Answers
ω in terms of m and k is expressed as [tex]\omega = \sqrt{\frac{k}{m} }[/tex]
The given expression is as follows;
[tex]T_s = 2\pi \sqrt{\frac{m}{k} } , \ \ \\\\ T_s = \frac{2\pi}{\omega}[/tex]
To find:
ω in terms of m and k;From the given expression above make ω the subject of the formula;
[tex]T_s = \frac{2\pi}{\omega} = 2\pi \sqrt{\frac{m}{k} } \\\\ \frac{2\pi}{\omega} = 2\pi \sqrt{\frac{m}{k} }\\\\ \frac{2\pi}{\omega} = \sqrt{4\pi^2\frac{m}{k} }\\\\square \ both \ sides \ of \ the \ equation;\\\\(\frac{2\pi}{\omega})^2 = 4\pi^2\frac{m}{k} \\\\\frac{4\pi^2}{\omega^2}= \frac{4\pi^2m}{k} \\\\\omega^2 4\pi^2m = k4\pi^2 \\\\divide \ both \ side \ by \ 4\pi ^2 \\\\\omega^2 m = k\\\\divide \ both \ sides \ by \ m\\\\\omega^2 = \frac{k}{m} \\\\[/tex]
[tex]take \ the \ square \ root \ of \ both \ sides \ of \ the \ equation\\\\\omega = \sqrt{\frac{k}{m} }[/tex]
Therefore, ω in terms of m and k is expressed as [tex]\omega = \sqrt{\frac{k}{m} }[/tex]
To learn more about subject of formula visit: https://brainly.com/question/15469690
Related Questions
Applying a Level of Significance
In this task, you’ll study the data from two experiments. For each data set, you will determine whether the difference of means between the treatment group and the control group is statistically significant and interpret the result in the context of the situation.
Question 1
Researchers want to find a way to increase the growth rate of corn so it can be harvested more often. To test the effectiveness of a new type of spray fertilizer, plants grown from 200 corn seeds were divided equally into two groups: a treatment group and a control group. The treatment group was frequently sprayed with the new type of fertilizer. The growth in centimeters of each corn plant was noted before and after the treatment.
The results showed that the mean change in the growth rate by the treatment group is 8 points more than that of the control group. To test whether the results could be explained by random chance, researchers created a table that summarizes the results of 1,000 re-randomizations of the data with differences of means rounded to the nearest 2 points.
Consider the significance level to be set at 5%, so results less than 5% can be considered statistically significant.
Answers
The calculation of the probability and interpretation of the difference in mean and the relation to level of significance between and the treatment and control groups are as follows;
Question 1; Part A
The probability that the treatment group mean is greater than the control group mean by 8 points or more is 3.6%
The completed statement is as follows;
The significance level is set at 5%, and the probability of the result is 3.6%, which is lower than significance level. The result is statistically significant
Part B
The result is statistically significant, which implies that spraying the corn plant with the new type of fertilizer does increase the growth rate
Question 2; Part A
The probability of the treatment group mean is lower than the control group mean by 15 points or more is 7.8%
The completed statement is as follows;
The significance level is set at 5%, and the probability of the result is 7.8% which is higher than the significance level. The result is not statistically significant
Part B;
The result is not statistically significant which implies that wearing a watch does not make people manage their time better
The reason for the above solutions is as follows;
Question 1;
The known parameters;
The significance level of the test, α = 5%
The frequencies of the difference in mean between the treatment and control groups given in the table
The number of randomizations, ∑f = 1,000
The required parameter
The probability of the treatment group mean is greater than the control group mean by 8 points or more
The significance of the result
The comparison between the given level of significance and the probability
Method
We find the probability for the required difference in mean from the data given in the table
The probability that the treatment group mean is greater than the control group mean by 8 points or more is given by the following formula;
[tex]\mathbf{P(8 \ or \ more) = \dfrac{\sum f(8 \ or \ more)}{\sum f}}[/tex]
From the table, we have;
∑f(8 or more) = 26 + 8 + 2 = 36
∑f = 1 + 10 + 28 + 58 +...+ 114 + 57 + 28 + 8 + 2 = 1,000
Therefore;
[tex]P(8 \ or \ more) = \dfrac{36}{1,000} = 0.036 = 3.6\%[/tex]
The probability, P(8 or more) 3.6%
Given that the significant level, α = 5% is higher than the probability of 3.6%, the result is statistically significant
Part B
The true statement is that the result is statistically significant, which implies that spraying the corn plant with the new type of fertilizer does increase the growth rate
Question 2;
The known parameters are;
The significance level of the test, α = 5%
The frequencies of the difference in mean between the treatment and control groups given in the table
The number of randomizations, ∑f = 1,000
The required parameter
The probability of the treatment group mean is lower than the control group mean by 15 points or more
The significance of the result
The comparison between the given level of significance and the probability
Method
Using the method from Question 1, we have;
Part A
[tex]\mathbf{P(15 \ or \ more) = \dfrac{\sum f(15 \ or \ less)}{\sum f}}[/tex]
From the table, we have;
∑f(15 or more) = 50 + 18 + 10 = 78
∑f = 10 + 18 + 50 + 127 + 195 + 226 + 180 + 117 + 48 + 17 + 12 = 1,000
Therefore;
[tex]P(15 \ or \ more) = \dfrac{78}{1,000} = 0.078 = 7.8\%[/tex]
The probability, P(15 or more) = 7.8%
Given that the significant level, α = 5% is lower than the probability of 7.8%, the result is not statistically significant
Therefore, we have;
The significance level is set at 5%, and the probability of the result is 7.8% which is higher than the significance level. The result is not statistically significant
Part B
The true statement is that the result is not statistically significant which implies that wearing a watch does not make people manage their time better
Learn more about hypothesis testing here;
https://brainly.com/question/4232174
Question 1;
Part A
The significance level is set at 5%, and the probability of the result is 3.6%, which is less than the significance level. The result is statistically significant
Part B
A) The result is statistically significant, which implies that spraying the corn plants with the new type of fertilizer does increase the growth rate.
Question 2;
Part A
The significance level is set at 5%, and the probability of the result is 7.8% which is higher than the significance level. The result is NOT statistically significant
Part B;
B) The result is not statistically significant, which implies that wearing a watch does not help people manage their time better.
If I start a road trip with 10,425 miles on my auto meter and I end it with 23,840 miles showing how many miles was my trip
Answers
Answer:
13,415 miles
Step-by-step explanation:
Final position - initial position = Miles traveled:
23,840 miles - 10,425 miles = 13,415 miles
solve for x: 3x²-243
Answers
3x²–243=0 —> 3 (x²–81) = 0 —>
x²–81=0 —> (x-9)(x+9)=0
x-9=0 —> x=9
x+9=0 —> x=–9
I hope I helped you^_^
Question 2 Evaluate the expression 2(x - 3) + 3y when x = 5 and y = 3. Mark the correct answer.
A. 13
B. 15
C. 16
D. 25
Answers
Answer:
A. 13
Step-by-step explanation:
2(x - 3) + 3y
2(5 - 3) + 3×3
2× 2 + 3×3
4 + 9
13
Answer:
The correct answer is A
Step-by-step explanation:
2(x-3) + 3y so you replace them and get 2( 5 - 3) +3(3)
next,
you would solve it
2 x 5 and 2 x 3 you get 10-6 + 9, the 9 is from multiplying 3 by 3
finally you solve it
10-6 = 4 +9
= 13!
The terminal of theta is (sqrt2/2, sqrt2/2) what is tan theta?
Answers
Answer:
D
Step-by-step explanation:
tan(theta) = y/x
tan(theta) = (sqrt(2)/2)/(sqrt(2)/2)=1
Use graphing technology to find the range of the function f(x)=|x-3|
Answers
Answer:
[0,infinity)
Step-by-step explanation:
Since it's a modulus function, f(x) will have a range of [0,infinity). Use desmos for graphing it
Which function is represented by this graph?
Answers
Answer:
it is an absolute function
or more precisely
y = - I x - 1 I + 8 (shown in the screenshot)
Anyone know how to do this?
Answers
Use Euclid’s Ladder (or a factor tree) to write the prime factorization.
1. 64
2. 100
3. 54
Answers
Answer:
64
Step-by-step explanation:
the answer is 64 hope this helps
64 =
32, 2 =
16, 2, 2 =
8, 2, 2, 2 =
4, 2, 2, 2, 2 =
2, 2, 2, 2, 2 =
2^5
100 =
50, 2 =
25, 2, 2 =
5, 5, 2, 2 =
2^2 * 5^2
54 =
27, 2 =
9, 3, 2 =
3, 3, 3, 2 =
3^3 * 2
A vehicle is travelling from rest. After 10 seconds its velocity will be 20ms find acceleration?
Answers
Initial velocity (u) = 0m/s
Final velocity (v) = 20m/s
Time (t) = 10 s
Acceleration (a)
= (v - u)/t
= [(20m/s) - (0m/s)]/10s
= (20m/s)/10s
= (20m/s²)/10
=> 2m/s²
3) Suppose Sandra makes credit card purchase for $4,000 that compounds interest daily. The APR is 3%. How much interest is earned on Sandra’s card after 1 year if Sandra makes no payments? (Use the formula below for help).
A=P(1+r/n)nt
Answers
Answer:
$121.81
Step-by-step explanation:
A= 4000(1+.03/365)^365
[tex]4000\left(1+\frac{0.03}{365}\right)^{365}=4121.81305\dots[/tex]
Total interest earned on Sandra’s card after 1 year is $4,121.81
What is compound interest?Compound interest is defined as interest paid on the original principal and the interest earned on the interest of the principal.
A=P(1+r/n[tex])^{nt}[/tex]
Where:
A = the future value of the investment or loan
P = the principal investment or loan amount
r = the interest rate (decimal)
n = the number of compound periods
Given,
A=P(1+r/n[tex])^{nt}[/tex]
Sandra makes a credit card purchase for $4,000 that compounds interest daily.
P = $4,000
r =3%
t = 1 year
A=P(1+r/n[tex])^{nt}[/tex]
Substitute the values of P, r and t in the formula,
First, convert R as a percent to r as a decimal
r = R/100
r = 3/100
r = 0.03 rate per year,
Then solve the equation for A
A = P(1 + r/n)nt
A = 4,000.00(1 + 0.03/365)(365)(1)
A = 4,000.00(1 + 8.2191780821918E-5)(365)
A = $4,121.81
Therefore, total interest earned on Sandra’s card after 1 year is $4,121.81.
To learn more about the compound interest rate;
https://brainly.com/question/13307568
#SPJ5
help pls i need this done asap ty
Answers
Answer:
b) 7.89*10^4
c) 3.15*10^3
Step-by-step explanation:
2-42)
the coefficient in scientific notation (the number that is not 10^x) has to be greater or equal to 1 and less than 10. so c and b are incorrect.
b) 0.789*10^5
c) 31.5*10^2
b) 0.789*10^5
in order to make 0.789 greater than 1, I would just multiply it by 10. shown below
=0.789*10*10*10*10*10
=7.89*10*10*10*10
=7.89*10^4
c) 31.5*10^2
same concept but this time divide by 10 to make 3.15 which will add another *10 to the exponent
=31.5*10*10
=3.15*10*10*10
=3.15*10^3
Answer:
Step-by-step explanation:
I forgot
If A = {2,4,6,8,}, write the set A by description method
Answers
Step-by-step explanation:
Set-builder notation is a notation for describing a set by indicating the properties that its members must satisfy.
C={2,4,6,8}
C={2×1,2×2,2×3,2×4}
thus set builder form is:
{x:x=2n,n∈N} and this set is also call even number set in description mathod
HELP ASAP!!!!!
thanksssssss
Answers
Answer:
[tex]9(c+5)=9c+45[/tex]
Step-by-step explanation:
Multiply 9 by the variable and the number
Which one of the following equations is equivalent to 3x - 12 = -9 ?
A= 2x = 4
B= x - 5 = -6
C= x + 3 = x - 1
D= 7x - 3 = 4
Answers
Step-by-step explanation:
, it's was helpful to you
[tex]3x - 12 = - 9 \\ x - 4 = - 3 \\ x = - 3 + 4 \\ x = 1 \\ \\ 2x = 4 \\ x = \frac{4}{2} \\ x = 2 \\ \\ x - 5 = - 6 \\ x = - 6 + 5 \\ x = - 1 \\ \\ x + 3 = x - 1 \\ x - x = - 1 - 3 \\ x = - 1 - 3 \\ x = - 4 \\ \\ 7x - 3 = 4 \\ 7x = 4 + 3 \\ 7x = x \\ x = \frac{7}{7} \\ x = 1[/tex]
express y=2x²+9x+4 in the form a(x+b)²+c . where a ,b,c are constant
Answers
Answer:
2(x+9)^2 + 4
Step-by-step explanation:
.............
The water level in a plastic pool changed
by −8 gallons each hour due to a small
hole in the bottom. After 6 hours, the pool
contained 132 gallons. How much water
was in the pool originally?
Answers
Answer: 180 gallons
Step-by-step explanation:
If you take 8 times 6 you get 48, now take 132 plus 48 and you get 180.(hope this helped):)
This is Solving Linear Equations.
Answers
Answer:
x=12
Step-by-step explanation:
you have to group the like terms in order to solve this equation, this will result to;
5/2x-3/4x=14+7
1.75x/1.75=21/1.75
x=12
I hope this helps
Required solution :
The given equation is,
(5 / 2)x - 7 = (3 / 4)x + 14⇒ 5x - 14 / 2 = (3 / 4)x + 14
Transposing 14 from R.H.S. to L.H.S.,
⇒ (5x - 14 / 2) - 14 = (3/4)x
⇒ 5x - 14 - 28 / 2 = 3x / 4
⇒ 5x - 42 / 2 = 3x / 4
⇒ 4 (5x - 42) / 2 = 3x
⇒ 4 × (5x - 42) / 2 = 3x
⇒ 2 (5x - 42) = 3x
⇒ 10x - 84 = 3x
⇒ 10x - 3x = 84
⇒ 7x = 84
⇒ x = 84 / 7
⇒ x = 12
Therefore, option d that is 12 is correct.
help i m not smart at all see alot
Answers
Answer:
-3
Step-by-step explanation:
You have to bring -16 to the other side by adding.
It would make it: -7a=21
Then you hve to diving the -7.
-7a/-7=21/-7
That would equal -3
Answer:
A= -3
Step-by-step explanation:
-7a - 16 = 5
( -7a - 16) + 16 = 5 + 16
-7a - 16 + 16 = 21
-7a = 21
7a/7 = - 21/7
a = -3
Hope this helps you
Brainless please
What is the decimal equivalent of 9.7x10^5
A. 0.000097
B. 970,000
C. 9,700,000
D. 97,000,000
Answers
Answer:
B. 970,000
Step-by-step explanation:
Move the decimal 5 places to the right, since the exponent is a positive 5.
9.7 x 10⁵ = 970,000.
If it is a negative exponent, you would have to move the decimal to the left.
If the function f is given by f(x)= 4x -3, find the value of f(2+h)
Answers
[tex]\\ \sf\longmapsto f(2+h)[/tex]
[tex]\\ \sf\longmapsto 4(2+h)-3[/tex]
[tex]\\ \sf\longmapsto 4h+8-3[/tex]
[tex]\\ \sf\longmapsto 4h+5[/tex]
A polynomial has one root that equals 2 + i. Name one other root of this
polynomial.
Answers
Answer:
sorry
Step-by-step explanation:
polynomial is not given
question is incomplete
3/2x + 7/2 = 2x what is the solution to the equation
Answers
Answer:
x=7
Step-by-step explanation:
3/2x + 7/2 = 2x
Subtract 3/2x from each side
3/2x -3/2x + 7/2 = 2x-3/2x
7/2 = 2x -3/2x
Get a common denominator
7/2 = 4/2x - 3/2x
7/2 = 1/2 x
Multiply each side by 2
7/2 *2 = 1/2x*2
7 =x
Answer:
x=7
Step-by-step explanation:
im smart
3 angles
triangle
in
ratio 1:3:3
3:.
Find the angles
Answers
Answer:
1st angle = 30
2nd angle = 60
3rd angle = 90
Step-by-step explanation:
let ,1st angle be x , 2nd angle be 2x and 3rd angle be 3xx+2x +3x =1806X =180x =180/6x =30You are looking at your power bill for the month, you pay 15 cents per kilowatt-hour. Your power bill came out to $70.74 how many KWH of energy were used in your house this month?
Answers
The number of kilowatt-hours used KWH is 471.6 KWH.
Since the power bill for the month says you pay 15 cents per kilowatt-hour, this is the rate of the bill. We convert this a a dollar rate.
So, 15 cents per kilowatt-hour = 15 cents × $ 1/100 cents per kilowatt-hour (since $ 1 = 100 cents)
= 15 cents/100 × $ 1/100 cents per kilowatt-hour
= 0.15 × $ 1/100 cents per kilowatt-hour
= $ 0.15 cents per kilowatt-hour.
Since the power bill came out to be $ 70.74, we need to find the number of kilowatt-hours used KWH.
The total amount on bill = rate of bill × number of kilowatt-hours used.
So, number of kilowatt-hours used = total amount on bill/rate of bill
Total amount on bill = $ 70.74 and rate of bill = $ 0.15 cents per kilowatt-hour.
So, number of kilowatt-hours used = total amount on bill/rate of bill
number of kilowatt-hours used = $ 70.74 /$ 0.15 cents per kilowatt-hour.
number of kilowatt-hours used = 471.6 KWH
So, number of kilowatt-hours used KWH is 471.6 KWH.
Learn more about power bill here:
https://brainly.com/question/1401925
The average price for a new car is $30,000. Each year, the value of that car decreases by 15%.
Explain the meaning of the y-intercept, appropriate domain and range, and whether the function is increasing or decreasing.
Answers
Answer:
y int: The starting value. Domain: All Real Numbers. Range: y<=30,000. The Function is decreasing
Step-by-step explanation:
The y int. is the starting value because it is the point where no years have started yet on the x axis so that means that the value of the car will be as if you had just bought it. The domain is all real numbers because the number of years you could have the car could be infinate. The range is the y axis part meaning that it could be any number starting from 30,000 and decreasing because the car value is constantly decreasing. And due to the fact that the price is going down every year by 15%, the function is decreasing.
how many solutions does the equation below have? 3x-8=-2x+9/3
Answers
Answer:
1
Step-by-step explanation:
[tex]\\ \sf\longmapsto 3x-8=-2x+\dfrac{9}{3}[/tex]
[tex]\\ \sf\longmapsto 3x-8=-2x+3[/tex]
[tex]\\ \sf\longmapsto 3x+2x=3+8[/tex]
[tex]\\ \sf\longmapsto 5x=11[/tex]
[tex]\\ \sf\longmapsto x=\dfrac{11}{5}[/tex]
19= 7z -2z
-------------
Answers
Answer:
19 = 7z - 2z
19 = 5z
z = 19/5
Hope this helps!
Answer:
z = 3.8
Step-by-step explanation:
19 = 7z - 2z
19 = 5z
19/5 = z
3.8 = z
Identify the table function represented by f(x)=4•3×
Answers
Answer: exponential growth
Step-by-step explanation:
Answer:
Exponential functions have a horizontal asymptote. The equation of the horizontal asymptote is y=0.Horizontal Asymptote: y=0.
Can you please answer this answer with a step by step explanation?
the BEST answer gets the BRAINLIEST answer mark!
Answers
Answer:
Step-by-step explanation:
If K is square number, then exponents in number N are even.
