A block is set in motion hanging from a spring and oscillates about its resting position
x = 0
according to the function
x = 0.6sin(2t)+0.4cos(2t),
where x is in centimeters and t is in seconds. For what values of t in the interval [0,3] is the block at its resting position
x =0?

Answers

Answer 1

Answer:

t = 1.277 sec and t = 2.848 sec

Step-by-step explanation:

This problem is much more easily done by graphing it than by computing it using algebra.

The values of t we're looking for are the ones that make x = 0, so we want the solutions of [tex]0.6sin(2t)+0.4cos(2t)=0[/tex] on the interval [0, 3].

According to the graph, this is true when t = 1.277 seconds and t = 2.848 seconds.

A Block Is Set In Motion Hanging From A Spring And Oscillates About Its Resting Positionx = 0according
Answer 2

Answer:

t = 1.28, 2.85

Step-by-step explanation:

x = 0.6sin(2t)+0.4cos(2t)

x = 0, so

0.6sin(2t)+0.4cos(2t) = 0

0.6sin(2t) = -0.4cos(2t)

Convert into tan(2t) by dividing both sides by 0.6cos(2t):

tan(2t) = -0.4/0.6

tan(2t) =-2/3

Since t lies in [0,3] ,

2t lies in [0,6]

tan(2t) =-2/3

Basic angle:

0.5880026035

Tan is negative is second and fourth quadrants

2t = 2.553590005, 5.695182704

t = 1.276795025, 2.847591352


Related Questions

Find the median for the frequency table above

Answers

Answer:3

Step-by-step explanation:

the median is always the middle number

hope this helps.

The answer is 3

You get this answer by lining the numbers up from smallest to largest, then crossing off one from each side until you reach the middle and that is your median.

Round 18.4049629645 to 4 decimal places

Answers

18.4050
Find the fourth decimal place and look at the number before it. If the number is less than 5 it stays the same, if it is greater than 5 go up one

The coned shaped room has a height of 15 ft and a radius of 72. Find the volume

Answers

Answer:

81430.08

Step-by-step explanation:

Final answer:

The volume of a cone with a height of 15 ft and a radius of 72 ft is found using the formula V = (1/3)πr²h, and the calculated volume is approximately 81457.9 cubic feet.

Explanation:

The question is asking to find the volume of a cone, which has a height of 15 ft and a radius of 72 ft. The formula to calculate the volume of a cone is V = (1/3)πr²h, where 'V' represents the volume, 'r' is the radius of the base, and 'h' is the height of the cone.

To solve for the volume:
V = (1/3)π(72 ft)²(15 ft)
V = (1/3)π(5184 ft²)(15 ft)
V = (1/3)π(77760 ft³)
V = 25920π ft³
Therefore, the volume of the cone is approximately 25920π cubic feet, or when π is approximated as 3.14159, the volume is about 81457.9 cubic feet.

Determine the vertex of the function f(x) =
-4(x-3)^2+ 6.
(6,-3)
(6,3)
(3,6)
O (-3, 6)

Answers

Answer:

C

Step-by-step explanation:

A fair 6 numbered die is rolled. What is the probability that the number rolled is greater that 3

Answers

Answer:

½

Step-by-step explanation:

Greater than 3: 4,5,6

3/6 = 1/2

Answer:

1/2

Step-by-step explanation:

there is 6 numbers and 3 numbers greater than 3. so put that in fraction form 3/6 then simplify to 1/2

What is the ratio of the volume of Sphere A to the volume of Sphere B

Answers

Answer:1

Step-by-step explanation:

To find the ratio of the volume of sphere A to B

We get

A:B

V=4/3πr^3:4/3πr^3

4/3πr^3×3/4πr^3

Ratio of A to B

=1

Answer: 27

Step-by-step explanation:

What should you do to get the two terms with variables on the left side of the equation?

Answers

Answer:

Either divide or multiply

Answer: you would subtract 3/4 from both sides of the equation

Step-by-step explanation:

Find the surface area of the rectangular prism with l=15m, w=16m and h=4. im confused pls help me

Answers

Answer:

surface area= 728

please give me brainliest!! :)

Step-by-step explanation:

A = 2 ( w*l + h*l + h*w )

2 · ( 16 · 15 + 4 · 15 + 4 · 16 ) = 728

The answer is 728 squared meters

Does it seem fair to you that a hit could be a home run at one stadium but not at others?Explain.

Answers

Answer:

No. If standards differ at different sports stadiums, that makes the game unfair for one team or the other. A win at one stadium could be a loss at another. To make the game fair, all facilities should be equal.

Step-by-step explanation:

Final answer:

The unique dimensions and characteristics of each baseball stadium, known as park factors, can impact whether a hit becomes a home run. Although it might seem unfair, it's the same for all teams and is part of the game's complexity. Not only the player's skill but also their knowledge of the park's attributes can influence the outcome of the game.

Explanation:

The different sizes and features of baseball stadiums, known as park factors, can impact game dynamics, including whether a hit results in a home run. This is part of the sport's complexity and challenge, as players must adapt their strategies for different venues. It might seem unfair, but it's the same for all teams as they each host and visit various stadiums throughout the season.

In some parks, for example, the distance from home plate to the outfield wall is less, which could make it easier for a hit to become a home run. In contrast, larger parks or those at higher altitudes, where the air is thinner and ball travels further, might be tougher to score a home run.

All these make baseball a fascinating sport, where not only the player's skill but also nuanced aspects like knowledge of the park play an essential role in the outcome of the game. Thus, by definition, a home run is still a successful hit, but where that hit ends up can depend on numerous variables, including the park's attributes.

Learn more about Baseball Stadiums here:

https://brainly.com/question/23524538

#SPJ12

A circle is shown. Secants R S and R T intersect at point R outside of the circle. Secant R S intersects the circle at point U. Secant R T intersects the circle at point V. The length of R U is 6, the length of U S is 10, and the length of R V is 8.
If secant segments SR and TR intersect at point R, find the length of VT.

Start by relating the secants and segments theorem to this diagram:

(RS)() = ()(RV)

Substitute values from the diagram into the equation:

(16)() = ()(8)

Solve for VT:

VT =

Answers

Answer:

Everything in -> [x]

(RS) [(RU)] = [(RT)] (RV)

(16) [(6)] = [(8+VT)] (8)

VT = [4]

Step-by-step explanation:

I just did the assignment, you're welcome.

Answer:

(RS) [(RU)] = [(RT)] (RV)

(16) [(6)] = [(8+VT)] (8)

VT = [4]

Step-by-step explanation:

Here mi amor

jk

Lol

Can you solve for x please.

Answers

Answer:

3/4

Step-by-step explanation:

Multiply both sides by x

2x/3 = 1/2

Multiply both sides by 3

2x = 3/2

Divide both sides by 2

x = 3/4

The dot plot shows the number of raffle tickets bought by each person.

Number of Raffle Tickets Bought
A dot plot going from 0 to 5. 0 has 4 dots, 1 has 0 dots, 2 has 4 dots, 3 has 6 dots, 4 has 3 dots, 5 has 5 dots.

Where is the peak of the dot plot?
A. 1
B. 3
C. 5
D. 6

Answers

the answer is B since 3 has the most dots

The peak of the dot plot with the given data set is: B. 3

What is a Dot Plot?A dot plot is a graphical tool used to represent data set that do not have ranges.Each dot represents a data point.The peak of a dot plot is where you have the more frequency of a data point.

Therefore, the peak of the dot plot with the given data set is: B. 3

Learn more about dot plots on:

https://brainly.com/question/25957672

find missing angle..x=??

Answers

a straight line = 180° so 180-33= 147° so that’s the missing angle.

Answer:

X=147°

Step-by-step explanation:

Angle on a straight line is 180

And x,33 is given on a straight line

It will be solved as

X+33=180

Substrate 33 from both sides

X=147°

Therefore x=147°

Casandra finds a treasure chest packed with metallic coins.The chest has a volume of 0.25 m3. The coins have a combined mass of 4825 kg. Hoping to find gold, she calculates the density to determine the metal of the coins. What kind of the coins made of

Answers

Missing information

Options

What kind of metal are the coins made of?

Bronze (8700 kg per cubic meter)

Silver (10500 kg per cubic meter)

Lead (11300 kg per cubic meter)

Gold (19300 kg per cubic meter)

Answer:

Gold

Step-by-step explanation:

Density is mass per unit volume of an object hence calculated as

d=m/v

Where m is the mass of an object, v is the volume and d is rhe density.

Substituting 4825 Kg for m and 0.25 m3 for v then

D=4825/0.25=19300 kg/m3

From the options given, this density is equivalent to that of gold.

Can you answer part B? I will mark you as brainliest

Answers

Answer:

The fraction is 2/10

Step-by-step explanation:

Barney is an ecologist who studies the change in the tiger population of Siberia over time.
The relationship between the elapsed time t, in decades, since Barney started studying the population, and the
number of tigers, N(t), is modeled by the following function:
N() = 710 (35)
Complete the following sentence about the rate of change in the tiger population. Round your answer to two
decimal places.
The tiger population loses
3/5
of its size every____ decades

Answers

Final answer:

The tiger population loses approximately 3/5 of its size every 97.14 decades.

Explanation:

The rate of change in the tiger population can be determined by examining the equation N(t) = 710(35). The coefficient of 35 represents the exponential growth factor of the population, which can be interpreted as the population multiplying by 35 over each time period.

To determine the rate of change in terms of the percentage size lost, we can calculate the fractional change by subtracting 1 from the growth factor. In this case, 35 minus 1 equals 34. The percentage size lost can then be calculated by dividing the fractional change by the growth factor and multiplying by 100, giving us (34/35) x 100 = 97.14%.

Therefore, the tiger population loses approximately 3/5 of its size every 97.14 decades.

what does 2(5*-3) =

Answers

Answer:

[tex]-30[/tex]

Step-by-step explanation:

Step 1:  Multiply inside the parenthesis

[tex]2(5 * -3)[/tex]

[tex]2(-15)[/tex]

Step 2:  Multiply

[tex]2(-15)[/tex]

[tex]2 * -15[/tex]

[tex]-30[/tex]

Answer:  [tex]-30[/tex]

NUMBER 10 PLS SOLVE

Answers

Answer:

D

Step-by-step explanation:

Answer:

Option C: Multiply 15 ft by 12 in/1 ft and 2.54 cm/1 in

Step-by-step explanation:

to convert feet to centimeter, we first convert to inches and from iches to centimeter

1 feet = 12 inches and 1 inches = 2.54 cm

∴ 15 feet = 180 inches and 180 inches = 457.2

This means to convert from feet to centimeter

Multiply 15 ft by 12 in/1 ft and 2.54 cm/1 in

Use the number line to show 2\3 divided by 1\12.

What is the quotient?

Answers

Step-by-step explanation:

[tex] \frac{2}{3} \div \frac{1}{12} \\ \\ = \frac{2}{3} \times \frac{12}{1} \\ \\ = \frac{2}{1} \times \frac{4}{1} \\ \\ = 8[/tex]

The quotient of the division is 8. It is shown on a number line.

What is a number line?

A number line is a representation of real numbers in the form of a graded straight line.

The given expression is 2/3 ÷ 1/12.

Simplify the expression as follows:

2/3 ÷ 1/12

=2/3 × 12

= 2 ×4

= 8

Hence, the quotient of the division is 8. It is shown on a number line.

To learn more about the number lines, click here:

https://brainly.com/question/13189025

#SPJ5

Option 2: Senator Kennedy's Initiative proposed extending the school day by 30%-a radical increase. If each 6-hour
school day were extended according to Senator Kennedy's plan, each day would be how many hours?

Answers

Answer: ok

Step-by-step explanation:

Factor completely. 1+12x+36x^2 what is the answer

Answers

Step-by-step explanation:

Factor using the perfect square rule.

( 1 + 6 x ) 2

Answer:

(1+6x)^2

Step-by-step explanation:


Select all the families that -3.7 belongs to.


Natural
Whole
Integer

Rational
Irrational

Answers

Irrational, It is irrational because it cannot be written as a ratio (or fraction), ... So we can tell if it is Rational or Irrational by trying to write the number as a simple fraction.

what is missing blank

Answers

Answer:

-1

Step-by-step explanation:

the y s are decreasing by 3 while the x s are increasing by 2.

brainliest?

Answer:

-1

Step-by-step explanation:

if you look at the pattern, the x's pattern is minus 2, and the y's pattern is minus 3. to find the answer you just continue the pattern.

Hope this helps!

What is the mode of the following set of numbers? 15, 20, 18, 20, 15, 20 A 20 B 18 C 5 D 19 .

Answers

Answer:

A

Step-by-step explanation:

Mode is the one that appears the most. The number that is there the most is 20 that makes it the mode.

The correct answer is A. 20.

To find the mode of a set of numbers, one must identify the number that appears most frequently in the list. In the given set of numbers: 15, 20, 18, 20, 15, 20, we can see that the number 20 appears three times, which is more frequent than any other number in the set. The number 15 appears twice, while the numbers 18 and 20 each appear once. Since 20 is the number with the highest frequency, it is the mode of the set.

Therefore, the mode of the given set of numbers is 20.

a rectangles perimeter and area have the same numerical value. the width of the rectangle is 3 units . what is the length of the rectangle in units?

Answers

Answer:

6

Step-by-step explanation:

Answer:

The length is 6

Step-by-step explanation:

P= L+ L + W+ W

P = L + L + 3 x 3

P = L + L + 6

We check A and enter below.

P  = 12-6 + 18-6  = 18

A = L x W = 18

A = L x 3 = 18

A = 6 x 3 =18

A box shaped like a right rectangular prism

measures 5 centimeters by 3 centimeters by

2 centimeters. What is the length of the interior

diagonal of the prism to the nearest hundredth?

Answers

Answer:

[tex]\sqrt{38}[/tex]

Step-by-step explanation:

Given that:

The 3 demensions of the right rectangular prism measures 5 centimeters by 3 centimeters by  2 centimeters.

Because we do not know which one is the height, the length and the width of the box, so we assume them (it does not affect the length of the interior

diagonal )

the height : 5 centimetersthe length :  3 centimeters the width : 2 centimeters

To find the length of the interior  diagonal of the prism, we use the following formula:

d = [tex]\sqrt{l^{2} +w^{2} +h^{2} }[/tex] = [tex]\sqrt{5^{2} +3^{2} + 2^{2} } = \sqrt{38}[/tex]  

Hope it will find you well.

Answer

38 or about 6.16

Marty and Juan took turns driving a cargo truck. The ratio of the miles Marty drove to the miles Juan drove is 6 to 7. Juan drove 150 more miles than Marty. How many miles did Marty and Juan drive in all?

Answers

The total miles are 1950 miles. Marty drove 900 miles and Juan drove 1050 miles, if the ratio of the miles Marty drove to the miles Juan drove is 6 to 7 and Juan drove 150 more miles than Marty.

Step-by-step explanation:

The given is,

                    Ratio of the miles Marty drove to the miles Juan drove is 6 to 7

                    Juan drove 150 more miles than Marty

Step:1

         Calculate the difference in the ratio of the miles Marty drove to the miles Juan drove,

                                         X = 7-6 = 1

         Calculate the difference in the miles of Marty drove to the miles of Juan drove,

                                         X = 150     ( Juan drove 150 more miles than Marty)

          Equate the Difference between ratio and miles,

          From the above values,

                                        X = 150 miles

Step:2

         From the ratio of Marty : Juan = 6 : 7

         Distance drove by Marty,

                                             = 6X = ( 6 × 150 ) = 900

                               Distance drove by Marty = 900 miles

          Distance drove by Juan,

                                             = 7X = ( 7 × 150 ) = 1050

                                Distance drove by Juan = 1050 miles

Step:3

           Check for solution,

           Difference in the miles of Marty drove to the miles of Juan drove              

                                            150 = 1050 - 900

                                            150 = 150

Result:

           The total miles are is 1950 miles. Marty drove 900 miles and Juan drove 1050 miles, if the ratio of the miles Marty drove to the miles Juan drove is 6 to 7. Juan drove 150 more miles than Marty

                 

               

Ava has a bag with 3 red, 2 blue, and 11 green beads.
She selects a bead at random. What is the probability that Ava does not select a green bead?

Answers

Answer:

5/16 or 31.25%

Step-by-step explanation:

There are 16 beads altogether 11 are green and the rest aren't so there for is 5 out of 16 chance green won't be selected

Answer:

5/16

Step-by-step explanation:

2.457 x 10^5 in standard form.

Answers

Answer:

245700

Step-by-step explanation:

2.457×10^5

Which means that the decimal point will be moved to the right side 5 times

Which means that

2.457×10^5

=245700

Or

It can also be written as 2.457×100000

It will give

245700

Answer:

245700

Step-by-step explanation:

2.457 × 10⁵

2.457 × 100000

245700

can 60/5 be simplified

Answers

To simplify the fraction, we can divide.

60 / 5 = 12

Best of Luck!

Answer: yes

Step-by-step explanation: 60 divided by 5 is 7

Other Questions
TheThe point (2,6) is on the line given by which equation below? Imagine you are studying a population of finches on one of the Galpagos Islands. You have been recording many of the birds' physical traits, including the length of both wings. You observe that for 80% of individuals measured, the length of the left wing is not significantly different from the length of the right wing (in other words, they are symmetrical). But for about 20% of birds measured, the wing lengths are asymmetrical. This distribution is true from generation to generation. Suddenly, a rare 5-day windstorm takes over the island. After the storm, you spend the next several days netting each bird on the island that survived the storm. You discover that 85% of the birds with symmetrical wings survived the storm, whereas only 5% of the birds with asymmetrical wings did. Propose a hypothesis to explain this observation. 1 Which of the following is not a household use of water?A. laundryB. drip irrigationC. bathingD. watering the lawn Match each type of asexual reproduction with its description.BuddingA new organism grows from the body of theparentFragmentationThe parent cell divides to produce agenetically identical cellBinary fissionThe parent breaks into parts that mayregenerate into offspring What achievement of Caesar Augustus does this statement reference? According to the bar chart, what is the median of number of times a teenager reminded to do chores a week?A) 1 B) 2 C) 3 D) 3.1 If cos 0 = 0.3846 where 3pi/2 is less than 0 is less than 2pi, what is the approximate value of sin 0? Why are some scientists concerned about an increase in the amount of carbon dioxide in the atmosphere Firms classified as being part of the sharing economy and collaborative consumption are still considered too risky to attract substantial venture capital investment. True or False What is the median of the data set?87, 98, 106, 82, 111, 120 A researcher studying public opinion of proposed Social Security changes obtains a simple random sample of 35 adult Americans and asks them whether or not they support the proposed changes. To say that the distribution of the sample proportion of adults who respond yes, is approximately normal, how many more adult Americans does the researcher need to sample in the following cases? why didn't bob drink a glass of water with 8 pieces of ice Huan deposited $850 into a college savings account earning 4.8% interest compounded annually. He also deposited $850 into a second account earning 4.8% simple interest. He made no additional deposits. How much interest does the first account earn in 10 years? The number of chocolate chips in an 18-ounce bag of chocolate chip cookies is approximately normally distributed with mean 12521252 and standard deviation 129129 chips. (a) what is the probability that a randomly selected bag contains between 11001100 and 14001400 chocolate chips? (b) what is the probability that a randomly selected bag contains fewer than 10001000 chocolate chips? (c) what proportion of bags contains more than 12001200 chocolate chips? (d) what is the percentile rank of a bag that contains 10501050 chocolate chips? solve for y 6=2(y+2) Which is the principal value of arctan (3.7)?PLEASE HELPP CANT GET IT WRONG I just need help asap Combining Like Terms to Solve Equationsq/3+7=12show how you got the answer Which scientist and atomic model are correctly matched? Six pounds of grapefruit costs $3.00 5 pounds of apple costs $2.65.What is the cost per pound for each fruit.