A robust explicit integration of elasto-plastic constitutive models, based on simple subincrement size estimation
Answers
The subincrement size estimation technique adaptively determines the appropriate time step size for each subincrement based on the estimated level of nonlinearity in the material response, ensuring accuracy and stability in the simulation.
A robust explicit integration scheme for elasto-plastic constitutive models, based on simple subincrement size estimation, refers to a numerical method used to simulate the behavior of materials that exhibit both elastic and plastic deformation.
This integration scheme allows for accurate and efficient computation of the material response under various loading conditions.
In explicit integration schemes, the equations of motion are solved incrementally over small time steps. The key challenge in elasto-plastic simulations is to accurately capture the nonlinear behavior of the material while maintaining numerical stability.
This requires carefully choosing the subincrement size, which represents the size of each time step within the larger time step.
The subincrement size estimation technique used in this approach is designed to adaptively determine the appropriate time step size for each subincrement. The goal is to strike a balance between accuracy and computational efficiency.
By estimating the level of nonlinearity in the material response, the subincrement size can be adjusted accordingly.
The following steps outline a simple subincrement size estimation process for robust explicit integration of elasto-plastic constitutive models:
1. Initialize the material state variables, such as stress and strain, at the beginning of the simulation.
2. Specify the desired total time for the simulation and divide it into smaller time steps.
3. For each time step, estimate the level of nonlinearity in the material response. This can be done by considering factors such as the magnitude of the applied loads, the material's yield strength, and the rate of deformation.
4. Based on the estimated nonlinearity, determine an appropriate subincrement size for the current time step. A higher level of nonlinearity may require smaller subincrements to accurately capture the material's behavior.
5. Within each time step, divide the subincrements and perform the following calculations iteratively:
a. Compute the incremental strain and stress using the current state variables and the subincrement size.
b. Update the state variables using the computed increments.
c. Check for convergence or any other termination criteria.
d. If the termination criteria are not met, repeat steps a to c until convergence or until the maximum number of iterations is reached.
6. After completing the subincrements for the current time step, update the material state variables and proceed to the next time step.
By using this explicit integration scheme with a simple subincrement size estimation technique, you can achieve accurate and efficient simulations of elasto-plastic behavior.
However, it's worth noting that the specific implementation details and equations involved may vary depending on the constitutive model being used.
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The complete question is:
A robust explicit integration of elasto-plastic constitutive models, based on simple subincrement size estimation, sounds promising. Could you provide more details on how the subincrement size estimation technique adaptively determines the appropriate time step size for each subincrement?
Related Questions
Two students rented instruments from the same music store. They paid the same total amount for their rentals. The first student rented an instrument for 9 months and spent $18 on a one-time fee. The second student rented an instrument for 12 months and spent $6 on a one-time fee. Both students paid the same rental fee per month for their instruments. What is the rental fee, in dollars, per month?
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Answer:
Step-by-step explanation:
jack borrowed $600 from his dad and paid him back $475 how much does he still owe his dad
Answers
Answer:
125
Step-by-step explanation:
600-475=
Answer:
125
Step-by-step explanation:
$600 subtract 475 = 125
You roll 2 dice. If the sum of the dice is: 2, 3, 4 you win $20. If the sum is 5, 6, 7, 8 you win $10. If the sum is 9, 10, 11 you lose $20. If the sum is 12 you lose $25. It costs $5 to play. Create a probability distribution of the random variable, "winnings" including the cost to play, for this game. What is the expected value of the "winnings" for this game? What is the variance for the "winnings" for this game? What is the standard deviation? Is this game a "fair game"? Why or why not?
