Answer:
n ∝ (1/l) (√F/m)
Step-by-step explanation:
Since frequency, n of vibration of a stretched string is a function of its tension F, the length l and the mass per unit length m, and has dimensions [T]⁻¹ where T = time, its dimension must be equal to that of the combination of F, L and m
Since n = f(F,L,m)
n = kFᵃLᵇmˣ
dimension of n = (dimension of F)ᵃ × (dimension of L)ᵇ × (dimension of m)ˣ
Since n = frequency, dimension of n = [T]⁻¹
F = Force, dimension of F = [M][L][T]⁻²
Also, L = length, dimension of L = [L] and
m = mass per unit length, dimension of m = [M][L]⁻¹
So, n = FᵃLᵇmˣ
[T]⁻¹ = ([M][L][T]⁻²)ᵃ( [L] )ᵇ([M][L]⁻¹)ˣ
[T]⁻¹ = ([M]ᵃ[L]ᵃ[T]⁻²ᵃ[L]ᵇ([M]ˣ[L]⁻ˣ
[M]⁰[L]⁰[T]⁻¹ = ([M]ᵃ ⁺ˣ)([L]ᵃ ⁺ ᵇ ⁻ˣ)([T]⁻²ᵃ)
equating the exponents on both sides, we have
a + x = 0 (1 )⇒ x = -a
a + b - x = 0 (2) ⇒
-2a = -1 (3) ⇒ a = 1/2
Substituting x into 2, we have
a + b -(-a) = 0
a + b + a = 0
2a + b = 0
b = -2a
b = -2 (1/2)
b = -1
x = -a = -1/2
So, substituting the variables into n, we have
n = kFᵃLᵇmˣ
n = kFᵃLᵇmˣ
[tex]n = kF^{\frac{1}{2} }L^{-1}m^{-\frac{1}{2} }[/tex]
n = k/l(√F/m)
n ∝ (1/l) (√F/m)
(6,1) (7, 2) (8, 2) (9, 1) is this a function
Answer:
Function
Step-by-step explanation:
This is a function
Each input goes to only one output
For each of the following, shade the portion of the Venn diagram that illustrates the set. ( A ∩ B ) ∪ ( A ∩ C )
Answer:
Here's what that would look like on a venn diagram
Step-by-step explanation:
If the width of the rectangle increases by 4 and the length decreases by 3, by how much will the area change? Express the difference as a simplified expression (View attachment)
Answer:
this might be the answer..
Step-by-step explanation:
m²+6m+9
One number is two greater than another—the product of the numbers 1s 143. Find the numbers. One pair of numbers, both of which are positive, is _____
Answer:
11 and 13
Step-by-step explanation:
The square root of 144 is 12 so the numbers must be close to that
since one number is two greater go up 1 and down 1 from 12
12 - 1 = 11
12 + 1 = 13
11 * 13 = 143
What is the range for any polynomial function with an odd degree? Why?
Answer:
All real numbers
[tex]( - \infty . + \infty )[/tex]
Step-by-step explanation:
because the domain is R and range depends of domain and it also depends on the leading coefficient
for example f(x) = x^3+1
the range is
[tex]y \geqslant 1[/tex]
When sample size increases:____.
A. Standard deviation of the sample mean increases.
B. Confidence interval remains the same.
C. Confidence interval increases.
D. Confidence interval decreases.
Answer:
D. Confidence interval decreases.
Step-by-step explanation:
Central Limit Theorem
The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]
When sample size increases:
The standard deviation of the sample mean is:
[tex]s = \frac{\sigma}{\sqrt{n}}[/tex]
That is, it is inversely proportional to the sample size, so if the sample size incerases, the standard deviation decreases, and so does the confidence interval.
This means that the correct answer is given by option D.
can anyone help???????????
Given:
The distance between the two buildings on a map = 14 cm
The scale is 1:35000.
To find:
The actual distance in km.
Solution:
The scale is 1:35000.
It means 1 cm on map = 35000 cm in actual.
Using this conversion, we get
14 cm on map = [tex]14\times 35000[/tex] cm in actual.
= [tex]490000[/tex] cm in actual.
= [tex]4.9\times 1000o0[/tex] cm in actual.
= [tex]4.9[/tex] km in actual. [tex][1\text{ km}=100000\text{ cm}][/tex]
Therefore, the actual distance between two buildings is 4.9 km.
In the figure, ∆AMH ≅ ∆HTA by Side-Side-Side (SSS). Which angles are congruent by CPCTC?
Answer:
it is option a. pls mark me brainliest. hope this helps you
Triangle A'B'C' is the image of triangle ABC after a dilation with a scale factor of 1/2 and centered at point A. Is triangle ABC congruent to triangle A'B'C'? Explain your answer.
Answer:
See below
Step-by-step explanation:
Congruent means having the same size and shape.
If triangle A'B'C' is the image of triangle ABC after a dilation with a scale factor of 1/2 then the two triangles will not acquire the same size
This is because when a shape undergoes a dilation the dilated image is either larger or smaller and can therefore not maintain the same size as the pre image. Hence the triangles are not congruent.
Triangle ABC is not congruent to triangle A'B'C'
How to determine the congruent statement?The triangles are given as:
Triangle ABC and A'B'C'
The other parameters are:
Scale factor, k = 1/2
Center = Point A
Since the scale factor is not 1, then the triangles would not be congruent; but they would be similar
Hence, triangle ABC is not congruent to triangle A'B'C'
Read more about dilation at:
https://brainly.com/question/9791066
Evaluate 64 to the power of 2/3
Answer:
[tex]16[/tex]
Step-by-step explanation:
[tex] {64}^{ \frac{2}{3} } \\ {2}^{6 \times \frac{2}{3} } \\ {2}^{ \frac{12}{3} } \\ {2}^{4} \\ = 16[/tex]
hope this helps you
have a nice day!
Answer:
16
Step-by-step explanation:
Using the rule of exponents/ radicals
[tex]a^{\frac{m}{n} }[/tex] = [tex](\sqrt[n]{a}) ^{m}[/tex] , then
[tex]64^{\frac{2}{3} }[/tex] = [tex](\sqrt[3]{64}) ^{2}[/tex] = 4² = 16
During the past year, Zara and Ivan each read 2 books, but George read 7, Ali read 12, and Marsha read 25. The median number of books read by these individuals was A. 10. B. 9. C. 2. D. 7.
Answer:
D = 7
Step-by-step explanation:
To find the median, we must first list the amount of books each person read, and then put them in order.
2, 2, 7, 12, 25
These are already in order from smallest to greatest, which is awesome. We can then cross out one number from each side until we end up with either one or two numbers. We then find the average of those 1 or 2 numbers to find our median.
2, 3, 7, 12, 25
cross 2 and 25 out
3, 7, 12
cross 3 and 12 out
7
Our median is thus 7
Beth corbin's regular hourly wage are is $16,and she receives an hourly rate of $24 for work in excess of 40 hours. During a January pay period,Beth works 45 hours. Beth's federal income tax withholding is $95, she has no voluntary deductions, and the FICA tax rate is 7.65%. Compute Beth corbi's gross earnings and net pay for the pay period
Answer:
$760 gross
$614.13 is net
Step-by-step explanation:
Beth earns $16 x 40 for the first 40 hours she works.
Then she earns overtime--> 5 hours at $24 per hour
Her "gross" earnings are before any deductions or taxes.
So 16x40 = 640 and 5x24= 120 so her January gross earnings are 640+120=
$760 gross
Her "net" pay is what is left over after taxes.
So take the $760 and subtract the $95 withholding = $665
Taxes are 7.65% so multiply 665 x 0.0765 = 50.8725 and subtract that also.
614.1275 rounded to $614.13 is net.
Find the sum and difference (first mixed number minus the second mixed number) for the following pair of mixed numbers. The answer should be written as a mixed number.
Answer:
Sum = 15 8/15, Difference = 1 2/15
Step-by-step explanation:
8⅓, 71/5
A. Sum
8⅓ + 7 1/5
Convert to improper fraction
25/3 + 36/5
Find the LCM of 3 and 5. The result is 15. Divide 15 by the denominator of each fraction and multiply the result obtained with the numerator. The result is shown below:
[(25×5) + (36×3)] / 15
[125 + 108] / 15
233 / 15
Convert to mixed fraction
15 8/15
B. Difference
8⅓ – 7 1/5
Convert to improper fraction
25/3 – 36/5
Find the LCM of 3 and 5. The result is 15. Divide 15 by the denominator of each fraction and multiply the result obtained with the numerator. The result is shown below:
[(25×5) – (36×3)] / 15
[125 – 108] / 15
17 / 15
Convert to mixed fraction
1 2/15
SUMMARY:
Sum = 15 8/15, Difference = 1 2/15
Use Simpson’s Rule with n = 10 to approximate the area of the surface obtained by rotating the curve about the x-axis. Compare your answer with the value of the integral produced by your calculator.
Answer:
The answer is "7.248934".
Step-by-step explanation:
The area of the curve obtained after rotating it about the x-axis is :
[tex]2 \pi \int^2_1 y \sqrt{1+ \{ \frac{dy}{dx}\}^2 \ dx}\\\\y=x\ \ln \ x \ And \ \frac{dy}{dx}=1+ \lh\ x[/tex]
So, The area of the curve obtained after rotating it about the x-axis is : [tex]2 \pi \int^2_1 (x \ln \ x) \sqrt{(\ln\ x)^2+ 2 \ln \ x+ 2\ dx}\\\\[/tex]
Simpson's rule approximation with n=10 is:
[tex](\frac{1}{3})\times (0.1) \times ( f(1) + 4 \times f(1.1) + 2\times f(1.2) + 4 \times f(1.3) + 2 \times f(1.4) + 4 \times f(1.5) + 2 \times f(1.6) + 4 \times f(1.7) + 2 \times f(1.8) + 4 \times f(1.9) + f(2) ) = 7.248933= 7.248934[/tex]
Write an expression to represent the perimeter of a rectangle with a length of 4x+14 and a width of 2x-9. Simplify your answer.
Answer:
[tex]{ \boxed{ \bf{formular : } \: \tt{perimeter = 2(length + width)}}} \\ perimeter = 2((4x + 14) + (2x - 9)) \\ perimeter = 2(6x + 5) \\ perimeter = 12x + 10 \\ \\ { \tt{expression : 12x + 10}} \\ \\ { \underline{ \blue{ \tt{becker \: jnr}}}}[/tex]
Answer these please!!!
Answer:
(upper left) 3 triangles
(upper right) 5 triangles
(lower left) 9 rectangles
(lower right) next pattern is a grid that is 8 by 8.
The pattern is the previous side multiplied by 2
first block is 1x1
second block is 2x2
third block is 4x4
next block would be 8x8
Step-by-step explanation:
Find the value of y for a given value of x, if y varies directly with x. If y = 0.15 when x = 1.5, what is y when x = 6.3? a. –0.63 b. 0.63 c. 63 d. –63 Please select the best answer from the choices provided A B C D
Answer:
b
Step-by-step explanation:
I believe its b, because1.5 is 10 times 0.15
and 6.3 is 10 times 0.63
What is the formula of a palindrome?
Answer:
For example, 6(1001) + 3(110) = 6006 + 330 = 6336 is a palindrome. Since 11 is a factor of both 1001 and 110, we conclude that all four digit palindromes are divisible by 11.
find the surface area of the composite figure
Answer:
276 cm^2
Step-by-step explanation:
Separate figure into triangular and rectangular prisms.
SA of triangular prism (finding each area of a face and add them all up)
4 x 5 = 20 cm^2
13 x 4 = 52 cm^2
1/2 x 12 x 5 = 30 cm^2
1/2 x 12 x 5 = 30 cm^2
20 + 52 + 30 + 30 = 132 cm^2
SA of triangular prism is 132 cm^2
SA of rectangular prism (do the same thing):
12 x 4 = 48 cm^2
12 x 3 = 36 cm^2
12 x 3 = 36 cm^2
3 x 4 = 12 cm^2
3 x 4 = 12 cm^2
48 + 36 +36 + 12 + 12 = 144
Add the SA OF BOTH PRISMS:
144 + 132 = 276 cm^2
What are the odds against choosing a red marble from a bag that contains two blue marbles, one green marble, seven white marbles, and four red marbles?
Answer:
4/14
Step-by-step explanation:
2+1+7+4=14
red marbles are 4/14
Answer:
2/7
Step-by-step explanation:
Probability = Number of ways event can occur/ total number of possible outcomes.
Total number of possible outcomes = 2+1+7+4=14 = 4/14.
And if you break that down, 2 will go into four, twice and into fourteen, seven times = 2/7.
Brainliest?
Liner equation with a rapid change over time
Answer:
y=130(2.5) ^(x-1)
Step-by-step explanation:
This should give you an exponential growth curve. I'm assuming this is what you meant by "rapid change over time".
Use the following rules/intervals: Function 1: (-∞, -5) Function 2: [-5, 0) Function 3: [0,5) Function 4: [5, ∞) If the function is undefined over a given interval then pick another function and include an explanation as to why the original function did not work. Make one of the functions linear, one of the functions square root, one of the functions absolute value, and the last function either exponential, quadratic or square root (one that you will be able to graph).
Answer:
67.87
Step-by-step explanation:
One canned juice drink is 15% orange juice; another is 5% orange juice. How many liters of each should be mixed together in order to get 10 L that is 10% orange juice?
Please help!
Answer:
9 liters of 15% orange juice and 1 liter of 5 % orange juice
Step-by-step explanation:
2.) Find the zeros of the quadratic function y = x2 – 3x + 2 by factoring method.
Answer:
The zeros are 1 and 2
Step-by-step explanation:
Given
[tex]y =x^2 - 3x + 2[/tex]
Required
The zeros
[tex]y =x^2 - 3x + 2[/tex]
Expand
[tex]y =x^2 - 2x-x + 2[/tex]
Factorize
[tex]y =x(x - 2)-1(x - 2)[/tex]
Factor out x - 2
[tex]y =(x - 1)(x - 2)[/tex]
Set to 0
[tex](x - 1)(x - 2)=0[/tex]
Solve for x
[tex]x - 1 = 0 \to x =1[/tex]
[tex]x - 2 = 0 \to x =2[/tex]
Hence, the zeros are 1 and 2
Somebody please help asap
Answer:
B. [tex] 4x^2 + \frac{3}{2}x - 7 [/tex]
Step-by-step explanation:
[tex] f(x) = \frac{x}{2} - 3 [/tex]
[tex] g(x) = 4x^2 + x - 4 [/tex]
(f + g)(x) = f(x) - g(x)
= [tex] \frac{x}{2} - 3 + 4x^2 + x - 4 [/tex]
Add like terms
[tex] = 4x^2 + \frac{x}{2} + x - 3 - 4 [/tex]
[tex] = 4x^2 + \frac{3x}{2} - 7 [/tex]
[tex] = 4x^2 + \frac{3}{2}x - 7 [/tex]
A sports trainer has monthly costs of $80 for phone service and $40 for his website and advertising. In addition he pays a $15 fee to the gym for each session in which he works with a client.
Required:
a. Write a function representing the average cost
b. Find the number of sessions the trainer needs if he wants the average cost to drop below $16 per session.
Answer:
Step-by-step explanation:
The average cost for the training session provided he is a sports trainer can be computed as follows:
Let's assume that;
average cost = C(x)
the no. of session = x
Then:
[tex]C(x) = \dfrac{\text{Total cost}}{\text{no. \ of sessions}}[/tex]
[tex]C(x) = \dfrac{\text{80 + 40 + 15x}}{\text{x}}[/tex]
[tex]C(x) = \dfrac{\text{120+ 15x}}{\text{x}}[/tex]
Now, suppose the trainer wants the average cost C(x) to drop below $16;
Then, we have the following function:
[tex]\dfrac{120+15x}{x}\leq C(x)[/tex]
[tex]\dfrac{120+15x}{x}\leq16[/tex]
By cross multiply:
120 + 15x ≤ 16x
120 ≤ 16x - 15x
120 ≤ x
Therefore, the required no. of session, if the average cost should drop below $16, is 120.
Following are the solution to the required points:
Assuming that he's also a sports trainer, the typical cost of such a training program is just as follows:Total cost = C(x)
Total session = x
Then:
[tex]\to C(x)=\frac{\text{Total cost}}{\text{Total sessions}}=\frac{80+40+15x}{x}= \frac{120+15x}{x}[/tex]
Assume the trainer desires that the average cost C(x) be less than $16. So function is therefore available:[tex]\to \frac{120+15x}{x} \leq C(x)\\\\\to \frac{120+15x}{x} \leq 16\\\\[/tex]
By cross multiply:
[tex]\to 120 + 15x \leq 16x\\\\\to 120 \leq 16x - 15x\\\\ \to 120 \leq x[/tex]
As a result, if the average cost drops below $16, the required number of sessions is 120.
Learn more:
brainly.com/question/24859268
Solve the following system of equations graphically on the set of axes below.
y= x+2
y= -1/2x+8
Hi there!
»»————- ★ ————-««
I believe your answer is:
(4,6)
»»————- ★ ————-««
Here’s why:
I have graphed the two equations in a program. The point of intersection would be the solution to the system.When graphed, the lines intersect at point (4, 6). (4,6) is the solution.⸻⸻⸻⸻
See the graph attached.
⸻⸻⸻⸻
»»————- ★ ————-««
Hope this helps you. I apologize if it’s incorrect.
*An Old man bought a goat for R60us and sold it for R70. Then Bought it back for R80us and sold it for R90us .Whats the profit he made ?*
A. R10
B. R20
C. R0
D. R-20
Answer:
20
Step-by-step explanation:
(90+70)-(80+60)=20
just minus the total selling price to the total cost price
how do I find angle 1?
Answer:
60º
Step-by-step explanation:
The two triangles on the left are equilateral as the sides are all conguent.
The angles of an equilateral triangle are all 60º
Therefor the two angles to the left of angle 1 are both 60º for a combined value of 120º
Angle 1 must be 180 - 120 = 60º
To find angle 1, you have to add all adjacent angles, which equal 180°
Amanda buye a book for $7.85. If the tax added on to the price lis $0.75 how much will the book cost in total? What if Amanda donates SLSO to the Love of Reading Foundation? How will thie affect the total coet of the book? (Hint: there is no tax added on to the donation). Estimate what the total cost will be and then check your answer.
Answer:
$8.60 I don't know what SLSO means
Step-by-step explanation: