To solve this problem, we have to write out the simple harmonic motion equation and then use the respective formula to solve. The maximum kinetic energy, maximum potential energy and the maximum mechanical energy is equal to 7.56J.
Simple Harmonic MotionThe given equation of the simple harmonic motion is
[tex]x = 3.5sin(\frac{\pi}{2t} + \frac{5\pi}{4})\\[/tex]
Data;
ω = π/2k = 1.254N/mSolving this
[tex]\frac{dx}{dt} = \theta = -3.5 * \frac{\pi}{2} cos (\frac{\pi }{2}t + \frac{5\pi}{4})\\[/tex]
Let's calculate the maximum velocity.
[tex]V_m = \frac{3.5\pi}{2}[/tex]
This is only possible when cos θ = -1
The maximum kinetic energy is
[tex]K_m = \frac{1}{2}mv_m^2 = \frac{1}{2}* \frac{500}{1000} * (\frac{7\pi}{4} )^2\\K_m = 7.56J[/tex]
The maximum kinetic energy is 7.56J
The maximum potential energy can be calculated as
[tex]\omega^2 = \frac{k}{m} \\k = \omega^2 m \\k = \frac{\pi^2}{4} * \frac{500}{1000}\\ k= 1.254 N/m[/tex]
Using the value of spring constant, we can find the maximum potential energy
[tex]P.E = \frac{1}{2}kx^2\\P.E = \frac{1}{2} * 1.234 * 3.5^2\\P.E = 7.56J[/tex]
The maximum potential energy is 7.56J
The maximum mechanical energy is equal to the sum of maximum potential energy and the maximum kinetic energy.
[tex]ME = P.E + K.E\\ME = 7.56J[/tex]
The reason ME is equal to 7.56J is because when x is at maximum, v = 0 and makes kinetic energy equal to zero.
ME = 7.56J
From the calculations above, the maximum kinetic energy, maximum potential energy and the maximum mechanical energy is equal to 7.56J.
Learn more on simple harmonic motion here;
https://brainly.com/question/15556430
#SPJ1
3. Seth uses a bowl to fill a container with soil. The
bowl holds 3/4 cup of soil. How many cups of soil
does the container hold if it takes 13 full bowls of soil
to fill it?
There is 80% milk in 400 litre misture of milk and water. What will be the percentage of milk in the new mixture when 80 litre more water is added in the mixture?
Step-by-step explanation:
[tex] \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \error \\ \madeindonesia[/tex]
Select all the correct answers.
Which four inequalities can be used to find the solution to this absolute value inequality?
Answer:Which four inequalities can be used to find the solution to this absolute value inequality?3+2|x-11 <9
2(x - 1) <-3
x-1 <9
X-1 >-9
-2(x - 1) > 3
x-1-3
X-1 <3
Step-by-step explanation:
There is no document, so nobody could answer.
In a motor alignment, the following pieces of steel are used under the base: one piece 5/16 inch thick, one piece 5/8 inch thick, one piece 5/32 inch thick, and one piece 5/64 inch thick, and one piece 564 inch thick. What is the total thickness of all these pieces?
Answer:
1 11/64 inches
Step-by-step explanation:
Total thickness
5/16 + 5/8 + 5/32 + 5/6420/64 + 40/64 + 10/64 + 5/6475/641 11/64 inchesPlease help! If you dont know, then dont answer please and thank you
Answer:
327.5
Step-by-step explanation:
What is the volume of this figure?
2520 in³
1638 in³
1323 in³
935 in³
Answer:
935
Step-by-step explanation:
Let's solve the rectangle first. We are dividing this figure into two sepreate shapes, can you see that?
-
1/2*B*h
630
-
Now for the other shape.
Volume = 315
630+315=935
Answer: 1323
Step-by-step explanation: took test with proof and more
If EH = w and GH = 4w - 51, what is GH?
Answer:
Step-by-step explanation:
EH=w
then it is as simple as pluggin in
gh=4(eh)-51
A girl is given 500 stamps to start a collection . If she adds 5 stamps a week , how many will she have at the end of n weeks ?
Answer:
T=(5×n)+500
Step-by-step explanation:
T=Total Stamps
In this case, there is no need to find the answer. All you need is the equation. N would be the multiplier in this case because it's the one that's changing since you're using a variable. If 3 weeks were to pass, then N would equal 3 weeks.
