The moment about the y-axis, with respect to the center of mass of the triangular lamina D, is given by: Moss_y = ρ * (27/2 - 27/4 - 27/54 + 27/108).
The moment about the y-axis can be calculated by finding the moment of each infinitesimal mass element and integrating over the entire lamina.
The y-component of the center of mass can also be determined.
To start, let's calculate the moment about the y-axis.
The moment of each infinitesimal mass element is given by:
dM = ρ * x * dA
where x is the distance from the infinitesimal mass element to the y-axis, and dA is the infinitesimal area.
Since we are integrating with respect to y, we can express the coordinates of the vertices in terms of y as follows:
Vertex A(0,0) remains the same.
Vertex B(0,1) becomes B(y) = (0, y).
Vertex C(3,0) becomes C(y) = (3 - y/3, 0).
Now, let's calculate the moment of each infinitesimal mass element about the y-axis:
For vertex A(0,0):
dM₁ = ρ * 0 * dA₁ = 0
For vertex B(y):
dM₂ = ρ * 0 * dA₂ = 0
For vertex C(y):
dM₃ = ρ * (3 - y/3) * dA₃
To calculate the infinitesimal areas, we can use the formula for the area of a triangle:
dA₁ = (1/2) * 0 * dy = 0
dA₂ = (1/2) * 0 * dy = 0
dA₃ = (1/2) * (3 - y/3) * dy = (3/2 - y/6) * dy
Now, we can integrate the moments over the entire lamina:
Moss_y = ∫(dM₁ + dM₂ + dM₃)
Moss_y = ∫(0 + 0 + ρ * (3 - y/3) * (3/2 - y/6) * dy)
Moss_y = ρ * ∫((9/2 - 3y/2 - y^2/18 + y^2/36) * dy)
Moss_y = ρ * ∫((9/2 - 3y/2 - y^2/18 + y^2/36) * dy) evaluated from y = 0 to y = 3
Moss_y = ρ * [(9y/2 - 3y^2/4 - y^3/54 + y^3/108)] evaluated from y = 0 to y = 3
Moss_y = ρ * [(27/2 - 27/4 - 27/54 + 27/108) - (0)]
Simplifying the expression:
Moss_y = ρ * (27/2 - 27/4 - 27/54 + 27/108)
Finally, the moment about the y-axis, with respect to the center of mass of the triangular lamina D, is given by:
Moss_y = ρ * (27/2 - 27/4 - 27/54 + 27/108
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The probable question may be:
Find the moment about the y-axis and the y-component of the center of mass of a triangular lamina D with vertices A(0,0), B(0,1), and C(3,0).
What is the measure of the other acute angle ?
Answer:
[tex]62^{o}[/tex]
Step-by-step explanation:
All the angles in a triangle add up to [tex]180^{o}[/tex]
Every right angle triangle has a right angle in it which is [tex]90^{o}[/tex]
So to find the remaining angle, you do [tex]180^{o}[/tex] - [tex]90^{o}[/tex] - [tex]28^{o}[/tex] = [tex]62^{o}[/tex]
Exercises 2.17 Interpolate a cubic spline between the three
points (0, 1), (2, 2) and (4, 0).
To interpolate a cubic spline between the points (0, 1), (2, 2), and (4, 0), we can use the concept of spline interpolation. A cubic spline is a piecewise-defined function consisting of cubic polynomials, which smoothly connects the given points.
In order to construct a cubic spline, we need to determine the coefficients of the cubic polynomials for each interval between the given points. The spline should satisfy three conditions: it must pass through each of the given points, it should have continuous first and second derivatives at the interior points, and it should have zero second derivatives at the endpoints to ensure a smooth connection.
We start by dividing the interval into three subintervals: [0, 2], [2, 4]. For each subinterval, we construct a cubic polynomial that satisfies the interpolation conditions. By imposing the continuity and smoothness conditions at the interior point (2, 2), we can obtain a system of equations. Solving this system gives us the coefficients of the cubic polynomials.
Once we have the coefficients, we can express the cubic spline as a piecewise function. The resulting cubic spline will smoothly connect the given points (0, 1), (2, 2), and (4, 0) and provide an interpolation function between them. This interpolation technique ensures a smooth and continuous curve, which can be useful for approximating values between the given data points.
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An 18-foot ladder leaning against a wall makes an angle of elevation of 70° with the ground. How far up the wall is the ladder, to the nearest foot?
Answer:
17 ft
Step-by-step explanation:
An 18-foot ladder leaning against a wall makes an angle of elevation of 70° with the ground. How far up the wall is the ladder, to the nearest foot?
