The final speed v2 is √6 times the initial speed v1, when the net force is 2f1 and the object moves the same distance d while the force is being applied.
We can use the work-energy theorem to solve this problem, which states that the work done on an object by a net force is equal to the change in its kinetic energy.
When the force has magnitude f1 and the object moves a distance d, the work done is:
W = f1 * d
This work changes the kinetic energy of the object from zero to (1/2) * m * v1^2, where m is the mass of the object. Therefore, we have:
f1 * d = (1/2) * m * v1^2
Solving for v1, we get:
v1 = sqrt((2 * f1 * d) / m)
Now, when the net force has magnitude f2 = 2f1 and the object moves the same distance d, the work done is:
W = f2 * d = 2f1 * d
This work changes the kinetic energy of the object from (1/2) * m * v1^2 to (1/2) * m * v2^2, where v2 is the final speed of the object. Therefore, we have:
2f1 * d = (1/2) * m * (v2^2 - v1^2)
Solving for v2, we get:
v2 = sqrt(v1^2 + (4 * f1 * d) / m)
Substituting the expression for v1, we get:
v2 = sqrt((4 * f1 * d) / m + (2 * f1 * d) / m)
Simplifying, we get:
v2 = sqrt(6) * v1
Therefore, the final speed v2 is sqrt(6) times the initial speed v1.
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What is the domain of the function y=2~/x-6 ?
A singular value decomposition of A is as follows: A = UΣV^Τ = 0.5 -0.5 0.5 -0.5 [5 0] 0.5 0.5 -0.5 -0.5 [0 5] [0.8 0.6]
0 5 -0.5 -0.5 0.5 [0 0] [0.6 -0.8]
0.5 0.5 0.5 0.5 [0 0] Find the least-squares solution of the linear system AX = b, where b = [ 3 ]
[ 3 ]
[-1 ]
[-4 ]
x1 = ____
x2 = ____
The least-squares solution of the linear system AX = b, x1 = -1.2 and x2 = 0.8.
To solve for the least-squares solution of the linear system AX = b, we need to use the formula X = VΣ^(-1)U^Tb.
First, we need to calculate the inverse of Σ by taking the reciprocal of the non-zero diagonal elements and setting the zero diagonal elements to zero. So,
Σ^(-1) = [1/5 0]
[0 1/5]
Next, we calculate U^Tb by multiplying U^T and b:
U^Tb = [-3]
[ 1]
[-4]
[ 3]
Now, we can calculate X:
X = VΣ^(-1)U^Tb
= [ 0.8 0.6][1/5 0][-3]
[-0.6 0.8][0 1/5][ 1]
[0 0 ][-4]
[0 0 ][ 3]
= [-1.2]
[ 0.8]
[ 1.6]
[ 0.6]
Therefore, the least-squares solution are x1 = -1.2 and x2 = 0.8.
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Given the following confidence interval for a population mean, compute the margin of error, E.16.86 < µ < 17.66
E = 0.40
The margin of error, E, for the given confidence interval 16.86 < µ < 17.66 is calculated as follows:
E = (upper bound of the confidence interval – lower bound of the confidence interval) / 2
E = (17.66 – 16.86) / 2
E = 0.80 / 2
E = 0.40
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For the simple harmonic motion described by the trigonometric function, find the maximum displacement, the frequency, the value of d when t = 5, and the least positive value of t for which d = 0. Use a graphing utility to verify your results.
The maximum displacement is A, the frequency is ω/2π, the value of d when t = 5 is A * cos(ω*5 + φ), and the least positive value of t for which d = 0 is (π/2 - φ)/ω.
The equation for simple harmonic motion is d = A * cos(ωt + φ), where d is the displacement, A is the amplitude, ω is the angular frequency, t is the time, and φ is the phase shift.
To find the maximum displacement, we need to find the value of A. The maximum displacement occurs when cos(ωt + φ) = 1, so A is the maximum displacement.
To find the frequency, we need to find the value of ω. The frequency is given by f = ω/2π, so we can rearrange this equation to find ω = 2πf.
To find the value of d when t = 5, we can simply plug t = 5 into the equation for d and solve.
To find the least positive value of t for which d = 0, we need to find the value of t that makes cos(ωt + φ) = 0. This occurs when ωt + φ = π/2 + 2πn, where n is an integer. We can rearrange this equation to find t = (π/2 + 2πn - φ)/ω. The least positive value of t will occur when n = 0, so we can plug n = 0 into the equation and solve for t.
Finally, we can use a graphing utility to verify our results. We can graph the equation for d and look at the maximum displacement, the frequency, the value of d when t = 5, and the least positive value of t for which d = 0.
Overall, the maximum displacement is A, the frequency is ω/2π, the value of d when t = 5 is A * cos(ω*5 + φ), and the least positive value of t for which d = 0 is (π/2 - φ)/ω.
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I need help quickly || 4.72 x 56 = ___.
26,432
4,472
264.32
44.72
Answer:264.32
Step-by-step explanation: multiply 4.72 x 56 to get the answer of 264.32
Answer:
hdhdieidjdjjdjdjdufufifuififif
Write the Riemann sum to find the area under the graph of the function f(x) = x3 from x = 2 to x = 5.
the summation from i equals 1 to n of the product of the 3rd power of the quantity 2 plus 5 times i over n and 3 over n
the summation from i equals 1 to n of the product of the 3rd power of the quantity 2 times i over n and 3 over n
the limit as n goes to infinity of the summation from i equals 1 to n of the product of the 3rd power of the quantity 3 times i over n and 3 over n
the limit as n goes to infinity of the summation from i equals 1 to n of the product of the 3rd power of the quantity 2 plus 3 times i over n and 3 over n
The area under the curve is then approximated by the sum of the areas of n rectangles of height [(2 + (3i/n))³] and width (3/n), which represents the Riemann sum.
What is the area of the rectangle?
To find the area of a rectangle, we multiply the length of the rectangle by the width of the rectangle.
The correct Riemann sum to find the area under the graph of the function f(x) = x³ from x = 2 to x = 5 is:
the limit as n goes to infinity of the summation from i equals 1 to n of the product of the 3rd power of the quantity 2 plus 3 times i over n and 3 over n
This can be written as:
lim(n → ∞) ∑(i=1 to n) [(2 + (3i/n))³ * (3/n)]
Here, the interval [2, 5] is divided into n subintervals of equal width (Δx) = (5 - 2)/n = 3/n.
The right endpoint of each subinterval is represented by (2 + (3i/n)), and the function value at that endpoint is given by [(2 + (3i/n))³].
The area under the curve is then approximated by the sum of the areas of n rectangles of height [(2 + (3i/n))³] and width (3/n), which represents the Riemann sum.
As n approaches infinity, the width of the rectangles approaches zero, and the sum becomes an integral that represents the exact area under the curve.
Hence, The area under the curve is then approximated by the sum of the areas of n rectangles of height [(2 + (3i/n))³] and width (3/n), which represents the Riemann sum.
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mymaths speed harder questions
Answer:
its true
Step-by-step explanation:
maths may be difficult, but if you practice it, you'll be able to solve any maths question
in january 1906 the magnitude of the earthquake in ecuador colombia was 8.8 on the richter scale. july 1971 the earthquake in papua new guinea has 5 times lower amplitude than the ecuador colombia earthquake. what was the magnitude of the earthquake in papua new guinea? round your answer to the nearest tenth
A . 1.8
B . 3.8
C . 8.1
D . 9.5
What is 4,500 milliliters equivalent to in liters
Answer:
4.5 liters
Step-by-step explanation:
1 liter = 1000 milliliters
4500 milliliters = ? liters
We take
4500 / 1000 = 4.5 liters
So, 4,500 milliliters is equivalent to 4.5 liters.
Answer:
4.5 liters
Step-by-step explanation:
1 liter = 1000 milliliters
To get your answer, just divide by 1000.
4500 / 1000 = 4.5 liters
May I please have a Brainliest? I put a lot of thought and effort into my answers, so I would really appreciate it!
Your answer must be simplified
-7x > 10
Solve for x
Answer:
x<10/7
Step-by-step explanation:
-7x>10
divide both sides by -7
-7x/-7>10/-7
x>-10/7
so,
x<10/7
Answer:
[tex]\boxed{\tt x=-\cfrac{10}{7}\: or\:\tt -1.428571}[/tex]
Step-by-step explanation:
[tex]\tt -7x > 10[/tex]
Divide both sides by -7:-
[tex]\tt \cfrac{-7x}{-7} > \cfrac{10}{-7}[/tex]
[tex]\tt x=-\cfrac{10}{7}[/tex]
or
[tex]\tt -1.428571[/tex]
________________________
Hope this helps!
One year, the population of a city was 50,000. Several years later it was 57,000. Find the percent increase
Answer:the percentage increase is 14%
Step-by-step explanation:the difference between 57000 and 50000=7000
so therefore
% increase=7000/50000*100%
=14%
three puls sevendfive
Answer:
78
Step-by-step explanation:
[tex]75+3[/tex]
All we have to do is add 3 to the number 75.
We can do this by counting.
76, 77, 78
So 75 + 3 = 78
Answer:
3 + 75 = 78
Step-by-step explanation:
Split the 75 to make 70 and 5. Now add 3 to the 5.
3 + 5 = 8
Now add the 70 back to the 8. Now you have 78.
You could also count up from 70 3 times. 76 77, 78
a company produces optical-fiber cable with a mean of 0.7 flaws per 100 feet. what is the probability that there will be exactly 4 flaws in 1400 feet of cable? round your answer to four decimal places.
The probability that there will be exactly 4 flaws in 1400 feet of cable is 2.39 x 10^-6.
Given that a company produces optical-fiber cable with a mean of 0.7 flaws per 100 feet. To find the probability that there will be exactly 4 flaws in 1400 feet of cable, we have to use the Poisson probability distribution formula.Poisson Probability Distribution Formula:
The probability of x successes in a Poisson experiment is given by:
P(x; λ) = (e-λ λx)/x!
Where,
λ = mean rate of success per unit time or unit area or unit volume.In the given question,
λ = 0.7 flaws per 100 feet = 0.7/100 = 0.007 flaws per feet
Total distance of cable = 1400 feet
Let x = number of flaws in 1400 feet of cable
To find:
P (x = 4), λ = 0.007 and x = 4
Putting the values in the Poisson probability distribution formula:
[tex]P(x = 4; 0.007) = (e^-0.007 × 0.007^4)/4! = (0.00005736)/24 = 2.39 x 10^-6[/tex]
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Evaluate ln 4.
0.60
0.92
1.38
1.39
We discοver the expression ln4 is apprοximately 1.386. The answer is 1.39, which is option d.
Dοes rοughly mean an estimate?Apprοximate implies "tο estimate" as a verb. A prοcess οf lοgic οr mathematics is implied by using the wοrd apprοximate as οppοsed tο the phrase guess. Yοu cοuld predict a friend's height based οn the initial figure that thοughts οf, but yοu can alsο get an idea οf his height by cοmpared it tο yοur οwn.
Is the wοrd "rοughly" a guess?The actiοn οf estimating sοmething, οr making a guess abοut its amοunt, quality, οr anοther feature, is knοwn as a guess. A persοn οr thing that apprοximates sοmething else but dοes nοt quite match cοuld be the result οf a flaw in cοnstructiοn οr a design flaw.
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Complete question:
Vector A⃗ points in the negative y direction and has a magnitude of 9 units. Vector B has twice the magnitude and points in the positive x direction.
A)Find the direction and magnitude of A +B. Express your answer as a whole number.
B)|A+B| =?
C)Find the direction and magnitude of A −B .
D)|A −B | = ?
E)Find the direction and magnitude of B −A.
F)|B −A| =
|A + B| = √405 ≈ 20.1
The direction of B - A is 26.6°, and the magnitude is 20.1 units.
To find the direction and magnitude of A + B, we first need to find the x and y components of each vector. The x component of vector A is 0 since it points in the negative y direction, and the y component is -9. The x component of vector B is 18 since it points in the positive x direction and has twice the magnitude of vector A, and the y component is 0.
Now we can add the x and y components of each vector to find the components of A + B:
x component of A + B = 0 + 18 = 18
y component of A + B = -9 + 0 = -9
To find the magnitude of A + B, we can use the Pythagorean theorem:
|A + B| = √(182 + (-9)2) = √(324 + 81) = √405 ≈ 20.1
To find the direction of A + B, we can use the inverse tangent function:
tan-1(y/x) = tan-1(-9/18) = -26.6°
So the direction of A + B is -26.6°, and the magnitude is 20.1 units.
To find the direction and magnitude of A - B, we can subtract the x and y components of each vector:
x component of A - B = 0 - 18 = -18
y component of A - B = -9 - 0 = -9
The magnitude of A - B is:
|A - B| = √((-18)2 + (-9)2) = √(324 + 81) = √405 ≈ 20.1
The direction of A - B is:
tan-1(y/x) = tan-1(-9/-18) = 26.6°
So the direction of A - B is 26.6°, and the magnitude is 20.1 units.
To find the direction and magnitude of B - A, we can subtract the x and y components of each vector in the opposite order:
x component of B - A = 18 - 0 = 18
y component of B - A = 0 - (-9) = 9
The magnitude of B - A is:
|B - A| = √(182 + 92) = √(324 + 81) = √405 ≈ 20.1
The direction of B - A is:
tan-1(y/x) = tan-1(9/18) = 26.6°
So the direction of B - A is 26.6°, and the magnitude is 20.1 units.
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Cual es el resultado de (3/4)²
Answer:
Step-by-step explanation:
1. (3/4)^2 = 3/4 * 3/4
2. numerator * numerator so 3 * 3 = 9
3. denominator * denominator so 4 * 4 = 16
Hence, the answer is 9/16
Step-by-step explanation:
(3/4)² = 3²/4² = 9/16
(a×b×c×d×...×z)² = a²×b²×c²×d²×...×z²
Given f(x) = x2 – 7x + 12 and g(x) = x2 – x – 6, find the y-intercept of open parentheses g over f close parentheses of x
0
–2
2 over 3
negative one half
The y-intercept of open parentheses g over f close parentheses of x is negative one half.
What is an intercept?
The x-intercept and y-intercept of a line are the locations where the line intersects the axis.
We are given two functions as
f(x) = [tex]x^{2}[/tex] - 7x + 12
g(x) = [tex]x^{2}[/tex] - x - 6
So,
[tex]\frac{g(x)}{f(x)}[/tex] = [tex]\frac{ x^{2} - x - 6}{x^{2} - 7x + 12}[/tex]
We know that the y-intercept is the point where x is equal to zero.
So, by substituting x = 0 in the above function, we get
⇒[tex]\frac{g(x)}{f(x)}[/tex] = [tex]\frac{ x^{2} - x - 6}{x^{2} - 7x + 12}[/tex]
⇒[tex]\frac{g(0)}{f(0)}[/tex] = [tex]\frac{ 0^{2} - 0 - 6}{0^{2} - 0 + 12}[/tex]
⇒[tex]\frac{g(0)}{f(0)}[/tex] = [tex]\frac{ - 6}{12}[/tex]
⇒[tex]\frac{g(0)}{f(0)}[/tex] = [tex]\frac{ - 1}{2}[/tex]
Hence, the y-intercept of open parentheses g over f close parentheses of x is negative one half.
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Find the value of h that causes the system (x + y- 2z = -1 2x + hy - z = 3 x + 3y + 2z =1) to be inconsistent.
The value of h that causes the system to be inconsistent is h = 15. the value of h that causes the system to be inconsistent, we can use the determinant method.
The determinant of a system of equations is given by : [tex]| a b c || d e f || g h i |[/tex]
Where a, b, c, d, e, f, g, h, and i are the coefficients of the variables in the system of equations. If the determinant is equal to zero, then the system is inconsistent.
For the given system of equations:[tex]x + y - 2z = -12x + hy - z = 3x + 3y + 2z = 1[/tex]
The determinant is:
[tex]| 1 1 -2 || 2 h -1 || 1 3 2 |[/tex]
Determinant by using the formula:
[tex]D = aei + bfg + cdh - ceg - bdi - afh[/tex]
Plugging in the values from the determinant:
[tex]D = (1)(-1)(2) + (1)(-1)(3) + (-2)(2)(3) - (-2)(-1)(3) - (1)(2)(2) - (1)(h)(-1)[/tex]
Simplifying:
D = -2 - 3 - 12 + 6 - 4 + h
D = -15 + h
For the system to be inconsistent, the determinant must be equal to zero: -15 + h = 0, Solving for h: h = 15. Therefore, the value of h that causes the system to be inconsistent is h = 15.
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Adrian has a length of a network cable. it can be cut into exactly 9cm or 15cm lengths. What is the shortest length that Adrian’s cable could be?
The shortest length that Adrian’s cable could be is 3cm.
How to calculate the shortest length that Adrian’s cable could beTo find the shortest length of Adrian's cable, we need to find the greatest common divisor (GCD) of 9cm and 15cm.
The GCD is the largest positive integer that divides both 9 and 15 without leaving a remainder.
We can use the Euclidean algorithm to find the GCD:
15 = 1 x 9 + 6
9 = 1 x 6 + 3
6 = 2 x 3 + 0
Since the remainder is 0 when we divide 6 by 3, the GCD of 9 and 15 is 3cm.
Therefore, Adrian's cable must be a multiple of 3cm in length in order to be cut into either 9cm or 15cm lengths.
The shortest possible length of the cable that satisfies this condition is 3cm.
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what ratio is equivelant to 36:27
Answer:
Therefore, 36/27 simplified to lowest terms is 4/3.Step-by-step explanation:
i hope this answer helpful for you
evaluate the expression 3•5x when x =3
Answer:
45.
Step-by-step explanation:
Given: 3×5x when x = 3.
First write in x:
3×5×3, when two digits, or variables are together, there's always a multiplication sign.
Then calculate:
3×5×3
15×3
= 45
Round 0.5809 to the nearest hundred
Answer:
0.58
Step-by-step explanation:
0.5809
0.0009 is the ten thousandths
0.000 is the thousandths
0.08 is the hundreds
0.5 is the tens
so the answer must only have two decimal places:
0.5809 rounded to the thousandth is 0.581, because 9 is closer to 10 then 0
0.581 rounded to the hundredth is 0.58, because 1 is closer to 0 then 10
Serena purchased CDs from Hopeful Books & CDs. The number of items she bought at each price is shown in the graph.
The number of items Serena purchased about 64.5% of her CDs for less than her $5.
How to calculate the percentage?To find the percentage of CDs Serena bought for less than $5, you need to sum the number of CDs purchased for less than $5 and divide by the total number of CDs purchased.
From the graph, we can see that the number of CDs she bought for her under $5 was her 499. To find the total number of CDs she has purchased, we need to sum the number of CDs she purchased at each price.
Total CDs purchased = 158 + 499 + 108 + 0 + 8 = 773
So the percentage of CDs she bought under her $5 would be:
(499/773) * 100% ≒ 64.5D
44 As a result, Serena purchased about 64.5% of her CDs for less than her $5.
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The complete question is
'Serena purchased CDs from Hopeful Books & CDs. The number of items she bought at each price is shown in the graph. What percent of the CDs did she purchase for less than $5? Enter your answer in the box. GD Prkces J L00-2. 499 4490 "5,00 0, 158 0 8.98 108" L,00-10,98 Price'
Compare m∠cab and m∠cdb from question 1. how are the measures of the two angles related?
The measure of ∠BOD = ∠AOC = 90 since opposite angles of a parallelogram are equal. m∠cab = m∠cdb as they are corresponding angles since AC ∥ DB.
To find ∠BOD, we can use the fact that opposite angles of a parallelogram are equal. Since AC ∥ DB, we have:
∠BOD = ∠AOC
Now, we can use the fact that the sum of angles in a triangle is 180 degrees to find ∠AOC:
∠AOC = 180 - ∠CAB - ∠CDB
∠AOC = 180 - 35 - 55
∠AOC = 90
Therefore, we have:
∠BOD = ∠AOC = 90
So, ∠BOD is a right angle.
To compare m∠cab and m∠cdb, we can use the fact that corresponding angles are equal when two parallel lines are intersected by a transversal. Since AC ∥ DB, we have:
m∠cab = m∠cdb
Therefore, the measures of the two angles are equal.
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_____The given question is incomplete, the complete question is given below:
Line segments AB and CD intersect at O such that AC ∥ DB. It ∠CAB = 35 and ∠CDB= 55. Find ∠BOD. Compare m∠cab and m∠cdb from question 1. how are the measures of the two angles related?
is 11 a solution to 36=4y
Answer:
No
Step-by-step explanation:
Plug it in to check. 36 is not equal to 4(11) becuase 4(11)=44.
36 never equals 44.
In AHIJ, j = 91 inches, i = 90 inches and ZI=106°. Find all possible values of ZJ, to
the nearest degree.
The possible values of angle J is 76 degrees
How to determine the possible values of angle JGiven that
Triangle = Triangle HIJ
j = 91 inches
i = 90 inches
Angle I = 106 degrees
The possible values of angle J can be calculated using the following law of sines
sin(J)/j = sin(I)/i
By substituion, we have
sin(J)/91 = sin(106)/90
So, we have
sin(J) = 0.9719
Take the arc sin of both sies
J = 76 and 104 degrees
The measure 104 degrees is not possible because a triangle cannot have two obtuse angles
Hence, the measure of J is 76 degrees
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Help! With steps pls
Solve for x
4(1.7)^(x)=7(1.08)^(x)
the solution to the equation [tex]4(1.7)^(x) = 7(1.08)^(x)[/tex] is approximately
x = 8.732.
What are logarithms?The other technique to write exponents in mathematics is using logarithms. A number's base-based logarithm is equal to another number. A logarithm performs exponentiation's exact opposite function. For instance, log10 100 = 2 if 102 = 100.
from the question:
By separating the variable on one side of the equation and then taking the logarithm of both sides, we can find the value of x.
Starting with:
[tex]4(1.7)^(^x^) = 7(1.08)^(^x^)[/tex]
Dividing both sides by [tex]7(1.08)^(x)[/tex], we get:
[tex](4/7)(1.7)^(^x^) = (1.08)^(^x^)[/tex]
Taking the logarithm of both sides (with any base), we get:
[tex]log[(4/7)(1.7)^(^x^)] = log[(1.08)^(^x^)][/tex]
Using the properties of logarithms, we can simplify this to:
log(4/7) + xlog(1.7) = xlog(1.08)
Subtracting x*log(1.7) from both sides, we get:
log(4/7) = xlog(1.08) - xlog(1.7)
Factoring out x, we get:
log(4/7) = x*[log(1.08) - log(1.7)]
Dividing both sides by [log(1.08) - log(1.7)], we get:
x = log(4/7) / [log(1.08) - log(1.7)]
We can evaluate this statement with a calculator and obtain:
x ≈ 8.732
As a result, x = 8.732 is about the answer to the equation 4(1.7)(x) = 7(1.08)(x).
