Answer:
Step-by-step explanation:
Given that:
mass m = 100 g = 0.1 kg
Length of the spring = 5 cm = 0.05 m
The set in motion from the equilibrium position u(0) = 0
The set in motion from its equilibrium position with a downward velocity u'(0) = 50 cm/s = 0.5 m/s
The spring constant (k) = [tex]\dfrac{0.1 \times 9.8}{0.05}[/tex]
The equation of the system is expressed as:
[tex]\dfrac{1}{10} u'' + \dfrac{98}{5} u =0[/tex]
By estimating the characteristics equation, we have r = ± 14[tex]i[/tex]
Thus; the general solution is:
[tex]u(t) = c_1cos \ 14t + c_2 sin 14 \ t[/tex]
By applying the initial condition:
u(0) = 0
⇒ 0 = [tex]c_1[/tex]
∴
[tex]\dfrac{du}{dt} = ( - c_1 \ sin 14 t )\times 14 +14c_2 \ cos 14 t[/tex]
u'(0) = 0.5
0.5 = 14 × c₂
c₂ = 0.5/14
c₂ = 1/28
∴
[tex]\mathbf{u(t) = \dfrac{1}{28} sin 14 t}[/tex]
Equating u(t) = 0, we have t = π/14sec as the time when the mass first returns to its equilibrium position.
A large bucket of 200 golf balls is divided into 4 smaller buckets. How many golf balls are in each small bucket?
Answer:
50 golf balls
Step-by-step explanation:
200/4 is 50. I did that because it says the golf balls are DIVIDED into 4 smaller buckets.
To check the answer you do 50 times four.
Answer:
50 in each small bucket
A certain fraction is greater than 2. The denominator is 8. What must be true about the numerator?
Answer:
The numerator must be greater than 16
Step-by-step explanation:
We are told that a certain fraction is greater than 2. Thus, if the numerator and denominator are x and y respectively, then we have;
x/y > 2
We are further told that the denominator is 8.
Thus;
x/8 > 2
Multiply both sides by 8 to give;
x > 16
Thus,the numerator must be greater than 16.
The highest location in a certain country is 14,864 feet above sea level. The lowest point in the same country is 141 feet below sea level.
Find the difference of the two elevations.
A city is 7,642 feet above sea level. Is this elevation closer to the highest point or the lowest point?
Answer:
15,003 and Highest Point
Step-by-step explanation:
The highest point is at a positive 14,864 feet so we will use the number 14, 864.
The lowest is at a negative (below sea level) 141, so we will use the number -141.
The difference between them means that you subtract.
14,862-(-141)= x
Note that there is a double negative so it is positive.
14862+141=15,003 feet difference between them.
A city at 7642 above sea level is:
7642-14862=7222 feet away. The city is 7222 feet away from the highest point.
7642--141=7783 feet away. The city is 7783 feet away from the lowest point.
7222 is less than 7783, so the city is closest to the highest point.
Answer:
The difference is 15,005 and for the second part its closer to the highest point
Hope this helps!
Ms Gibson made an initial deposit of 500$ when opening a bank account. After the initial deposit, she deposited the same amount of money of each month-
A) a=250t
B) a=500t
C)a =250t+500
D)a=500+250
Which of the following angles is not congruent to angle 3
Answer:
angle 2
Step-by-step explanation:
they aren't equal.
Angle 3 is not equal to angle 2.
What is property of parallel lines?Properties of Parallel Lines Cut by a Transversal
For the parallel lines cut by a transversal, the following properties hold true:
Two lines cut by a transversal line are parallel if the corresponding angles so formed are equal. In general, the corresponding angles are in relative positions and lie along the same side of the transversal.Two lines cut by a transversal line are parallel if the alternate interior angles so formed are equal. In general, the pairs of the alternate interior are found in the inner side but lie on the opposite sides of the transversal.Two lines cut by a transversal line are parallel if the alternate exterior angles so formed are equal. In general, the pairs of alternate exterior angles are found on the outer side but lie opposite each other.As,
angle 3 = angle 1 (Corresponding angle)
angle 3 = angle 6 ( alternate interior angle)
angle 3= angle 8 (vertically opposite angle)
But there is no relation between angle 3 and angle 2.
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Solve Sec(2x)-4=0 for the first two positive solutions. thanks!
sec(2x) - 4 = 0
sec(2x) = 4
1 / cos(2x) = 4
cos(2x) = 1/4
2x = cos⁻¹(1/4) + 2nπ or 2x = -cos⁻¹(1/4) + 2nπ
(where n is any integer)
x = 1/2 cos⁻¹(1/4) + nπ or x = -1/2 cos⁻¹(1/4) + nπ
The first two positive solutions occur for n = 0 in the first family of solutions, and for n = 1 in the second family, so
x = 1/2 cos⁻¹(1/4) or x = π - 1/2 cos⁻¹(1/4)
x ≈ 0.659 or x ≈ 2.483
i√5
Find the square of the imaginary number.
Answer:
= [tex]-\sqrt{5} i[/tex]
Step-by-step explanation:
First, reorder the terms:
[tex]\sqrt{5} i[/tex]
Then, find the complex conjugate (a pure imaginary number is its opposite):
[tex]-\sqrt{5}i[/tex]
can 18 in, 6 in, 13 in form a triangle
Answer:
can bcz triangle has 3 sides here 3 cm are there
The four highest scores on the floor exercise at a gymnastics meet were 9.675, 9.25, 9.325, and 9.5. List the scores from least to greatest.
Answer:
9.25, 9.325, 9.5, 9.675
Step-by-step explanation:
Answer:
9.25, 9.325, 9.5, 9.675
(IM GIVING BRAINLIEST AND EXTRA POINTS TO WHO EVER HELPS ME!)
Watch the video of the can moving across the surface. What can the child do to create a greater force of friction?
*two hands moving a can back and forth on a table*
A) Make the table wet.
B) Place a cloth on the table.
C) Use less force when pushing the can.
D) Use more force when pushing the can.:(Inncorect)
(Here is an image) :
Answer:
i think its B
Step-by-step explanation:
D, C, and A are def wrong so i think its B
i hope i helped you!
Answer: that would be d
Step-by-step explanation:
write an integer to represent the situation. A deposit of $245
Answer:
+265
Step-by-step explanation:
a sum of money placed or kept in a bank account, usually to gain interest.
So basically your saving money instead of losing by, keeping it in the bank safely.
Amelia rented a dvd and it was due to be returned on 26 november
she actually returned it to the shop on 26 december
the rental shop applies a fine for 9p for every day the dvd is overdue
work out the total fine paid by amelia
give your answer in £?
Anyone help please!!!!!
Answer:
Step-by-step explanation:
I'm not familiar with the conversions from American dollars. I can help you solve it though.
Count how many days from Nov 26 to Dec 26 and multiply that by 9p.
It's 30 days by 9p. Take that total and convert it.
Hopefully this helps you.
Can somebody please help me with this please
Answer:
equilateral for the first one scalene for the second one scalene for the third one equilateral for the fourth one
Step-by-step explanation:
The population of a city grew from 43,209 to
45,687 in just five years. What was the percent
increase in the population to the nearest whole
percent?
Answer:
5 percent or 5.7349percent
divide 43209 by 45687 and get 1.0573491 subtract one
and get 0.0573491 make into a percentage 5.7percent depending on where you need to round.
I need help with some math problems, thank you
Answer: segundo
Step-by-step explanation:
The distance an object falls is directly proportional to the square of the time it falls. A ball falls 144 feet in 3 seconds. How far will an object fall in 4 seconds?
Answer:
d = 256 ft.
Step-by-step explanation:
The distance an object falls is directly proportional to the square of the time it falls.
First, we name the variables.
Let d= the distance.
t= time
Write the formula for direct variation, where y varies directly with the square of x.
y=kx2
We will use d in place of y and t in place of x.
d=kt2
Substitute the given values for the variables.
d=144whent=3144=k⋅32
Solve for the constant of variation.
144916=k⋅99=k
Write the equation that relates d and t.
d=kt2
Substitute in the constant of variation.
d=16t2
Find d when t=4.
Write the equation that relates d and t.
d=16t2
Substitute the given value for t.
d=16⋅42
Simplify.
d=256
An object will fall 256 feet in 4 seconds.
The required distance fall by fall in 4 seconds is 192 feet.
Given that,
The distance an object falls is directly proportional to the square of the time it falls. A ball falls 144 feet in 3 seconds, how far will an object fall in 4 seconds is to be determined.
In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication, and division.
here,
The rate of fall of the ball = 144 / 3
= 48 feet second
Now distance fall by the ball in 4 seconds = 48 * 4 = 192 feets.
Thus, the required distance fall by fall in 4 seconds is 192 feet.
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At the carnival, the ratio of people who won the ring toss game to lost it was 8 : 5. If 56
people won, how many people would have lost?
Answer:
The answer is 35
Step-by-step explanation:
First of all, note that 56 is the same as 56/1 since 56 divided by 1 is 56. Therefore, start by setting up the problem like this:
Step 1: 56/1 x 8/5 =
Step 2: Multiply the numerators together (56 x 8 = 448) and multiply the denominators together (1 x 5 = 5) and make it into one fraction like so 448/5 Step 3: Convert the improper fraction above to a mixed number to get the answer: 89 3/5
That's it! Now you know how to calculate 56 times 8:5.
Answer:
35
Step-by-step explanation:
can somebody help
me
Answer: answer 2
Step-by-step explanation:
I need help I am in 3grade and I need help with it so if you can please help
Answer:
what do you need help with exactly?
Step-by-step explanation:
Answer:
your supposed to ask a question
Step-by-step explanation:
what is 3/4 and 5/12 simplified in fraction form plz idk
Answer:
Well 3/4 & 5/12 are already simplified and in fraction form, if youre
looking for decimal form its gonna be .75 &.41
Step-by-step explanation:
PLEASE HELP!
What is the result when the number 78 is increased by 55%?
Answer:
hope this helps
Step-by-step explanation:
.55×78=42.9
78+42.9
=120.9 round off 121
Answer: 120.9 I believe.
Step-by-step explanation:
55% of 78 is 42.9.
(55 x 78 over 100 = 42.9)
Therefore take 78 + 42.9.
120.9
In the equation y=kx, which variable is the constant of proportionality?
Answer:the variable k is the constant of proportionality
Step-by-step explanation:
This can be proven when the equation is used to find different values of y. To find these different values, the x variable is substituted for different values while the k value stays the same. hope this helps!!
Describe your understanding of finding percents of a whole.
Step-by-step explanation: Write down the whole number amount, for example: 500. Calculate the equation. The result is the decimal equivalent of the percentage. Multiply the decimal equivalent of the percentage by 100; or move the number's decimal point over two places to the right.
What fraction of the diagram above
is not shaded? (All the squares are
equal in area).
Enter the correct answer in the box.
This graph represents a transformation of the parent cube root function.
Answer: h is 5 and k is 2
Step-by-step explanation:
The equation of the transformed of the parent cube root function is
y = ∛(x-4) - 1.
How to know if a point lies in the graph of a function?All the points (and only those points) which lie on the graph of the function satisfy its equation.
Thus, if a point lies on the graph of a function, then it must also satisfy the function.
The given graph represents a transformation of the parent cube root function.
The Parent cube root function is
y = ∛(x -h) - k
where the value of h and k is equal to 0
h=0, k=0 in parent function
The graph changes direction at (0,0) in parent function.
From the given graph we can see that the graph changes direction at (4,-1) which means the graph is shifted 4 units to the right and 1 unit down
So, the value of h=4 and value of k=1
The equation of the transformed function,
y = ∛(x-4) - 1
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what’s the value of x?
Answer:
x = -11
Step-by-step explanation:
The sum of the angles of a triangle add to 180
x+50 + 72+ x+80 = 180
Combine like terms
2x + 202 = 180
Subtract 202 from each side
2x+202-202 = 180-202
2x =-22
Divide each side by 2
2x/2 = -22/2
x = -11
A store pays $49.14 for an easel. The Store markes up the price by %50. What is the amount the make-up
Answer:
$56.51
Step-by-step explanation:
Given parameters:
Cost price by the store = $49.14
Amount of mark up = 50%
Unknown:
Make- up price = ?
Solution:
Since the price was increased by 50% more, to find the mark up price, we can find 50% of the cost price and add the value to the cost price.
Also;
Make-up price =( 1 + [tex]\frac{50}{100}[/tex] ) x $49.14
= 1.15 x $49.14
= $56.51
find the equation of circle whose centre is at (3,4) and passing through (1,5)
Answer:
Step-by-step explanation:
Answer:
[tex](x-3)^{2} + (y-4)^{2} = r^{2} \\\\(1-3)^{2} + (5-4)^{2} = r^{2}\\r^{2} = 5 \\so the equation is \\(x-3)^{2} + (y-4)^{2} = 5[/tex]
Step-by-step explanation:
A merchant instructs his agent to buy 1,000 micro tip pens and sell them at 15% above the purchase price. the agent charges 1% commission on the purchase and 3% commission on sales and earns Rs.534/- as commission.find the price and which the agent buys the pen
Answer:
Thank you and please rate me as brainliest as it will help me to level up
The price of the pen is "12", and the cost price of 1000 pens is "12000".
Calculating the price of the pen:Assume the number of Pens[tex]= x[/tex]
commission price of 1000 Pens[tex]=1000 x[/tex]
The selling price of Pens:
[tex]=\frac{1000\times 115x}{100}\\\\ ={10\times 115 x}{}\\\\= 1150x[/tex]
Commission price on Purchase:
[tex]= \frac{1000\times 1 x}{100}\\\\= \frac{10\times 1 x}{1}\\\\= 10x[/tex]
commission price on sales:
[tex]=\frac{1150x \times 3}{100}\\\\=\frac{115 x \times 3}{10}\\\\=\frac{345 x }{10}\\\\=34.5\ x[/tex]
Calculating the total commission:
[tex]\to 10x+34.5x=44.5x=534\\\\\to 44.5x=534\\\\\to x = \frac{534}{ 44.5}=12[/tex]
Therefore, the agent buys a pen at 12 rupees and the cost price of 1,000 pens is 12000.
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What is the inverse operations of the equation shown n+4=
Answer:
i aint never seen two pretty bestfriends
Step-by-step explanation: