An object oscillates as it moves along the
X-axis. Its displacement varies with time
according to the equation
x = 4 sin(pi t + pi/6)
where t = time in seconds and
x = displacement in meters
What is the displacement between t= 0
and t = 1 second?

Answers

Answer 1

Using it's formula, it is found that the displacement between t= 0  and t = 1 second is of 0 m.

The equation of motion is given by:

[tex]x(t) = 4\sin{\left(\pi t + \frac{\pi}{6}\right)}[/tex]

The displacement between t= 0  and t = 1 second is given by:

[tex]d = x(1) - x(0)[/tex]

Hence:

[tex]x(1) = 4\sin{\left(\pi + \frac{\pi}{6}\right)} = 4\sin{\left(\frac{7\pi}{6}\right)} = -\frac{4}{2} = -2[/tex]

[tex]x(0) = 4\sin{\left(\frac{\pi}{6}\right)} = \frac{4}{2} = 2[/tex]

Then:

[tex]d = x(1) - x(0) = -2 + 2 = 0[/tex]

The displacement is of 0 m.

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Related Questions

Please help I am stuck on this

Answers

Answer: B. y = 1/2x - 1

Explanation:
I know someone else already answered, but I wanted to explain why the answer is B.

Consider an equation of a line in slope-intercept form: y = mx + b

Since the line intersects the y-axis at -1, that’s the y intercept, or b. We know the slope of the line is positive because it slopes upward from left to right. From each whole number solution point, the line goes up one and two to the right. Slope, represented by m, is “rise” over “run”, or the change in y over the change in x. This makes the slope 1/2.

I hope this helps.

You want to order posters to advertise your band. A company charges $109.95 for the first 100 posters and $65 for each additional 100 posters. Write an equation that represents the total cost y (in dollars) as a function of the number (in hundreds) of posters ordered, x. Find the total cost of 1000 posters.

Answers

The equation that represents the total cost as a function of the number (in hundreds) of posters ordered, x is f(y) = 109.95 + 65x

let

y = total cost

x = numbers in hundreds

cost of first hundred = $109.95

Cost of additional hundred = $65

f(y) = 109.95 + 65x

The total cost of 1000 posters

1000 - first hundred = 900

additional hundreds = 900/100

= 9

So,

f(y) = 109.95 + 65x

= 109.95 + 65(9)

= 109.95 + 585

= 694.95

f(y) = $694.95

Therefore, the total cost of 1000 posters is f(y) = $694.95

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The y-intercept of a line has the same value as its gradient. If this line cuts the curve y = [tex]x^{3}[/tex] – 2[tex]x^{2}[/tex] – 3x – 8 at x = 3, find the equation of the line.



Select one:


a. 2x − y + 2 = 0


b. 2x + y + 2 = 0


c. 2x + y − 2 = 0


d. None of these

Answers

Answer:

B. 2x+y+2+=0

Step-by-step explanation:

Given: x=3

First: you substitute for x in y=x^3-2x^2-3x-8

y=(3)^3-2(3)^2-3(3)-8

y=-8

Now all you have to do is plug y in each of the answers until you get 3 for x.

A. 2x-(-8)+2=0

   2x+10=0

   2x=-10

   x=-5

B. 2x+(-8)+2=0

   2x-6=0

   2x=6

   x=3

C. 2x+(-8)-2=0

   2x-10=0

   2x=10

   x=5

in the equation 3/4y+1/2=31/4 the fractional cofficient

Answers

Answer:

The coefficient is 32.

Step-by-step explanation:

I hope I have helped you if not tell me.

A water tank is being filled by two inlet pipes. Pipe A can fill the tank in 4 hours, while both pipes
together can fill the tank in 2 hours. How long does it take to fill the tank using only Pipe B?

Answers

2 Hours

this is because one pipe takes 4 hours, and if both pipes take 2 hours, that is cutting the time in half, meaning both pipes pour the same amount and take the same time.

hope this is helpful!

Ayo runs a fairground game.In each turn, a player rolls a fair dice numbered 1 - 6 and spins a fair spinner numbered 1 - 12.It costs a player £1.40 for a turn.A player can win £6 or £3 as in the diagrams:If 216 people are to play, how much profit can Ayo expect to make?

Answers

Using the definition of expected value, it is found that Ayo can be expected to make a profit of £55.8.

The expected value is given by the sum of each outcome multiplied by it's respective probability.