Find the missing factor. Write your answer in
exponential form.
5^-7 = ___ X 5^-9
Answer
5^- 7=X 5^- 9 X = 7 9
Find the slope easy giving brainlest
Answer:
Problem 20: [tex]m[/tex] = [tex]2[/tex]
Problem 21: [tex]m[/tex] = [tex]-2[/tex]
Problem 22: [tex]m[/tex] = [tex]1[/tex]
Problem 23: [tex]m[/tex] = [tex]3[/tex]
Step-by-step explanation:
The formula to find the slope of a line: [tex]m = \frac{y_{2} - y_{1}}{x_{2}-x_{1}}[/tex].
Problem 20:
1) Substitute the values into the formula and solve it.
[tex]m[/tex] = [tex]\frac{3-7}{2-4}[/tex]
[tex]m[/tex] = [tex]\frac{-4}{-2}[/tex]
[tex]m[/tex] = [tex]2[/tex]
Problem 21:
1) Substitute the values into the formula and solve it.
[tex]m[/tex] = [tex]\frac{-5-1}{2--1}[/tex]
[tex]m[/tex] = [tex]\frac{-6}{3}[/tex]
[tex]m[/tex] = [tex]-2[/tex]
Problem 22:
1) Substitute the values into the formula and solve it.
[tex]m[/tex] = [tex]\frac{3-7}{-6--2}[/tex]
[tex]m[/tex] = [tex]\frac{-4}{-4}[/tex]
[tex]m[/tex] = [tex]1[/tex]
Problem 23:
1) Substitute the values into the formula and solve it.
[tex]m[/tex] = [tex]\frac{-4-2}{-4--2}[/tex]
[tex]m[/tex] = [tex]\frac{-6}{-2}[/tex]
[tex]m[/tex] = [tex]3[/tex]
*Extra*: The equation of a line is written in this form: [tex]y = mx+b[/tex], where [tex]m[/tex] is the slope and [tex]b[/tex] is [tex]y[/tex]-intercept
In a random sample of 2500 sports fans, 61% prefer basketball over soccer.
What is the Margin of error in this survey?
Margin of error = [m]%
The margin of error is a statistic that expresses how much random sampling error there is in a survey's results. The Margin of error in this survey is 1%.
What is the margin of error?The margin of error is a statistic that expresses how much random sampling error there is in a survey's results. The wider the margin of error, the less confident one should be that a poll result reflects the outcome of a population-wide survey.
The random sample of 2500 sports fans, out of which 61% prefer basketball over soccer, therefore, we can write n=2500 and p=0.61. Thus, the margin of error can be written as,
[tex]MOE=\sqrt{\dfrac{\hat p(1-\hat p)}{n}} = \sqrt{\dfrac{0.61(1-0.61)}{2500}} = 0.00975 = 0.975\% \approx 1\%[/tex]
Hence, the Margin of error in this survey is 1%.
Learn more about Margin of Error:
https://brainly.com/question/13990500
#SPJ1
Write the standard form of the equation of a circle with radius 3 and center (11, 3)
Answer:
x² - 22x + y² - 6y + 121 = 0
Step-by-step explanation:
General Form of Equation
(x - h)² + (y - k)² = r²Solving
(x - 11)² + (y - 3)² = (3)²x² - 22x + 121 + y² - 6y + 9 = 9x² - 22x + y² - 6y + 121 = 0Answer:
(x+11)2+(y−3)2=81
mark me brainliest
Step-by-step explanation:
Find the volume of the shape.
Round to 2 decimal places.
22 cm
14 cm
Answer:
The volume is about 1,128.88 cubic cm.
Step-by-step explanation:
[tex] \frac{1}{3} \pi( {7}^{2} )(22) = 1128.88[/tex]
Find the Interquartile Range for the following test scores: 98, 93, 75, 86, 79, 82, 77 (Remember to put in order)
The graph of Fx), shown below, resembles the graph of G(x) = x, but it has
been changed somewhat. Which of the following could be the equation of
Fx)?
5
GO) = x2
5
FOO = ?
+
O A. F(x) = -x2 - 4
O B. FX) = x2 - 4
O C. Fx) = -(x - 4)2
O D. Fx) = -(x+4)2
Using translation concepts, it is found that the equation of F(x) could be given by:
A. F(x) = -x² - 4.
What is a translation?A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction in it's definition.