We solve the above question using the Trigonometric function of Sine
sine theta = Opposite/Hypotenuse
theta = Angle of elevation = 70°
Hypotenuse =Length of the ladder = 18ft
Opposite = Height of the wall = x
Therefore
sin 70 = x/ 18 ft
Cross Multiply
x = sin 70 × 18 ft
x = 16.914467174 ft
Approximately = 17 ft
A coach buys a uniform and a basketball for each of the 20 players on the team. Each
basketball costs $10.40. The coach spends a total of $620 for uniforms and basketballs
What was the cost of a single uniform?
Answer:
$20.60
Step-by-step explanation:
You find how much it costs for the total amount of basketballs (10.40×20=208), then you subtract that number from the total cost of everything to get the cost of all the uniforms (620-208=412), then you divide the total costs for all uniforms by 20 to find the cost for a single uniform (412÷20=20.6). Always make sure that the decimals go until the hundredths place for USD.
Hope this helps!
I DON'T WANT A LINK I WANT AN ANSWER CAN YOU ANSWER THIS QUESTION I NEED IT DONE ASSP How large is the distance from one end of your state to the other (North to South)? What is the distance from the east coast to the west coast of your state? Your state is the ___________ largest in the United States.
My state is Virginia
Select all the equations that represent functions that are non-linear.
A. y = x
B. 2y = 1/2x
C. y = 8 + x
D. y - 6 = x^2
E. y= 1/3-5x
F. y= 2x^2 + 5 - 3x^2
Answer:
D, F.
Step-by-step explanation:
D and F contain x^2.
Question 5 Multiple Choice Worth 1 points)
(05.02 MC)
Find the measure of angle x in the figure below.
52
59
X
63
O 35
O 48°
0 69
O 789
Answer:
your answer should be 48 degrees
Find the value of the variables in the simplest form
Answer:
x = 2
Step-by-step explanation:
Using Pythagoras' identity in the right triangle
x² + x² = (2[tex]\sqrt{2}[/tex] )² , that is
2x² = 8 ( divide both sides by 2 )
x² = 4 ( take the square root of both sides )
x = [tex]\sqrt{4}[/tex] = 2
Use a normal approximation to find the probability of the indicated number of voters. In this case, assume that
108108
eligible voters aged 18-24 are randomly selected. Suppose a previous study showed that among eligible voters aged 18-24, 22% of them voted.
Probability that exactly 29 voted
The probability that exactly 29 of 108 eligible voters voted is
Using normal approximation, the probability that exactly 29 out of 108 eligible voters voted is approximately 0.2346, or 23.46%.
What is the probability that exactly 29 out of 108 eligible voters voted?To find the probability that exactly 29 out of 108 eligible voters voted, we can use a normal approximation.
First, we need to calculate the mean (μ) and standard deviation (σ) for the binomial distribution, which can be approximated using the formula:
μ = n * p
σ = √(n * p * (1 - p))
where n is the number of trials (108 in this case) and p is the probability of success (22% or 0.22).
μ = 108 * 0.22 = 23.76
σ = √(108 * 0.22 * (1 - 0.22)) = 4.3
Next, we use the normal distribution to approximate the probability of exactly 29 voters. We will use the continuity correction by considering the interval between 28.5 and 29.5.
P(28.5 < X < 29.5) ≈ P(28.5 - 0.5 < X < 29.5 + 0.5) ≈ P(28 < X < 30)
To find this probability, we calculate the z-scores for 28 and 30 using the mean and standard deviation:
z₁ = (28 - μ) / σ
z₂ = (30 - μ) / σ
Then, we use a standard normal distribution table or calculator to find the probability associated with each z-score:
P(28 < X < 30) ≈ P(z₁ < Z < z₂)
Let's calculate the z-scores and find the corresponding probabilities:
z₁ = (28 - 23.76) / 4.61 ≈ 0.92
z₂ = (30 - 23.76) / 4.61 ≈ 1.35
Using the standard normal distribution table or calculator, we find the probabilities associated with these z-scores:
P(0.92 < Z < 1.35) ≈ 0.4082 - 0.1736 = 0.2346
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Alternate Sources of Fuel Seventy-five percent of Americans favor spending government money to develop alternative sources of fuel for automobiles. For a random sample of 140 Americans, find the mean, variance, and standard deviation for the number who favor government spending for alternative fuels. Round your answers to three decimal places.
Part: 0/2 ______
Part 1 of 2
(a) Find the mean.
Mean: μ= _____
The mean number of Americans who favor government spending for alternative fuels can be calculated by multiplying the percentage of Americans who favor such spending by the total sample size. In this case, 75% of Americans favor government spending, and the sample size is 140.
Mean = (Percentage of Americans who favor government spending) * (Sample size)
= 0.75 * 140
= 105
Therefore, the mean number of Americans who favor government spending for alternative fuels is 105.
The mean represents the average or central tendency of the data. In this context, it indicates the average number of Americans in the sample who support government spending for alternative fuels. It is obtained by multiplying the percentage of Americans who favor such spending by the sample size.
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what does this equal??
Answer:
I think 3
Step-by-step explanation:
Find (a) the range and (b) the standard deviation of the data set 40,35.45,55,60. Round to the nearest hundredth if necessary.
Answer:
(a) 25
(b) 9.27
Step-by-step explanation:
Step 1
We have to rearrange the given days set from least to highest
35, 40, 45, 55, 60
(a) the range
Range = The highest number - The least number
= 60 - 35
= 25
(b) the standard deviation of the data set
35, 40, 45, 55, 60.
We find the Mean
Mean = Sum of values/Number of values
= 35+40+45+55+60/5
= 235/5
= 47
We can find the standard deviation now.
The formula =
√(x - Mean)²/n
= √(35 - 47)²+ (40 + 47)² + (45 - 47)² + (55 - 47)² + (60 - 47)²/5
= √144 + 49 + 4 + 64 +169/5
= √430/5
= √86
= 9.273618495
Approximately = 9.27
URGENT!!!!HELP!!!!PLS!!!NOW!!!!!!HURRY!!!
Answer:
I'm guessing it's 4 i think but sorry if it's wrong
Step-by-step explanation:
Ms Carr made a mistake in her checkbook. she wrote a check for $8.98 to rent a video but mistakenly recoreded it in her checkbook as an $8.98 deposit on the blank slide represent each transaction with a rational number and explain the difference between the transactions
5x^2 divided by -45x
Answer: -1/9 * x.
Step-by-step explanation:
To simplify the expression (5x^2) / (-45x), we can divide the coefficients and subtract the exponents:
(5 / -45) * (x^2 / x)
Simplifying the coefficient:
-1/9 * (x^2 / x)
Now, simplify the variables:
-1/9 * x^(2-1) = -1/9 * x
Therefore, the simplified expression is -1/9 * x.
Elena is graduating from high school. She will attend a private, 4-year university and study to become a Certified Public Accountant. The annual cost for her tuition, room and board, and books is $22,255. Elena's parents have a college fund with $ 54,000 to help with the costs. Elena received a scholarship for $500 per semester for four years .
Answer:
Reminder to eat drink and take care. :)
Step-by-step explanation:
Answer:
8,255 reminder to eat today
"Write a cost function for each of the given scenarios. Identify all variables used. (See Example 1.) 1.) A chain-saw rental firm charges $25, plus $5 per hour. 2.) A trailer hauling service charge $95 plus $ 8 per mile
The cost function for each of the given scenarios are as follows:
1) Cost function for chain-saw rental firm = $25 + $5h
2) Cost function for trailer hauling service = $95 + $8m
1.)
Cost function for chain-saw rental firm = $25 + $5h
Where, h is the number of hours the chainsaw is rented
Variables used in this scenario are:
Cost = C ($), Renting time = h (hours),
Charge per hour = c ($)
2.)
Cost function for trailer hauling service = $95 + $8m
Where, m is the number of miles the trailer has traveled.
Variables used in this scenario are:
Cost = C ($),
Distance traveled = m (miles),
Charge per mile = c ($)
Therefore the two cost functions are:
1) Cost function for chain-saw rental firm = $25 + $5h
2) Cost function for trailer hauling service = $95 + $8m
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the base of the cylinder? Use 3.14 for n and round the answer
to the nearest hundredth.
h-13 in
r =
in.
Answer:
r = 7
Step-by-step explanation:
Volume of a cylinder:
V = πr²h
Given:
V = 2000
h = 13
Work:
V = πr²h
r² = V/(πh)
r² = 2000/(3.14 * 13)
r² = 2000/40.82
r² ≈ 49
[tex]\sqrt{r^2} =\sqrt{49}[/tex]
r = 7
Determine the measure of arc BC
Answer:
arc BC = 132°
Step-by-step explanation:
The central angle is equal to the arc that subtends it , then
arc BC = ∠ BOC = 132°
how can you find the diameter of this circke
Answer:
10cm
Step-by-step explanation:
pretty sure the diameter is measured by multiplying the radius twice :)
Answer:
Diameter = 10 cm
Circumference = 31.43 cm
Area = 78.57 cm²
OMG HELP PLS IM PANICKING OMG OMG I GOT A F IN MATH AND I ONLY HAVE 1 DAY TO CHANGE MY GRADE BECAUSE TOMORROW IS THE FINAL REPORT CARD RESULTS AND I DONT WANNA FAIL PLS HELP-
Answer: $1,800
Step-by-step explanation:
600x3=1,800
Answer:
1800 is the cost.
