A hollow steel ball weighing 4 pounds is suspended from a spring. This stretches the spring feet. The ball is started in motion from the equilibrium position with a downward velocity of feet per second. The air resistance (in pounds) of the moving ball numerically equals 4 times its velocity (in feet per second). Suppose that after t seconds the ball is y feet below its rest position. Find y in terms of t.
Answers
Answer:
The solution when after t seconds the ball is y feet below its rest position is y (t) =3 et ^⁻16
Step-by-step explanation:
Solution
Given that:
The hollow steel ball weight (W) = 4 pounds
We take acceleration, g. = 32 ft/sec
The mass m = W/g = 4/32
=1/8 slug
The damping constant β = 4
The starting displacement , y (0) = 0
The initial velocity y' (0) = 3
The ball stretches the spring = 1/8 feet
Now
From Hooke's Law, F =ks
here,
k = constant spring
so,
4 =k (1/8)
k= 32
Now from Newton's law,
my'' = -ky -βy'
= (1/8) y'' = -32y - 4y'
y'' = -256 y - 32 y'
y'' + 32y' + 256 = 0 this is the equation (1)
Thus,
we solve for DE (1)
The equation (auxiliary) is m² + 32m + 256 = 0
so,
m² + 16m + 16 m _ 256 =0
m (m + 16 ) + 16 (m +16) = 0
(m +16) (m + 16 ) = 0
m₁ = - 16,
m₂ = - 16
In this case, the root is known as repeated roots
Now,
The solution is y (t) = c₁e^⁻16 t + c₂ te^⁻16 t
Now, we make use of the initial condition y (0) =0
y(0) = c₁e^⁻16 (0) + c₂ (0)e^⁻16(0)
0 = c₁ e^0 + 0
c₁ = 0
Again, we apply the initial condition y' (0) = 3
y' (t)c₁e^⁻16 t (-16( + c₂ (te^⁻16 t (-16) + e^-16)
y' (t)= - 16c₁e^⁻16 t + c₂ ( -16te^ ⁻16 + e^-16)
y' (0) =- 16c₁e^⁻16 (0) + c₂ ( -16(0)e^ ⁻16 (0) + e^-16 (0))
3 = 16c₁ + c₂ (1)
So,
3 = -16(0) + c₂ (1)
c₂ = 3
Therefore, the required solution is y(t) = (0) e^⁻16 + 3 et ^⁻16
y (t) =3 et ^⁻16
Related Questions
The perimeter of a rectangle is 56mm. Three of the sides have a length of 15mm, 13mm, and 15mm. What is the side length?
Answers
Takeru has 4 bird feeders. It takes 4/3 bags of bird seeds to fill each feeder. what is the minimum number of bags Takeru needs to fill all the feeders?
Answers
Answer: 6
Step-by-step explanation: You would divide 4 by 3 and divide your answer by 2.
Last Wednesday, two friends met up after school to read the book they were both assigned in Literature class. Kylie can read 1 page per minute, and she had already read 81 pages. Adam, who has a reading speed of 2 pages per minute, had read 37 pages. Eventually they had read the same number of pages. How long did that take? How many pages had each of them read?
Answers
Answer:
45 minutes
Step-by-step explanation:
They both have 127 pages after 45 minutes.
If 3(x − 2) = −7, then x =?
Answers
Answer:
-5 2/3
Step-by-step explanation:
is 3(x-2) = -7 then it's same as 3x-6=-7
We simplify this by adding 6 and subtracting 6.
Our result is
3x=-17
-17/3=-5 2/3
If 3 gallons of paint are needed for 75 ft of fence, how many gallons are needed for 1200 ft of fence?
Answers
Answer:
48 gallons of paint are needed.
Step-by-step explanation:
Set up a proportion.
Like this: x is for the unknown number of gallons.
