer: hello your question has some missing information attached below is the missing information

we fail to reject H0 hence μ1 = μ2mean difference ( d )  = -2.444

Step-by-step explanation:

H0 : μ1 = μ2

Ha : μ1 ≠ μ2

where : μ1 = mean number of errors made in pretest

            μ2 = mean number of errors made in post test

n = 9

attached below is the detailed solution

Plz Help!Plz Help!Plz Help!Plz Help!Plz Help!Plz Help!Plz Help!Plz Help!Plz Help!Plz Help!Plz Help!Plz Help!Plz Help!Plz Help!Plz Help!Plz Help!Plz Help!

Answers

Answer: n=4

Step-by-step explanation:

Given

3n-(2+n)=6

Expand Parenthesis (REMEMBER TO CHANGE SIGNS)

3n-2-n=6

Combine like terms

2n-2=6

Add 2 on both sides

2n-2+2=6+2

2n=8

Divide both sides by 2

2n/2=8/2

n=4

Hope this helps!! :)

Please let me know if you have any questions

Answer:

4

Step-by-step explanation:

4 Is the Answer because you have to multiply 4 to all the N's. Which means you have to multiply 4 by 3 which equals 12. Then 2+4=6. Then you would do 12-6=6. There's your answer. Here is the equation if it were like the problem: 12 - (2+4). I'm sure you can figure out the rest. Thanks. If you find any fault in my answer let me know! Have a good day!

-4(z + 3) - 4(5 - 4z) solution

Answers

Answer:

12z-32

Step-by-step explanation:

-4z-12-20+16z

I need the answer fast please !

Answers

Answer:

30

Step-by-step explanation:

Angles on a straight line are equal to 180°

180°-120°= 60°

Sum of Co interior angles are equal to 180°

180°-60° =120°

90°+60°+ x = 180°

((180° - 90° - 60°= 30°))

Find the surface area.
24 in.
40 in.
10 in.
26 in.

Answers

Answer:

100 i think

Step-by-step explanation:

HELP ME UNSCRAMBLE THESE WORDS PLEASE!!! IGNORE THE SUBJECT I JUST DIDN'T KNOW WHAT TO PICK!! THANK YOU LOVELIES!!!

Answers

1) Play

2)Dribble

3)Paint

4)Center

5)Assists

6)Perimeter

7)Benchwarmer

8)Aboard

9)Technical

10)Rebound

11)Penalty

12)screen

13)Overtime

14)guard

15)? Host

16)Quarter

17) Bounce

18)Swish

19)Halftime

20)Backcourt

PLEASE HELP AND SHOW AN EXPLANATION ITS DUE IN 30 MINUTES!! Donna wants to create a stained glass window composed of one quarter circle, two semicircles, and one parallelogram. Which measurement is closest to the amount of stained glass in square inches Donna will
need to create the window?

Answers

I multiplied all the numbers together and I got 3,080 inches. I hope this is correct sorry if it’s not!!

Dani has only 1/2 of a cup of baking mix. She needs 3/4 of a cup for one batch of muffins. Which solution method shows how much of a batch of muffins Dani can make?

Answers

Answer:

Step-by-step explanation:

Dani has only 1/2 of a cup of baking mix. She needs 3/4 of a cup for one batch of muffins. Which solution method shows how much of a batch of muffins Dani can make?

Eu tenho um ovo de páscoa que custa 24,99 e tem 185 gramas, tbm tenho uma barra de chocolate q custa 5,10 e tem 90 gramad. Qual da mais vantagem para mim?

Answers

Answer:

A maior vantagem para mim é a barra de chocolate.

Step-by-step explanation:

Temos que encontrar o custo de 1 grama de ovo de Páscoa e barra de chocolate

Para o ovo de páscoa

Tenho um ovo de Páscoa que custa 24,99 e tem 185 gramas.

185 gramas = 24,99

1 grama = x

Multiplicação cruzada

185 gramas × x = 1 grama × 24,99

x = 1 grama × 24,99 / 185 gramas

x = 0,1612258065

Aproximadamente = 0,16

O custo de 1 grama de ovo de Páscoa = 0,15

Para a barra de chocolate

Também tenho uma barra de chocolate que custa 5,10 e tem 90 gramas.

90 gramas = 5,10

1 grama = x

Multiplicação cruzada

90 gramas × x = 1 grama × 5,10

x = 1 grama × 5,10 / 90 gramas

x = 0,0566666667

Aproximadamente = 0,06

O custo de 1 grama de barra de chocolate = 0,06

A maior vantagem para mim é a barra de chocolate.

Write an equation in slope intercept form that represents the line shown?

Answers

Answer:

I think the answer would be Y=-2X+5

Hope it helps you *^*

3. A system of functions is given. Select
ALL values where f(x) = g(x). Round all
answers to the nearest tenth
f(x) = - x - 2x + 6
g(x) = 2x2 + 5x + 3
a) -2.7
b) -1.8
c) -0.6
d) 0.4
e) 4.1
f) 5.1
g)7.0

Answers

Answer:

Step-by-step explanation:

The easiest way is to graph both functions and see where they intersect.  The intersection is where f(x) = g(x).

f(x) = -x² - 3x + 6

g(x) = 2x² + 5x + 3

Luba walked 5 miles in 1 1/2 hours. How fast did she walk in miles per hour?
A. 2/15 miles per hour
B. 9/10 miles per hour
C. 2 3/4 miles per hour
D. 3 1/3 miles per hour

Answers

Answer:

c or d sorry if I'm wrong

Step-by-step explanation:

I think it's your d because of the shortest answers and they're the only two that makes sense

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