Step-by-step explanation:
Each hoop costs 600 dollars and their are 3 hoops so multiply 600 times 3 or you can do 6 times 3 and add the zeros at the end which is 1800 dollars and btw you got this!!! don't give up. I believe in you :)
uh someone help D:
ill make the points high
Answer:
m = 18/4 = 9/2 = 4.5
Step-by-step explanation:
Notice that the line passes through (0, 0) and (4, 18). Thus, its 'rise' is 18 - 0, or 18, and its 'run' is 4 - 0, or 4, and the slope (which is the desired constant of proportionality) is m = 18/4 = 9/2 = 4.5 This is Answer B
What is the sign of −9⋅( 0/-3)
Answer:
hi
Step-by-step explanation:
sorry
Answer:
0
Step-by-step explanation:
The sine function of 0 is 0.
We got 0 because you multiplied -9 by 0 divided by -3. DIviding by 0 really doesn't have an answer, but it'd most logically be 0.
Ann prefers ice cream cups. Ben and Clay prefer ice cream sandwiches. The cafeteria manager puts one coupon for an ice cream cup and two coupons for ice cream sandwiches in a bag. Ann, Ben, and Clay each draw, without looking, one coupon from the bag. Each keeps the coupon he or she drew. What is the probability that all three get their preference?
a. 1/2
b. 1/3
c. 1/6
d. 2/3
A set of dolls is made so that the volume,V of each of them varies directly as the cube of its height h. The doll with a height of 3cm has a volume of 6.75 cm³.
A) find an equation for V in terms of H.
B) find the volume of a doll with a height of 2.5cm
Answer:
A v=2.25 H=1
b. 5.625
Step-by-step explanation:
Answer:
V = 3.90625 cm³
Step-by-step explanation:
Given that V varies directly as h³ then the equation relating them is
V = kh³ ← k is the constant of variation
To find k use the condition
V = 6.75 when h = 3 , then
6.75 = k × 3³ = 27k ( divide both sides by 27 )
0.25 = k
V = 0.25h³ ← equation of variation
(b)
When h = 2.5 , then
V = 0.25 × 2.5³ = 3.90625 cm³
what is the y-intercept of the graph of 4y - 1= 3
Answer:Using the slope-intercept form, the y-intercept is 1
1. The small bag of potting soil weighs 3 1/4 pounds. The large bag weighs 3 2/3 times more than the small bag. How much does the large bag weigh?
Answer:
11 11/12 lb
Step-by-step explanation:
"3 2/3 times more than the small bag" comes out to:
(3 2/3)*(3 1/4) lb.
Convert both mixed numbers to improper fractions:
11 13 143
--- * ---- = ----------- = 11.917
3 4 12
The large bag weighs 11.917 lb, which may be converted to the mixed number 11 11/12 lb
April has 6 fruit bars.she cuts them into halves. how many 1/2 size bar pieces does she have
Answer:
12
Step-by-step explanation:
If you cut them into halves then there will be twice as many pieces.
so you do:
6 x 2
= 12
A racing car is one of the many toys manufactured by Mack Corporation. The assembly time for this toy follows a normal distribution with a mean of 50 minutes and a standard deviation of 5 minutes. If one worker starts assembling a racing car, what is the probability that she will finish this job in more than 60 minutes? Find the z score? QUESTION 2 1 pol 1b. What do you get from Table A? QUESTION 3 3 point 10. What is the probability that she will finish this job in more than 60 minutos? (round to a percent with two decimals)
The probability that the worker will finish assembling the racing car in more than 60 minutes is approximately 0.1587. The z-score corresponding to 60 minutes is 2. The probability of completing the job in more than 60 minutes is 15.87%.
To find the probability that the worker will finish assembling the racing car in more than 60 minutes, we need to calculate the z-score and then find the corresponding probability from the standard normal distribution.
First, we calculate the z-score using the formula:
z = (x - μ) / σ
where x is the given time (60 minutes), μ is the mean (50 minutes), and σ is the standard deviation (5 minutes).
z = (60 - 50) / 5
z = 2
Next, we look up the probability corresponding to a z-score of 2 in Table A (standard normal distribution table). The value in the table represents the probability of a random variable being less than the given z-score. To find the probability of the worker finishing in more than 60 minutes, we subtract this value from 1.
From Table A, the probability corresponding to a z-score of 2 is approximately 0.9772.
Probability = 1 - 0.9772
Probability ≈ 0.0228
Therefore, the probability that the worker will finish assembling the racing car in more than 60 minutes is approximately 0.0228 or 2.28% (rounded to two decimal places).
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An inflatable figure is a decoration on Gabriella's lawn. A rope 42 in. long secures the top of the figure to the ground at an angle of 80°. About how tall is the figure?
round to the nearest tenth of an inch
Answer:
41.4 in
Step-by-step explanation:
(sin 80) opposite = x
hypotenuse 42
x = 42 * sin (80) = 41.4 in