Answers
Answer:
1) The expected value of the "winnings" is $(-0.97\(\overline 2\))
2) The variance for the "winnings" is $0.57966
3) The standard deviation for the "winnings" is$0.761354
4) The game is not a fair game because one is expected to lose $0.97\(\overline 2\)
Step-by-step explanation:
1) The probability of having a sum of 2 = 1/6×1/6 = 1/36
The probability of having a sum of 3 = 1/6×1/6 = 1/36
The probability of having a sum of 4 = 1/6×1/6 + 1/6×1/6 = 1/18
The probability of having a sum of 5 = 1/6×1/6 + 1/6×1/6 = 1/18
The probability of having a sum of 6 = 1/6×1/6 + 1/6×1/6 + 1/6×1/6 = 1/12
The probability of having a sum of 7 = 1/6×1/6 + 1/6×1/6 + 1/6×1/6 = 1/12
The probability of having a sum of 8 = 1/6×1/6 + 1/6×1/6 + 1/6×1/6 = 1/12
The probability of having a sum of 9 = 1/6×1/6 + 1/6×1/6 = 1/18
The probability of having a sum of 10 = 1/6×1/6 + 1/6×1/6 = 1/18
The probability of having a sum of 11 = 1/6×1/6 = 1/36
The probability of having a sum of 12 = 1/6×1/6 = 1/36
The values are;
For 2, we have 1/36 × (20 - 5) = 0.41\(\overline 6\)
For 3, we have 1/36 × (20 - 5) = 0.41\(\overline 6\)
For 4, we have 1/18 × (20 - 5) = 0.8\(\overline 3\)
For 5, we have 1/18 × (10 - 5) = 0.2\(\overline 7\)
For 6, we have 1/12 × (10 - 5) = 0.41\(\overline 6\)
For 7, we have 1/12 × (10 - 5) = 0.41\(\overline 6\)
For 8, we have 1/12 × (10 - 5) = 0.41\(\overline 6\)
For 9, we have 1/18 × (-20 - 5) = -1.3\(\overline 8\)
For 10, we have 1/18 × (-20 - 5) = -1.3\(\overline 8\)
For 11, we have 1/36 × (-20 - 5) = -0.69\(\overline 4\)
For 12, we have 1/36 × (-25 - 5) = -0.69\(\overline 4\)
The expected value of the winnings is given as follows;
0.41\(\overline 6\) + 0.41\(\overline 6\) + 0.8\(\overline 3\) + 0.8\(\overline 3\) + 0.8\(\overline 3\) + 0.41\(\overline 6\) + 0.41\(\overline 6\) + -1.3\(\overline 8\) -1.3 - 0.69\(\overline 4\) - 0.69\(\overline 4\) = -0.97\(\overline 2\)
Therefore, the expected value = $-0.97\(\overline 2\), which is one is expected to lose $0.97\(\overline 2\)
2) Using Microsoft Excel, we have;
The variance for the "winnings", σ² = $0.57966
3) The standard deviation for the "winnings" = √σ² = √(0.57966) ≈ $0.761354
4) The game is not a fair game because one is expected to lose $0.97\(\overline 2\)
Weatha rides her bike to the park. The park is 5 3/4miles from her house, and she's already ridden 1.4 miles. How many more miles does weatha still need to travel?
Answers
then
5.75 miles - 1.4 miles = 4.35 miles
answer 4.35 miles
Evaluate 2 |x-4| +6 when x=-3
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Answer:
use math w.a.y works like a dream
Step-by-step explanation:
find the total cost if the original price is $65.00 and sale tax is 7%
Answers
Answer:
$69.55
Explanation:
First, we need to calculate how much is the sales tax. So, 7% of $65.00 is equal to:
\(7\text{ \% }\times65.00=\frac{7}{100}\times65.00=\text{ \$4.55}\)Then, the total cost will be the original price added to the sales tax, so the total cost is equal to:
$65.00 + $4.55 = $69.55
So, the answer is $69.55
Find the Principal unit normal for r(t) = sintit cost; + tk Evaluate it at t = Tyz Sketch the situation
Answers
We can plot the vector r(t) and the vector N(T) at the given value of t = T.
To find the principal unit normal for the vector-valued function r(t) = sin(t)i + tcos(t)j + tk, we need to compute the derivative of r(t) with respect to t and then normalize it to obtain a unit vector.
First, let's find the derivative of r(t):
r'(t) = cos(t)i + (cos(t) - tsin(t))j + k
Next, we'll normalize the vector r'(t) to obtain the unit vector:
||r'(t)|| = sqrt((cos(t))^2 + (cos(t) - tsin(t))^2 + 1^2)
Now, we can find the principal unit normal vector by dividing r'(t) by its magnitude:
N(t) = r'(t) / ||r'(t)||
Let's evaluate the principal unit normal at t = T:
N(T) = (cos(T)i + (cos(T) - Tsin(T))j + k) / ||r'(T)||
To sketch the situation, we can plot the vector r(t) and the vector N(T) at the given value of t = T.
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Which statement BEST describes the function notation f(10)=3/2?
A. The output is 3/2 when the input is 10.
B. The output is 10 when the input is 3/2.
C. The output is f(x) when the input is 10.
D. The output is f(3/2) when the input is 10.
Answers
Answer: the answer is C I took the test
Step-by-step explanation:
The answer is Option A.
The output is 3/2 when the input is 10
What is a function rule?
The function rule is the relationship between the input or domain and the output or range. A relation is a function if and only if there exists one value in the range for every domain value.
A function is a relation from a set of inputs to a set of possible outputs where each input is related to exactly one output.
Given data ,
Let the function be f ( x ) = y
f ( x ) = f ( 10 ) = 3/2
So , the value of the function at x = 10 is y
Now , when the value of x is equal to 10 , the input is 10
And the function gives an output of 3/2 which is the value of y
Hence , the function gives an output of 3/2 when the input is 10
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I have three fair dice: one is 6-sided, one is 8-sided, and one is 12-sided. Each n-sided die has numbers 1 through 1 OH its sides, and each side is equally likely to come up. [roll the three dice at the same time. (a) What is the probability that [ roll the saine number on all three dice? (b) [ pick one of the dice at random, with all three equally likely to be picked. roll it and it comes up "4" What is the probability that the die [ rolled was the 6-sidled one? (c) What is the probability that the smallest number roll is at least 32 Hint: 'smallest number is at least 3" all 3 dice show 3 O1 higher" (d) What is the probability that the product of the three numbers roll is even"
Answers
The probability of rolling the same number on all three dice can be found by multiplying the probabilities of rolling the same number on each individual die. The probability of rolling the same number on the 6-sided die is 1/6, the probability of rolling the same number on the 8-sided die is 1/8, and the probability of rolling the same number on the 12-sided die is 1/12. Multiplying these probabilities together gives us the probability of rolling the same number on all three dice: (1/6) * (1/8) * (1/12) = 1/576.
The probability of rolling a "4" on one of the dice and it being the 6-sided die can be found by multiplying the probability of rolling a "4" on the 6-sided die (1/6) by the probability of picking the 6-sided die at random (1/3). This gives us a probability of (1/6) * (1/3) = 1/18.
The probability of the smallest number rolled being at least 3 can be found by subtracting the probability of the smallest number being less than 3 from 1. The probability of the smallest number being less than 3 is the probability of rolling a 1 or a 2 on each of the dice: (2/6) * (2/8) * (2/12) = 1/72. Therefore, the probability of the smallest number being at least 3 is 1 - (1/72) = 71/72.
The probability of the product of the three numbers rolled being even can be found by subtracting the probability of the product being odd from 1. The probability of the product being odd is the probability of rolling an odd number on each of the dice: (3/6) * (4/8) * (6/12) = 1/8. Therefore, the probability of the product being even is 1 - (1/8) = 7/8.
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find the area between a large loop and the enclosed small loop of the curve r = 2 + 4 cos(3θ).
Answers
Therefore, the area between the large loop and the small loop of the curve r = 2 + 4cos(3θ) is 70π/3.
To find the area between the large loop and the small loop of the curve, we need to find the points of intersection of the curve with itself.
Setting the equation of the curve equal to itself, we have:
2 + 4cos(3θ) = 2 + 4cos(3(θ + π))
Simplifying and solving for θ, we get:
cos(3θ) = -cos(3θ + 3π)
cos(3θ) + cos(3θ + 3π) = 0
Using the sum to product formula, we get:
2cos(3θ + 3π/2)cos(3π/2) = 0
cos(3θ + 3π/2) = 0
3θ + 3π/2 = π/2, 3π/2, 5π/2, 7π/2, ...
Solving for θ, we get:
θ = -π/6, -π/18, π/6, π/2, 5π/6, 7π/6, 3π/2, 11π/6
We can see that there are two small loops between θ = -π/6 and π/6, and two large loops between θ = π/6 and π/2, and between θ = 5π/6 and 7π/6.