In this problem:

The player wins $6, that is, Ayo loses £6, if he rolls a 6 and spins a 1, hence the probability is [tex]\frac{1}{6} \times \frac{1}{12} = \frac{1}{72}[/tex].The player wins $3, that is, Ayo loses £3, if he rolls a 3 on at least one of the spinner or the dice, hence, considering three cases(both and either the spinner of the dice), the probability is [tex]\frac{1}{6} \times \frac{1}{12} + \frac{1}{6} \times \frac{11}{12} + \frac{5}{6} \times \frac{1}{12} = \frac{1 + 11 + 5}{72} = \frac{17}{72}[/tex]In the other cases, Ayo wins £1.40, with [tex]1 - \frac{18}{72} = \frac{54}{72}[/tex] probability.

Hence, his expected profit for a single game is:

[tex]E(X) = -6\frac{1}{72} - 3\frac{17}{72} + 1.4\frac{54}{72} = \frac{-6 - 3(17) + 54(1.4)}{72} = 0.2583[/tex]

For 216 games, the expected value is:

[tex]E = 216(0.2583) = 55.8[/tex]

Ayo can be expected to make a profit of £55.8.

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Marlee had a certain amount of money (x) in her bank
account. She deposited $60.00 from her grandmother
for her birthday. She then spent of the money in her account on rent that totaled $550. Which equation represents this situation?

Answers

Answer:

x-490=t

Step-by-step explanation:

Marlee has x money

She deposited $60 meaning adding $60 to the bank

So x+60

THen Marlee need to withdraw $550 from her bank to rent

So the equation is now

x+60-550

60-550 is -490

Thus:

x-490

(I will represent (t) as the money she has left for the equation)

Thus the equation is

x-490=t

Hope this helps!

What is the maximum point OR minimun point of this equation?

y = 1.8 ( x + 2.4 ) 2 + 2.4

Thanks for ur help!!!!!!!!

Answers

Answer is 3 because when you solve its 3 or less

what is the answer, A, B, D, or E? Please Let me know????

Answers

Answer:

B and D

Step-by-step explanation:

B -> -1.4z multipled by 40 is - 56z, 0.7 multipled by 40 is 28, thus giving us - 56z + 28.

D -> When we expand (8z - 4)(-7) we will get -56z + 28 as 8z multipled by - 7 is - 56z (remember positive times negative equals negative) and - 4 multipled by - 7 is 28 (negative times negative equals positive)

What is the solution to -2(8x – 4) < 2x + 5?
o xs
oxca
O x>6
O x<6

Answers

[tex]-2(8x-4)<2x+5\\\\\implies -16x+8<2x+5\\\\\implies -16x+8-5<2x\\\\\implies 3<2x+16x\\\\\implies 3<18x\\\\\implies \dfrac3{18} <x\\\\\implies \dfrac 16 <x\\\\\implies x> \dfrac 16[/tex]

If f (x)= 3x - 5 and g(x) = x^2, find (f•g)(3).

Answers

Answer:

do it got a picture

on the edge2020

Step-by-step explanation:

Find the value of x, y, and z.

Answers

x is 90 degrees
i don’t know what the rest are

on a beautiful autumn-like day, Kamar went for a run. He ran 6 miles away from his house. Later, he began to run back towards home, a distance of 3 miles. After taking a rest, he continued to run the last 3 miles to his house.
a) How far did he run in total? ____________

b) How far from home did he end up, at the end of the day? _____________

c) When he took a rest, how far was he from home? _________

d) When he took a rest, how far had he run? __________

Answers

Answer:

A) 12 miles

B) 0 miles

C) 3 miles

D) 9 miles

Step-by-step explanation:

I tried my best.. hope it helps!

What is the answer to 2(2x-5)

Answers

Answer: The answer is 4x - 10.

Explanation: The explanation is in the image. The explanation is showing using the distributive property to multiply 2 by 2x - 5.

Answer:

4x-5

Step-by-step explanation:

An alloy is made with 3 gram of silver, 18 gram of copper, 6 gram of aluminium and 3 gram od zinc. Find what part of the total is used for each metal.​

Answers

Add each metal together:
3+18+6+3 = 30

Now put divide each metal by 30 and multiply by 100 to get what percentage is each metal is of the alloy:

Silver- 3/30 x 100 = 10%
Copper- 18/30 x 100 = 60%
Aluminium- 6/30 x 100 = 20%
Zinc- 3/30 x 100 = 10%

(Ensure they all total 100% - which they do)

will give brainliest

Answers

Answer: x > − 4

Step-by-step explanation: Divide each term in − 4 x < 16 by − 4 and simplify.

(Try to solve b. and c. with only these resources and if you still need help, let me know.)