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Recall from calculus that given some function g(x), the x you get from solving dg(x)/dx= 0 is called a critical point of g - this means it could be a minimizer or a maximizer for g. In this question, we will explore some basic properties and build some intuition on why, for certain loss functions such as the MSE loss, the critical point of the loss will always be the minimizer of the loss. Given some linear model f(x) = yx for some real scalar y, we can write the the mean squared error (MSE) loss of the model f given the observed data {li, Yi}, i = 1,... ...,n as n (Yi — Yz;)?
For the MSE loss of a linear model, the critical point is a minimizer. The second derivative test shows that any deviation results in a higher loss.
The mean squared error (MSE) loss of a linear model f(x) = yx, given the observed data {li, Yi}, i = 1,...,n, is given by:
L(y) = (1/n) * ∑i=1 to n (Yi - y*li)^2
To find the critical point of this function, we need to differentiate it with respect to y and set it equal to zero:
dL(y)/dy = (1/n) * ∑i=1 to n 2*(Yi - yli)(-li) = 0
Simplifying this expression, we get:
∑i=1 to n (Yi * li) - y * ∑i=1 to n (li^2) = 0
Rearranging the terms, we get:
y = (∑i=1 to n (Yi * li)) / ∑i=1 to n (li^2)
This is the critical point of the MSE loss function for the given linear model. To show that this critical point is indeed the minimizer of the loss, we can use the second derivative test. Taking the second derivative of the loss function with respect to y, we get:
d2L(y)/dy2 = (2/n) * ∑i=1 to n (li^2)
Since the second derivative is positive for all values of li, this means that the critical point is a minimum.
Intuitively, this makes sense because the MSE loss measures the average squared difference between the predicted values (y*li) and the actual values (Yi). By minimizing this difference, we are finding the best fit line for the given data points. The critical point is indeed the minimizer of the loss.
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I need your detail step by step ASAP
With a 14-board, a carpenter chopped three 4'6" shelves from it; the left part was [tex]6"[/tex].
Who are the "carpenters"?A person who crafts something out of wood is known as a carpenter. A carpenter could construct two long benches and a dining table for you. Carpenters are experts in woodworking, producing wooden structures and furniture as well as fixing other wooden objects.
What makes anything a carpenter?The word "carpenter," which has Roman and French roots, is derived from the Latin word "carpentum," which refers to a chariot or carriage, and then from the Old French word "carpentier," which was used to designate someone who worked with wood.
Note that [tex]1' = 12"[/tex]
So 14' will be [tex]14 * 12 = 168"[/tex]
A carpenter cut three [tex]4' 6"[/tex].
Convert [tex]4'[/tex] into inches, that will be[tex]4 * 12 = 48"[/tex]
Then add [tex]6"[/tex], that will be [tex]48" + 6" = 54"[/tex]
Multiply this by [tex]3[/tex] since the carpenter cut three pieces.
That will be [tex]54" * 3 = 162"[/tex]
So the carpenter cut a total of [tex]162"[/tex] from the [tex]168"[/tex] board.
The remaining size [tex]168" - 162" = 6"[/tex]
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The period in T(in seconds) of a pendulum is given by T=2pi√(L/32) , where L stands for the length (in feet) of the pendelum. If pi=3. 14, and the period is 12. 56 seconds, what is the length? what is the length of the pendelum
The length of the pendulum is approximately 100.06 feet
The period of a pendulum is the time it takes for one complete back-and-forth motion, or one oscillation. It is often denoted by the symbol T and is measured in units of time, such as seconds. The period of a pendulum depends on its length and the acceleration due to gravity
We can start by rearranging the formula of period in T to solve for L:
T = 2π√(L/32)
Square both sides:
T^2 = 4π^2(L/32)
Simplify
T^2 = π^2(L/8)
Multiply both sides by 8/π^2
8T^2/π^2 = L
Now we can substitute the given values
L = 8(12.56)^2/π^2
L ≈ 100.06 feet
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