To find the area between the large loop and the small loop, we need to integrate the area between the curve and the x-axis from θ = -π/6 to π/6, and subtract the area between the curve and the x-axis from θ = π/6 to π/2, and from θ = 5π/6 to 7π/6.
Using the formula for the area enclosed by a polar curve, we have:
A = 1/2 ∫[a,b] (r(θ))^2 dθ
where a and b are the angles of intersection.
For the small loops, we have:
A1 = 1/2 ∫[-π/6,π/6] (2 + 4cos(3θ))^2 dθ
Using trigonometric identities, we can simplify this to:
A1 = 1/2 ∫[-π/6,π/6] 20 + 16cos(6θ) + 8cos(3θ) dθ
Evaluating the integral, we get:
A1 = 10π/3
For the large loops, we have:
A2 = 1/2 (∫[π/6,π/2] (2 + 4cos(3θ))^2 dθ + ∫[5π/6,7π/6] (2 + 4cos(3θ))^2 dθ)
Using the same trigonometric identities, we can simplify this to:
A2 = 1/2 (∫[π/6,π/2] 20 + 16cos(6θ) + 8cos(3θ) dθ + ∫[5π/6,7π/6] 20 + 16cos(6θ) + 8cos(3θ) dθ)
Evaluating the integrals, we get:
A2 = 80π/3
Therefore, the area between the large loop and the small loop of the curve r = 2 + 4cos(3θ) is:
A = A2 - A1 = (80π/3) - (10π/3) = 70π/3
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An office supply company ordered 24 cartons of specialty paper. The regular price for a carton of specialty paper is $6.88. The company received a discount of $1.75 off each carton.
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Given :
An office supply company ordered 24 cartons of specialty paper.
The regular price for a carton of specialty paper is $6.88.
The company received a discount of $1.75 off each carton.
To Find :
Total amount company pay for paper.
Solution :
Discounted price of each carton , d = $(6.88-1.75) = $5.13.
Total price company has to pay , \(T=24d\)
\(T=24\times 5.13\\\\T=\$123.12\)
Hence , this is the required solution.
Find the total distance traveled by a particle according to the velocity function wt) = 3t - 9 m/sec over the time interval
[1, 5]. Enter your answer as an exact fraction, if necessary. Do not include units in your answer.
Answers
The total distance traveled by the particle over the time interval [1, 5] is 12 units.
To find the total distance traveled, we need to consider both the magnitude and direction of the velocity function. Since the velocity function given is in meters per second (m/sec), the total distance traveled will be measured in meters.
To calculate the total distance, we need to consider the intervals where the velocity function changes its sign. In this case, the velocity function is linear and increasing, starting at t = 1 with a velocity of 3 m/sec. From t = 1 to t = 3, the particle moves in the positive direction, covering a distance of (3t - 9) × (t - 1) = 12 units. From t = 3 to t = 5, the particle moves in the negative direction with the same magnitude, covering a distance of (-1) × (3t - 9) × (t - 3) = 12 unit
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PLEASE HELP ASAP!!!! i’ll mark brainlest
Answers
Answer:
D
Step-by-step explanation:
A or C don’t really make sense. 100 eggs would be greater than the amount of cartons and how many would fit.
The signal x[n] = u[n] - u[n − 3] is applied to an LTI system whose impulse response is: h[n] = = (1/2)^n u[n] - (a) Find the output y[n]. - (b) Show that the system is stable or unstable, as the case may be.
Answers
The impulse response is absolutely summable and hence, the system is stable. Therefore, the system is stable.
The given signal x[n] is;
\($$x[n] = u[n] - u[n-3]$$\)
The impulse response of the system is given as:
\($$h[n] = \left(\frac{1}{2}\right)^nu[n]$$\)
Now, the output of a linear time-invariant (LTI) system is given by;
\($$y[n] = x[n] * h[n]$$\)
Where, * represents the convolution operation. Hence, we need to find the convolution of the input signal x[n] with the impulse response of the system h[n].
(a) Convolution of the given input signal x[n] with the given impulse response h[n] is given as:
\($$\begin{aligned} y[n] &= x[n] * h[n] \\ &= \sum_{k=-\infty}^{\infty} x[k]h[n-k] \\ &= \sum_{k=-\infty}^{\infty} (u[k] - u[k-3]) \left(\frac{1}{2}\right)^{n-k} u[n-k] \end{aligned}$$\)
Now, let's break this equation into two parts, one for \($0 \leq n < 3$\) and other for \($n \geq 3$\).
For \($0 \leq n < 3$\), the above equation can be simplified as:
\($$\begin{aligned} y[n] &= \sum_{k=0}^{n} \left(\frac{1}{2}\right)^{n-k} \\ &= \frac{1}{2^n} \sum_{k=0}^{n} \left(\frac{1}{2}\right)^k \\ &= \frac{1}{2^n} \cdot \frac{1 - \left(\frac{1}{2}\right)^{n+1}}{1 - \frac{1}{2}} \\ &= 1 - \frac{1}{2^{n+1}} \end{aligned}$$\)
For\($n \geq 3$\), the above equation can be simplified as:
\($$\begin{aligned} y[n] &= \sum_{k=n-2}^{n} \left(\frac{1}{2}\right)^{n-k} \\ &= \frac{1}{2^3} + \frac{1}{2^2} + \frac{1}{2^1} \\ &= \frac{7}{8} \end{aligned}$$\)
Therefore, the output of the given system is:
\($$y[n] = \begin{cases} 1 - \frac{1}{2^{n+1}} & \text{for } 0 \leq n < 3 \\ \frac{7}{8} & \text{for } n \geq 3 \end{cases}$$\)
(b) The system is said to be stable if the impulse response is absolutely summable, that is,
\($$\sum_{n=-\infty}^{\infty} |h[n]| < \infty$$\)
Now, let's check whether the given system is stable or not:
\($$\sum_{n=-\infty}^{\infty} |h[n]| = \sum_{n=0}^{\infty} \left(\frac{1}{2}\right)^n = \frac{1}{1 - \frac{1}{2}} = 2 < \infty$$\)
Since the above sum is a finite quantity, the impulse response is absolutely summable and hence, the system is stable. Therefore, the system is stable.
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My brothers and sisters i need help asap please
Answers
Answer:
Step-by-step explanation:
I think it is D but I am not sure
IF YOU GUESS YOU WILL BE REPORTED, YOU MUST GIVE A REASONING FOR YOUR ANSWER//SHOW YOUR WORK/PROOF PLEASE!!
If you earn both hourly wages and a commission at your job, your gross wages, w, can be calculated with the following equation:
cs + rh = w
where c is your commission rate, s is your total sales in dollars, r is your hourly rate, and h is your hours worked.
Solve for s to rewrite the equation for total sales.
Question 1 options:
s = w + rhc
s = c(w + rh)
s = c(w − rh)
s = w − rhc
Answers
Applying the equation, it is found that the solution for s is given by:
\(s = \frac{w - rh}{c}\)
The equation we are going to work in this problem is given by:
\(cs + rh = w\)
We want to solve for s, hence, we have to isolate s, first placing rh on the other side with the inverse signal(subtraction).
\(cs = w - rh\)
Division is the inverse of multiplication, thus, c is multiplying s, it goes to the other side dividing:
\(s = \frac{w - rh}{c}\)
Which is the solution for s.
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In 1980, the average cost of a pack of cigarettes was $0.86. in 2000, the average cost was $4.95 per pack. find is the average rate of change of the cost of a pack of cigarettes. create a linear equation using the year 1980 as your starting year. what value did you put in for your starting point? round your answer to the nearest cent.
Answers
The cost of a pack of cigarettes was $0.86 in 1980 and in 2000, the average cost was $4.95 per pack.To find: The average rate of change of the cost of a pack of cigarettes and create a linear equation using the year 1980 as your starting year.
Average Rate of Change:Average rate of change of the cost of a pack of cigarettes is given by the formula:
Average rate of change = (Change in cost) / (Change in time)Change in cost
= ($4.95 - $0.86)
= $4.09
Change in time = (2000 - 1980)
= 20 years
Putting these values in the formula, we get
,Average rate of change = $4.09 / 20
Average rate of change = $0.2045 per year Linear equation:
We need to find a linear equation using the year 1980 as the starting year. To find this, we will use the point-slope form of a linear equation.
The point-slope form of a linear equation is given by,y - y1 = m(x - x1)
Where, y1 is the y-coordinate of the given point,x1 is the x-coordinate of the given point,m is the slope of the line Putting the values in the above formula, we get the linear equation for this problem:
y - 0.86 = 0.2045(x - 1980)
The value put in for the starting point is 1980
:The cost of a pack of cigarettes was $0.86 in 1980 and in 2000, the average cost was $4.95 per pack.Average rate of change of the cost of a pack of cigarettes is given by the formula:
rWe need to find a linear equation using the year 1980 as the starting year. To find this, we will use the point-slope form of a linear equation.The point-slope form of a linear equation is given by,
y - y1 = m(x - x1)Where, y1 is the y-coordinate of the given point,x1 is the x-coordinate of the given point,m is the slope of the line Putting the values in the above formula, we get the linear equation for this problem:y - 0.86 = 0.2045(x - 1980) The value put in for the starting point is 1980.
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The average rate of change of the cost of a pack of cigarettes can be found by subtracting the initial cost from the final cost and dividing it by the number of years that have passed. The average rate of change of the cost of a pack of cigarettes is approximately $0.2045 per year.
To calculate the average rate of change, we can use the formula:
Average rate of change = (final cost - initial cost) / number of years
In this case, the initial cost in 1980 was $0.86, and the final cost in 2000 was $4.95. The number of years that have passed is 2000 - 1980 = 20.
Plugging these values into the formula, we have:
Average rate of change = ($4.95 - $0.86) / 20
Calculating the numerator, we get:
Average rate of change = $4.09 / 20
Dividing, we find that the average rate of change is approximately $0.2045 per year.
To create a linear equation using the year 1980 as the starting point, we can use the point-slope form of a linear equation:
y - y1 = m(x - x1)
Where y represents the cost of a pack of cigarettes, x represents the number of years since 1980, m represents the average rate of change, and (x1, y1) represents the starting point.
Using the values we have, we can substitute x1 = 0 (since 1980 is the starting point) and y1 = 0.86 (the initial cost) into the equation:
y - 0.86 = 0.2045(x - 0)
Simplifying, we get:
y - 0.86 = 0.2045x
Rearranging, we have:
y = 0.2045x + 0.86
Therefore, the linear equation representing the average rate of change of the cost of a pack of cigarettes starting from 1980 is:
y = 0.2045x + 0.86
In this equation, x represents the number of years since 1980, and y represents the cost of a pack of cigarettes in dollars.
In conclusion, the average rate of change of the cost of a pack of cigarettes is approximately $0.2045 per year. The linear equation representing this average rate of change, starting from 1980, is y = 0.2045x + 0.86. In this equation, x represents the number of years since 1980, and y represents the cost of a pack of cigarettes in dollars.
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At a community bake sale, Justin earned $1.50c selling cookies, $2.25m selling muffins, and $1.90b selling brownies. He paid $0.30b for the ingredients for the brownies, $0.19c for the cookie ingredients, and $0.59m for the muffin ingredients.
Which expression represents his total profit?
1.2c+2.06m+1.31b
1.8c+2.44m+2.49b
1.31c+1.66m+1.6b
1.69c+2.84m+2.2b
Answers
The expression that represents the profit Justin made is 1.31c + 1.66m + 1.6b ( option C)
What is linear expression?A linear expression is an algebraic statement where each term is either a constant or a variable raised to the first power. In other words, none of the exponents can be greater than 1. For example, x² is a variable raised to the second power, but x is a variable raised to the first power.
Justin earned $1.50c selling cookies but he spent $0.19c. Therefore the profit on cookies = $(1.5-0.19)c. = $1.31c
He earned $2.25m by selling muffins and spent $0.59m on the ingredients. Therefore the profit He made on muffins = $(2.25-0.59) = $1.66m
He earned $1.90b selling brownies and he spent $0.30b on ingredients. The profit he made on brownies = $1.90-$0.30 = $1.60b
Therefore the expression for the total profit = $(1.31c+ 1.66m+1.6b)
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Find the slope of the graph of the equation show work
3x+15y=25
Answers
Veuillez m’aider s’il vous plaît à résoudre cette question merci !