4. Para el siguiente triángulo rectángulo, encuentra la medida del lado desconocido.

Answers

Usa b^2 - c^2 = -a^2, (5)^2 - (13)^2 = b^2, 25 - 169 = -b^2, -144 = -b^2, b=12

pls help me pls help me pls help me

Answers

Answer:

d. 210

Step-by-step explanation:

well for the first textbook you have 7 options

for the 2nd placeholder you have 6 options

and the 3rd you have 5

so its 7x6x5 which is 210 different combinations

thx for 50 points :D

Dan works in the sales department for sporting goods company. Dan gets a 15% commission on every bike he sells. If Dan sold 227 bikes at $70 each, how much money did Dan make?

Answers

Y = 70x • .15
y is his total money earned.
x is how many units he sells
so if he sells 227 bikes it’s 70 • 227 which is 15,890 then times it by .15 because he makes 15% and it’s 2.383.5. so he made $2,383 50¢!

what is -4(2x - 3) equal

Answers

Answer:

-8x + 12

Step-by-step explanation:

-4(2x - 3)

then -4*2x and -4*-3(an even number of negative signs multiplied equals to a positive sign)

therefore= -8x + 12

Complete the shape below so that AB is a line of symmetry

Answers

Here you go I hope it helps, image attached

i don't understand help me please math!!

Answers

Answer:

A. 315 degree

B. 6480 degree

C. 63^ over 2

D. 7^ over 4

E. 945 degree

hope it help:)


Based on the graph below, f(x) and g(x) where g(x) =f(x)+h are shown

Answers

Answer:

The value of h is 5

Step-by-step explanation:

Remember the if two lines are parallel and one is taller than the other and is asking for what that is the difference it is the y-intercept or what you call in this problem "h" since h is 5 digits above the answer is 5

find three consectutive integers such that the sum of the second and third is -17

Answers

Answer:

-7, -8, -9

Step-by-step explanation:

-8 + -9 is -17

A map of a nature park has a scale of 2 inches to 1.5 miles. There are two trails that are 8 inches apart on the map. What is the actual distance between the two trails?

Answers

Answer:

6 miles

Step-by-step explanation:

2 inches : 1.5 miles

8 inches : 4(2 inches)

8 inches : 4(1.5 miles)

8 inches : 6 miles

6 miles away

-Chetan K

The actual distance between the two trails is 6 miles.

Given the scale of the map is 2 inches to 1.5 miles, we can set up a proportion to find the actual distance between the two trails.

Let x represent the actual distance between the trails in miles. The proportion would be:

(2 inches / 1.5 miles) = (8 inches / x miles)

Now, solving for x:

2/1.5 = 8/x

Cross-multiplying:

2x = 1.5 × 8

2x = 12

Divide by 2:

x = 6

So, the actual distance between the two trails is 6 miles.

Learn more about proportion here:

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Find the area of this semi-circle with diameter,
d
= 60cm.
Give your answer rounded to 2 DP.

Answers

Answer:

3.14*15^2=706.5

706.5/2=353.25

Hope This Helps!!!

The area of the semi-circle with a diameter of 60 cm is approximately 1413 square centimeters.

What is the area of the semi-circle?

A semicircle is formed by simply dividing a circle into exactly two halves.

Hence, the area of a semi-circle is half the area of a circle.

Area of semi-circle = 1/2 × πr²

Given the parameters:

Diameter d = 60 cm

Radius r = diameter/2 = 60/2 = 30 cm

Area =?

To determine the area of the semi-circle, plug the value of the radius into the above formula and simplify:

Area of semi-circle = 1/2 × πr²

Area of semi-circle = 1/2 × 3.14 × 30²

Area of semi-circle = 1/2 × 3.14 × 900

Area of semi-circle = 3.14 × 450

Area of semi-circle = 1413 cm²

The area is approximately 1413 square centimeters.

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22.68 ÷ 14.65 ayuden pliss

Answers

Answer:

1.54

Step-by-step explanation:

5/12 of the pupils in yr9 say their favourite colour is red. There are 180 pupils in yr9. How many students said red is their favourite colour?

Answers

Answer:

75 students

Step-by-step explanation:

180*5/12=75

Solve for .
- 9x + 5 < 17
OR
13r + 25 < -1

Answers

For -9x + 5 it’s
x > −4/3
OR
For 13r + 25 <-1 it’s
R<-2

The angle measures of an isosceles triangle are shown. Find the value of w.

Answers

Answer:

w= 7

Step-by-step explanation:

8w + 9w - 1 + 62 = 180

17w + 61 = 180

17w = 119

w = 7

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