In this problem, the function g(x) = x² was reflected over the x-axis and shifted 4 units down, hence f(x) is given by:
A. F(x) = -x² - 4.
More can be learned about translation concepts at https://brainly.com/question/4521517
#SPJ1
What are the exact solutions of x2 − 3x − 5 = 0, where x equals negative b plus or minus the square root of b squared minus 4 times a times c all over 2 times a? x = the quantity of negative 3 plus or minus the square root of 29 all over 2 x = the quantity of 3 plus or minus the square root of 29 all over 2 x = the quantity of 3 plus or minus the square root of 11 all over 2 x = the quantity of negative 3 plus or minus the square root of 11 all over 2
Answer:
B. x = the quantity of 3 plus or minus the square root of 29 all over 2Step-by-step explanation:
Given equation
x² - 3x - 5 = 0The roots are
[tex]x=\cfrac{-b+- \sqrt{b^2-4ac} }{2a}[/tex]Substitute values into equation
[tex]x=\cfrac{3+- \sqrt{(-3)^2-4(1)(-5)} }{2(1)} =\cfrac{3+- \sqrt{9+20} }{2} =\cfrac{3+- \sqrt{29} }{2}[/tex]This is matching the option B
Answer:
[tex]x=\dfrac{3 \pm \sqrt{29}}{2}[/tex]
Step-by-step explanation:
Given equation:
[tex]x^2-3x-5=0[/tex]
To find the exact solutions of the given equation, use the quadratic formula or complete the square.
Method 1: Quadratic Formula
[tex]x=\dfrac{-b \pm \sqrt{b^2-4ac} }{2a}\quad\textsf{when }\:ax^2+bx+c=0[/tex]
Therefore:
[tex]a=1, \quad b=-3, \quad c=-5[/tex]
Substituting these values into the formula:
[tex]\implies x=\dfrac{-(-3) \pm \sqrt{(-3)^2-4(1)(-5)} }{2(1)}[/tex]
[tex]\implies x=\dfrac{3 \pm \sqrt{29}}{2}[/tex]
Method 2: Completing the square
Move the constant to the right side by adding 5 to both sides:
[tex]\implies x^2-3x-5+5=0+5[/tex]
[tex]\implies x^2-3x=5[/tex]
Add the square of half the coefficient of x to both sides:
[tex]\implies x^2-3x+\left(\dfrac{-3}{2}\right)^2=5+\left(\dfrac{-3}{2}\right)^2[/tex]
[tex]\implies x^2-3x+\dfrac{9}{4}=\dfrac{29}{4}[/tex]
Factor the perfect trinomial on the left side:
[tex]\implies \left(x-\dfrac{3}{2}\right)^2=\dfrac{29}{4}[/tex]
Square root both sides:
[tex]\implies \sqrt{\left(x-\dfrac{3}{2}\right)^2}=\sqrt{\dfrac{29}{4}}[/tex]
[tex]\implies x-\dfrac{3}{2}=\pm\dfrac{\sqrt{29}}{2}[/tex]
Add 3/2 to both sides:
[tex]\implies x-\dfrac{3}{2}+\dfrac{3}{2}=\pm\dfrac{\sqrt{29}}{2}+\dfrac{3}{2}[/tex]
[tex]\implies x=\dfrac{3 \pm \sqrt{29}}{2}[/tex]
Learn more about completing the square here:
https://brainly.com/question/27933930
Juan has 22 balloons and each balloon can hold up to 8.23 ounces of water. How much water would he use if he filled all the balloons completely?
Answer:
181.06
Step-by-step explanation:
Find the missing angle
Answer:
36 degrees
Step-by-step explanation:
We do bottom triangle first:
33+90=123. 180-123=57
Go to upper tri: 90-57=33
111+33=144. 180-144=36.
?=36 degrees
Hope it helps
Which scale you would use on the coordinate plane to plot each set of points? A Select . (1.-6).(-7,-8), (-3, 7), (0.9) • (-20, -30).(-40, 10), (20, -10), 5. -20) Select] Select) •,( (-3,-1), (§. -13), 3, 3), (1,0
Answer:qjs
Step-by-step explanation:
A
X= -7 to 1
Y= -8 to 9
B
X= -40 to 20
Y= -30 to 10
What is the 35th term in this sequence? 2, 7, 12
Answer:
172
Step-by-step explanation:
Formula to find the nth term =
a+(n-1)d
2+(35-1)*5
= 2+170
= 172
Sarah makes home-made jewelry sets. Each jewelry set includes a necklace, a bracelet and two earrings. Given below are the number of beads Sarah adds to each type of jewelry.