2. Un tableur a permis d'estimer l'évolution du taux de la population urbaine en France,
en pourcentage, par :
1(x)=0,00028x^3 -0,0276x^2 +0,968x+62,5
Lorsqu'on modélise
où x est le nombre d'années écoulées depuis 1960.
une évolution par une
Le rythme de croissance (instantané) du taux est assimilé à la dérivée de t. fonction, il faut que ses
a. Calculer la valeur estimée du taux de la population urbaine en 1968. valeurs, son sens de
Calculer le pourcentage d'erreur par rapport à la valeur effective de ce variation et son rythme
taux en 1968, donnée dans le texte.
de croissance soient
b. Exprimer t'(x), puis "(x) en fonction de .x.
compatibles avec les
c. Justifier que la fonction i est croissante sur [0;+ e[ . Interpréter.
données observées.
d. D'après le modèle, au cours de quelle année le rythme de croissance est-il le plus faible?
Est-ce compatible avec les données du texte ?
e. Expliquer pourquoi, à partir d'un moment, la fonction ne peut modéliser l'évolution du
taux de population urbaine.
Answers
Answer:
population and moment ne
Is this a function pls someone tell me
Answers
Functions must pass the vertical line test. This means that for every x value there must be ONLY ONE y value.
We can see in this table that the x value 25 has two different y values. Therefore, this is NOT a function.
Hope this helps!
Answer:
yes
Step-by-step explanation:
If the line only goes through one point once than yes. Vertical line test.
Note: "While a function may NOT have two y-values assigned to the same x-value, it may have two x-values assigned to the same y-value. Function: each x-value has only ONE y-value!"
3) Shelley deposits $605 into an account that earns 5% compound
interest each year. Calculate the interest she earns after 3 years.
Answers
Shelly earns $90.75 in compound interest after 3 years. All together she has $695.75.
a rectangle is drawn so the width is 49 inches longer than the height. if the rectangle's diagonal measurement is 61 inches, find the height.
Answers
Refer to the attachment for figure:
The height of the rectangle = 11 inches
What is rectangle?
A rectangle is a type of quadrilateral with parallel sides equal to each other and four equal 90-degree vertices. Because of this, it is also known as an equiangular quadrilateral. Because the opposite sides of a rectangle are equal and parallel, it can also be referred to as a parallelogram.
Let x= height
Width becomes x+49
Diagonal BD=61 inches
By pythagoras theorem,
BD²=BC²+CD²
61²= (x+49)²+x²
3721=x²+98x+2401+x²
On simplification,
x²+49x-660=0
Find the factors
(x+60)(x-11)=0
x=-60, x=11
Consider positive value for height
height = 11 inches
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Complete the missing steps to express in simplest radical form.
Answers
Check the attached image
Answers
B
Step-by-step explanation:
Note: This doesn’t go to all systems of equation
++++++++++++++++++++++++++++++++++
Here we are given a graph where there’s basically a inequality and we are trying to find out: “Which point is a solution to the inequality?”
Answer + explanation:
Answer: O B. (0, 5)
It would be (0, 5)
Explanation:
Any point inside the shaded area of the inequality would be a solution to the system of equation
Note: The type of inequality that we are taking a look at is a dash line
What do I mean by that? That any point that is in the dash CANNOT be a solution
Therefore our answer is B
2) The ratio of adults to children in the sports club is 5:2.
There are 120 adults in the club. How many children are
there?
Answers
Answer:
48 children
Step-by-step explanation:
For every 5 adults there are 2 children.
so for every 1 adult there is 2/5 of a child.
So number of children = 120 * 2/5
= 240/5
= 48.
I will MARK THE CROWN IF SOMEONE ANSWERS THESES
Answers
Answer:
the last picture answer is
[alternate exterior angle ]
the third picture answer is
[alternate interior angle]
Alisha needs to order a large number of T-shirt She has two print shops to choose from, Smith's T-Shirt Shop and Brilliant Print Shop The per-item price at Smith's T-Shirt Shop declines as the quantity ordered reaches certain numbers. The graph shows how much Smith's T-Shirt Shop charges based on the number of T -shirts ordered. Brilliant Print Shop also charges less as the quantity of T-shirts ordered increases. Its pricing structure is a flat fee of $200 plus $14 per T-shirt for orders of 1-100 T-shirts, no flat fee and $10 per T-shirt for orders of 101-200 T-shirts, and no flat fee and 8 per T -shirt for orders of 201 or more T-shirts. Write functions to describe the total charges from both shops as a function of the number of T -shirts in the order. Define the variables . Then graph the function for Brilliant Print Shop on the same coordinate grid as Smith's T-Shirt Shop Alisha needs 120 T -shirts. Which shop should she choose ? Provide evidence to support your answer . Next, compare the key features of the graphs of the functions in the context of the problem including the initial values and their end behaviors .
Answers
Alisha can choose either shop based on personal preference or other factors like turnaround time or quality of service, as both options have the same charge for her order of 120 T-shirts.
Let's define the variables for the two print shops:
- For Smith's T-Shirt Shop:
- Let x be the number of T-shirts ordered.
- Let S(x) be the total charge from Smith's T-Shirt Shop.
- For Brilliant Print Shop:
- Let y be the number of T-shirts ordered.
- Let B(y) be the total charge from Brilliant Print Shop.
Now let's write the functions for the total charges:
For Smith's T-Shirt Shop:
- For 0 ≤ x ≤ 100: S(x) = 12x
- For 101 ≤ x ≤ 200: S(x) = 10x
- For x ≥ 201: S(x) = 8x
For Brilliant Print Shop:
- For 1 ≤ y ≤ 100: B(y) = 200 + 14y
- For 101 ≤ y ≤ 200: B(y) = 10y
- For y ≥ 201: B(y) = 8y
To compare the two options, let's evaluate the charges for Alisha's order of 120 T-shirts:
For Smith's T-Shirt Shop:
- For 101 ≤ x ≤ 200: S(120) = 10 * 120 = $1,200
For Brilliant Print Shop:
- For 101 ≤ y ≤ 200: B(120) = 10 * 120 = $1,200
Both shops charge the same amount for 120 T-shirts, which is $1,200. Therefore, Alisha can choose either shop.
Now let's compare the key features of the graphs of the functions for both shops:
Smith's T-Shirt Shop:
- Initial Value: The total charge starts at $0 when no T-shirts are ordered.
- End Behavior: As the number of T-shirts ordered increases, the total charge decreases. The rate of decrease changes at 100 and 200 T-shirts.
Brilliant Print Shop:
- Initial Value: The total charge has a flat fee of $200 when ordering 1-100 T-shirts.
- End Behavior: As the number of T-shirts ordered increases, the total charge decreases. The rate of decrease changes at 100 and 200 T-shirts.
Both shops have different pricing structures, but they both decrease the total charge as the number of T-shirts ordered increases. Smith's T-Shirt Shop has a tiered pricing structure, while Brilliant Print Shop has different rates for different ranges. The key difference is that Brilliant Print Shop has a flat fee for the first range of T-shirts (1-100).
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Between 1998 and 2018, inflation for prices of goods and services has been about 51%. Suppose a salon charged $18 for a basic haircut in 1998 and has been raising prices by a steady percentage each year to keep up with inflation.
Answers
Answer: $22.12
Step-by-step explanation:
I just did the compound interest formula which is
starting amount * (1. interst rate) ^ number of years
example if you have 100$ and you want to know how much it is worth if it appretiates by 7% of a period of 20 years it would look something like this;
100 * (1.10) ^20 = 672.74$
but since you have to figure out what it was in 2008 which was exactly half way in the period you divide the exponent by half so your formula should be;
I know the answer is right because I asked my teacher and it's correct.
REAL EXAMPLE: 18 * (1.51) ^.5 = 22.12$
The amount should be $22.12.
Important information:Between 1998 and 2018, inflation for prices of goods and services has been about 51%. Suppose a salon charged $18 for a basic haircut in 1998calculation:\(= 18 \times (1.51) ^{.5}\)
= $22.12
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Jill babysat for 7 1/2 hours and earned $63.75. How much money does she earn per hour?
Answers
Answer:
$8.50 per hour
Step-by-step explanation:
63.75 / 7.5 = 8.5