\(\frac{3}{75} = \frac{x}{1200}\\ 75(x)= 3(1200)\\ 75x=3600\\x= 3600/75\\x= 48 Answer\)
75/3= 25
1,200/25= 48
Hope this helps
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What is the range of the function on the graph?
all the real numbers
O all the real numbers greater than or equal to 0
all the real numbers greater than or equal to 2
all the real numbers greater than or equal to -3
Answers
The range of the function on the graph is C. all the real numbers greater than or equal to –3 .
How to get the range?We can see by the graph maximum value of y of function is -3 and the graph continues to extend upward .
So, the range contain all the real numbers greater than or equal to –3 .
Therefore, the range contain all the real numbers greater than or equal to –3 .
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![1--5-4-3-2-11H5432Mark this and return-2+-3+AWN-4-5][C1 2 3 4 5 x]What is the range of the function on](https://i5t5.c14.e2-1.dev/h-images-qa/answers/attachments/Pvvk0ur2vkcYvR9Cj1BaBGmjR2vIazHt.jpeg)
Evaluate the expression 29-3(9-4)
Answers
Answer:
14
Step-by-step explanation:
PEMDAS - First Do Parentheses
29-3(5)
Then Do Multiplication
29-15
Then Finish with Subtraction
14
The value of the expression is 14.
We have,
Expression:
29 - 3 ( 9 - 4)
Remove the parenthesis.
29 - 3 x 9 + 3 x 4
29 - 27 + 12
Subtract and add the values.
14
Thus,
The value of the expression is 14.
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Simplify:
4(5y+9)
56y
9y + 13
20y + 36
I don't know.
Answers
Answer:
20y + 36
Step-by-step explanation:
Distribute the 4 to everything in the parenthesis (multiply).
4 x 5y = 20y
4 x 9 = 36
The solution of the expression 4(5y + 9 ) will be 20y + 36. The correct option is C.
What is an expression?Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.
The expression 4(5y+9) will be solved as below:-
E = 4 ( 5y+9 )
E = 20 y + 36
Therefore, the solution of the expression 4(5y + 9 ) will be 20y + 36. The correct option is C.
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The Department of Energy website contains data on 1209 model year 2016 cars and SUVs. Included in the data are the engine size, as measured by engine displacement in liters, and combined city and highway gas mileage, in miles per gallon. Examining the data, one finds that cars with bigger engines tend to have lower gas mileages. In a scatterplot of the engine size and the gas mileage, you expect to see:________
a. very little association.
b. a negative association.
c. a positive association for small engine sizes, and a negative association for large engine sizes.
d. a positive association.
Answers
Answer: B. A negative association.
Step-by-step explanation: The form of relationship which may exist between linear variables could either be positive, negative or no relationship. A positive relationship or association exists when an increase or decrease in the independent variable leads to a corresponding increase or decrease in the dependent variable. While no association exists in a scenario whereby there is no change in the dependent variable by varying values in our independent variable. However, in the scenario above, since bigger engines tends to result in a lower gas mileage, this shows that our scatter plot will likely depict a negative association whereby the gas mileage in cars by larger engines are lower while cars with smaller engines exhibit higher gas mileage.
coach Emanuel is trying to lose weight. the stars 2017 weighing 296 pounds. if he plans to burn enough calories to lose 3 pounds per week, then how many weeks will pass before Couch Emanuel is at most 251 pounds
Thank you to whoever answers this :)
Answers
Answer:
13 weeks because he loses 3 pounds per week
Step-by-step explanation:
269-251=39
39 divided by 3 = 13
13 weeks is your answer!
please mark brainliest please!!!
Write these fractions as percentage 2/3
Answers
Therefore 2/3 is 66.6%
Answer: 66%
Step-by-step explanation: To convert a fraction to a percentage, divide the top number by the bottom number. For example, \(\frac{1}{4}\) is 25% because if divide them, (1÷4=0.25) then we get 25%. So, for this problem, we solve 2÷3, which equals 0.66, or 66%.
hope this helps!
please give brainliest!
 A random sample of 1000 oranges showed that the mean amount of juice per orange was 8.4 fluid ounces, with a standard deviation of 1.3 fluid ounces.
(a) Determine the z-score, to the nearest hundredth, of an orange that produced 6.2 fluid ounces of juice.
[169
(b) The z-score for one orange was 3.09. How much juice was produced by this orange? Round to the nearest tenth of a fluid ounce.
Answers
The z-score of an orange that produced 6.2 fluid ounces of juice is approximately -1.69.
An orange with a z-score of 3.09 produced approximately 12.1 fluid ounces of juice.
We have,
(a)
To determine the z-score for an orange that produced 6.2 fluid ounces of juice, we can use the formula:
z = (x - μ) / σ
x = value of the observation
μ = the population mean,
σ = the population standard deviation.
Substituting the given values.
z = (6.2 - 8.4) / 1.3 = -1.69
z ≈ -1.69
(b)
To determine the amount of juice produced by an orange with a z-score of 3.09, we can rearrange the formula for the z-score as follows:
x = z x σ + μ
Substituting the given values.
x = 3.09 x 1.3 + 8.4
x = 12.097
Rounding to the nearest tenth of a fluid ounce.
x ≈ 12.1
Therefore,
The z-score of an orange that produced 6.2 fluid ounces of juice is approximately -1.69.
An orange with a z-score of 3.09 produced approximately 12.1 fluid ounces of juice.
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The midpoint of AB is M(-4,2). If the coordinates of A are (-7,3), what are the
coordinates of B?
Answers
The midpoint of AB is M(-4,2). If the coordinates of A are (-7,3), and the coordinates of B is (-1, 1).
To find the coordinates of point B, we can use the midpoint formula, which states that the coordinates of the midpoint between two points (A and B) can be found by averaging the corresponding coordinates.
Let's denote the coordinates of point A as (x1, y1) and the coordinates of point B as (x2, y2). The midpoint M is given as (-4, 2).
Using the midpoint formula, we can set up the following equations:
(x1 + x2) / 2 = -4
(y1 + y2) / 2 = 2
Substituting the coordinates of point A (-7, 3), we have:
(-7 + x2) / 2 = -4
(3 + y2) / 2 = 2
Simplifying the equations:
-7 + x2 = -8
3 + y2 = 4
Solving for x2 and y2:
x2 = -8 + 7 = -1
y2 = 4 - 3 = 1
Therefore, the coordinates of point B are (-1, 1).
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Refer from attachment and answer the question please
Answers
Answer:
\(option \: (b) \: is \: ur \: answer\)
To know the answer with Proove.See Above Attachment..
Step-by-step explanation:
Hope this helps you XD ✌️Carry on learning !!
The polynomial whole zeros are α+β and αβ is x^2 + x - 12
Given the quadratic equation x^2 - 3x - 4 = 0
From the equation, a = 1, b = -3 and c = -4
The sum of the equation α+β = -b/a
α+β = 3/1 = 3
The product of the equation αβ = c/a
αβ = -4/1 = -4
Get the polynomial equation with zeros of 3 and -4
f(x) = (x-3)(x+4)
f(x)= x^2 + 4x - 3x - 12
f(x) = x^2 + x - 12
Hence the polynomial whole zeros are α+β and αβ is x^2 + x - 12
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Edward opens a new account and makes a deposit of $150. He then makes withdrawals of $10, $20 and $25, before depositing $30 more. What is the new balance?
Answers
Explanation)
150-10-20-25 = 95
95 + 30 = 125
the new balance is $125 :)
Martha, Lee, Nancy, Paul, and Armando have all been invited to a dinner party. They arrive randomly, and each person arrives at a different time.
a. In how many ways can they arrive?
b. In how many ways can Martha arrive first and Armando last?
c. Find the probability that Martha will arrive first and Armando last.
Show your work
Answers
Answer:
a) 120
b) 6
c) 1/20
Step-by-step explanation:
a) 5! = 120
b) (5 - 2)! = 6
c) 6/120 = 1/20
Please see my question in the attachment, thanks!
Answers
The limit of the function As x → - ∞, f(x) → 2.
What is the limit of a function?The limit of a function is the value the function tends to as the independent variable tends to a given value.
Given the graph of the function above, to find the limit of the function As x → -∞, f(x) →? We proceed as follows
Looking at the graph, we see that f(x) has a horizontal asymptote at y = 2. Now, we see that As x → -∞, f(x) approaches 2.
So, As x → - ∞, f(x) → 2.
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When I was a child, I once got lost in the grocery store. I'd been begging for weeks to buy the latest new cereal that I thought would make me as strong as a superhero, and I'd found it! Just as my chest swelled as I just knew I would soon be able to fly, I looked around to realize that I had no idea where my mother was. Which would be the BEST detail to add next to the narrative in order to develop the story for the reader? A) Physical details about his mother B) Historical information about American superheroes C) Concrete details about what the author saw and looked for his mother D) None of these choices represent a detail that would advance the story.
Answers
Answer:
C) concrete details about what the author saw and looked for his mother
if A-B=2, B-C=7 and A+C=17, then (A+B+C) is equal to
Answers
Answer:
A+B+C=28
Step-by-step explanation:
let
A-B=2 -----1 EQUATION
B-C=7-------2
A+C=17------3
FROM 1 AND 2
A-C=9---------4
FROM 2 AND 3
A+B=24 -------5
FROM 3 AND 4
2A=26
A=13 SUBSTITUTING A=13 IN 5
WE GET B=11 SUBSTITUTING IT IN 2
WE GET C=4
NOW
A+B+C=13+11+4=28
Which situation results in a final value of zero
Answers
Answer:
Step-by-step explanation:
Estimate: 23.41 ÷ 3.1
Answers
Answer:
The answer is 8
The estimated answer is eight. Here‘s what I did. First, I rounded twenty three and forty-one hundredths to twenty-three. Then I rounded three and one-tenths to three.
I couldn’t quickly find an answer to twenty-three divided by three. So, I used compatible numbers, twenty-four divided by three… which equals eight.
10 Points!
Tyra competed on a trivia game show. 10 points were awarded for correct answers, and 5 points were deducted for incorrect answers. She answered 2 questions correctly, but answered one incorrectly. How many points does she have?
Answers
2 correct= 10+10=20
1 wrong= 20-5= 15
Answer:
Step-by-step explanation:
Answer = 15 points
Explain:
Correct answer gives you 10 points
incorrect answers subtract 5 points
She had to correct question which would be 20pts. (10 + 10 = 20)
She got one answer wrong which would subtract 5pts (20 - 5 = 15)
answer = 15pts
Help mee I’ll give u extra pointss
Answers
Answer:
x ≤ -6
Step-by-step explanation:
\(3x+5\leq -13\)
Step 1 (Subtract 5 from both sides):
\(3x+5-5\leq -13-5\\3x\leq -18\)
Step 2 (Divide both sides by 3):
\(\frac{3x}{3} \leq \frac{-18}{3}\\ x\leq -6\)
Solution set expressed in set-builder notation:
{x | x ≤ -6}
Solution set expressed in interval notation:
(-∞, -6]
Please Help! Very Urgent, i only have like half a hour. 20 points and brainiliest.
Answers
Answer:
Yes, they are similar.
\(AB\approx 127.3947\)
Step-by-step explanation:
Part 1)
Yes.
First, ∠D and ∠B are both right angles, so they are congruent.
Next, ∠DCE and ∠BCA are vertical angles. So, their measures are congruent.
Then by Angle-Angle Similarity, we acquire:
\(\Delta EDC\sim \Delta ABC\)
Part 2)
The corresponding sides of similar triangles are proportional.
Therefore:
\(\displaystyle \frac{DE}{DC}=\frac{AB}{BC}\)
By substitution:
\(\displaystyle \frac{103}{76}=\frac{AB}{94}\)
Cross-multiply:
\(76AB=9682\)
So:
\(AB=9682/76\approx127.3947\)
if the mean of x,x+3,x-5,2x and 3x then find the value of x
Answers
The Value of x is 2/3.
The value of x, we need to determine the mean of the given values and set it equal to the expression for the mean.
The mean (average) is calculated by adding up all the values and dividing by the number of values. In this case, we have five values: x, x+3, x-5, 2x, and 3x.
Mean = (x + x+3 + x-5 + 2x + 3x) / 5
Next, we simplify the expression:
Mean = (5x - 2 + 3x) / 5
Mean = (8x - 2) / 5
We are given that the mean is also equal to x:
Mean = x
Setting these two expressions equal to each other, we have:
(x) = (8x - 2) / 5
To solve for x, we can cross-multiply:
5x = 8x - 2
Bringing all the x terms to one side of the equation and the constant terms to the other side:
5x - 8x = -2
-3x = -2
Dividing both sides by -3:
x = -2 / -3
Simplifying, we get:
x = 2/3
Therefore, the value of x is 2/3.
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The figure shows four box-and-whisker plots. These represent variation in travel time for four different types of transportation from the beginning to the end of one route.
Conrad is at one end of the route. He is trying to decide how to get to an appointment at the other end. His appointment is in 30 minutes. Which type of transportation is LEAST likely to take more than 30 minutes?
Select one:
a.
bus
b.
car
c.
subway
d.
train
Answers
Comparing the median of each box-and-whisker plot, the type of transportation that is LEAST likely to take more than 30 minutes is: d. train.
How to Interpret a Box-and-whisker Plot?
In order to determine the transportation that is LEAST likely to take more than 30 minutes, we have to compare the median of each data set represented on the box-and-whisker plot for each transportation.
The box-and-whisker plot that has the lowest median would definitely represent the the transportation that is LEAST likely to take more than 30 minutes, since median represents the typical minutes or center of the data.
Therefore, from the box-and-whisker plots given, the one for train has the lowest median. Therefore train would LEAST likely take more than 30 minutes.
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Solve the equation.
x^2 − 4x + 4 = 3
Answers
There is a bag of marbles that contain 5 blues, 6 red, 3 black, and 2 yellow marbles. What is the probability that you select a blue marble
Answers
Answer:
\(\frac{5}{16}\)
Step-by-step explanation:
1) Find the total number of marbles
5 blue + 6 red + 3 black + 2 yellow
= 16 marbles
2) To find the probability of selecting a blue marble, divide the number of blue marbles by the number of total marbles:
5 blue marbles ÷16 marbles
\(= \frac{5}{16}\)
Therefore, the probability of selecting a blue marble is \(\frac{5}{16}\).
I hope this helps!
is it possible to write vector (-5,6) as a linear combination of vectors (1,2) and (3,4)
Answers
Answer:
Step-by-step explanation:
-5i+6j=x(1i+2j)+y(3i+4j)
-5=x+3y(multiply by 2)
6=2x+4y
-10=2x+6y
subtract
16=-2y
y=-8
-5=x+3(-8)
x=-5+24=19
-5i+6j=19(i+2j)-8(3i+4j)
so we can write (-5,6) as a linear combination of (1,2) and (3,4)
Explain how the written method shown can be used to solve the decimal expression: 3.62x 1.4.
Answers
Explanation:
We are told to explain how the written method shown in the question can be used to solve the decimal expression: 3.62 x 1.4
From the question, we have:
\(362\times14=5068\)Then, we can infer that 3.62 x 1.4 means that 362 was divided by 100 and 1.4 was divided by 10
\(3.62\times1.4=\frac{362}{100}\times\frac{14}{10}\)\(3.62\times1.4=\frac{362}{100}\times\frac{14}{10}=\frac{362\times14}{1000}=\frac{5068}{1000}\)Therefore we will have 5.068
Thus
3.62 x 1.4 = 5.068