Necklace: 48
Bracelet: 19
Earrings: 6 (both earrings combined)
What is the largest number of jewelry sets she can make with 7100 beads?
Based on the number of beads that are needed to make a jewelry set, the largest number of jewelry sets that Sarah can make with 7,100 beads is 97 jewelry sets.
What amount of jewelry sets can Sarah make?First find the total number of beads used per jewelry set:
= Necklace + Bracelet + Earrings
= 48 + 19 + 6
= 73 beads
If she had 7,100 beads, the sets she could make would be:
= Total number of beads / Beads per set
= 7,100 / 73
= 97 jewelry sets
Find out more on calculations involving largest producible quantities at
#SPJ1
Can someone help please?
See attached. The box-and-whisker plot gives us all the information we need to solve.
Minimum: 13
Maximum: 35
Range: 22
-> 35 - 13 = 22
Median: 20.5
Which of the following are roots of the polynomial function?
Check all that apply.
F(x) = x3 + 3x2 - 9x+ 5
O A. -5
OB. 1 + 3
O C. 3+2
O D. 1-3
O E. 1
O F. 3 - 2
Answer:
1 and -5
Step-by-step explanation:
[tex]~~~~~x^3+3x^2-9x+5=0\\\\\implies x^3-x^2+4x^2-4x-5x+5=0\\\\\implies x^2(x-1)+4x(x-1)-5(x-1)=0\\\\\implies (x-1)(x^2 +4x -5) = 0\\\\\implies (x-1)(x^2+5x -x -5) = 0\\\\\implies (x-1)[x(x+5) -(x+5)] =0\\\\\implies (x-1)(x-1)(x+5)= 0\\\\\implies (x-1)^2(x+5) = 0\\\\\implies x = 1,~~ x = -5[/tex]
Which sport is required to have both male and female competitors ?
A. Hockey
B. Water polo
C. Mixed doubles tennis
D. Swimming
Answer:
Mixed Doubles Tennis
Step-by-step explanation:
The key word is "mixed." In this case it means a male and female competitor
Solve the inequality and describe the solution set
12x = 36, WRONG LOOK AT THE PICTURE THAT I PUT.
PLEASE HELP EASY ASSIGNMENT!!! ( Kami )
Write the following as an inequality.
-2 is greater than x, and - 7 is less than or equal to x
Use x only once in your inequality.
Answer:
see below
Step-by-step explanation:
-2> x ≥ -7 can be written as -7 ≤ x < -2
Find the reference angle for 4pi/7
Find the Reference Angle (4pi)/7 4π 7 4 π 7 Since the angle 4π 7 4 π 7 is in the second quadrant, subtract 4π 7 4 π 7 from π π.
Thus, [tex]\frac{3\pi }{7}[/tex] is your answer
The histogram below represents the high tempatures recorded each day over a one month period. How many days had a tempature below 60
Answer: 22
Step-by-step explanation:
the student council at mountain view high school plans to conduct a survey to determine the student body's opinion of the new lunch menu. which of the following sampling methods would be most likely to result in self-selection bias?
A. obtaining an alphabetical list of all students and surveying every 10th student
B. setting up a booth in the lunchroom where students can give theirthoughts
C. handing out a questionnaire to students leaving campus at lunchtime
D. handing out a questionnaire to seniors only
The sampling method that would be most likely to result in self-selection bias is given by:
D. handing out a questionnaire to seniors only
What is sampling?It is a common statistics practice, when we want to study something from a population, we find a sample of this population, which is a group containing elements of a population. A sample has to be representative of the population, that is, it has to involve all segments of the population.
In this problem, in option D, only seniors are involved, that is, it does not involve all segements, hence it would be most likely to result in self-selection bias.
More can be learned about sampling concepts at https://brainly.com/question/25122507
#SPJ1
Answer: C. handing out a questionnaire to students leaving campus at lunchtime
Step-by-step explanation:
