Use the method of variation of parameters to find a particular solution of the differential equation 4y" – 4y +y = 16et/2 that does ' not involve any terms from the homogeneous solution. = Y(t) =
Answers
The particular solution that does not involve any terms from the homogeneous solution is given by:\(Y(t) = C3 + C4te^(-t/2).\)
To find a particular solution of the given differential equation using the method of variation of parameters, we follow these steps:
Solve the associated homogeneous equation: 4y" - 4y + y = 0.
The characteristic equation is:
\(4r^2 - 4r + 1 = 0.\)
Solving the quadratic equation, we find two repeated roots: r = 1/2.
Therefore, the homogeneous solution is given by: y_h(t) = C1\(e^(t/2)\) + C2t\(e^(t/2),\) where C1 and C2 are constants.
Find the particular solution using the variation of parameters.
Let's assume the particular solution has the form:
\(y_p(t) = u1(t)e^(t/2) + u2(t)te^(t/2).\)
To find u1(t) and u2(t), we differentiate this expression:
\(y_p'(t) = u1'(t)e^(t/2) + u1(t)(1/2)e^(t/2) + u2'(t)te^(t/2) + u2(t)e^(t/2) + u2(t)(1/2)te^(t/2).\)
We equate the coefficients of e^(t/2) and te^(t/2) on both sides of the original equation:
\((1/2)(u1(t) + u2(t)t)e^(t/2) = 16e^(t/2).\)
From this, we can deduce that u1(t) + u2(t)t = 32.
Differentiating again:
\(y_p''(t) = u1''(t)e^(t/2) + u1'(t)(1/2)e^(t/2) + u1'(t)(1/2)e^(t/2) + u1(t)(1/4)e^(t/2) + u2''(t)te^(t/2) + u2'(t)e^(t/2) + u2'(t)(1/2)te^(t/2) + u2(t)e^(t/2) + u2(t)(1/2)te^(t/2).\)
Setting the coefficient of \(e^(t/2)\)equal to zero:
\((u1''(t) + u1'(t) + (1/4)u1(t))e^(t/2) = 0.\)
Similarly, setting the coefficient of \(te^(t/2)\)equal to zero:
\((u2''(t) + u2'(t) + (1/2)u2(t))te^(t/2) = 0.\)
These two equations give us a system of differential equations for u1(t) and u2(t):
u1''(t) + u1'(t) + (1/4)u1(t) = 0,
u2''(t) + u2'(t) + (1/2)u2(t) = 0.
Solving these equations, we obtain:
u1(t) = C3\(e^(-t/2)\) + C4t\(e^(-t/2),\)
u2(t) = -4C3\(e^(-t/2)\) - 4C4t\(e^(-t/2).\)
Substitute the values of u1(t) and u2(t) into the assumed particular solution:
\(y_p(t) = (C3e^(-t/2) + C4te^(-t/2))e^(t/2) - 4C3e^(-t/2) - 4C4te^(-t/2).\)
Simplifying further:
\(y_p(t) = C3 + C4te^(-t/2) - 4C3e^(-t/2) - 4C4te^(-t/2).\)
So, the particular solution that does not involve any terms from the homogeneous solution is given by:
\(Y(t) = C3 + C4te^(-t/2).\)
Here, C3 and C4 are arbitrary constants that can be determined using initial conditions or boundary conditions if provided.
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Related Questions
Pls help quick this is timed DDDDD:
Answers
Answer:
1400
Step-by-step explanation:
it will be easier to first do 30 times 60, which is 180, then subtract the parts
the left up part is 100, the left bottom is 150, the top right is 150, added together, is 400
1800-400
1. An account is opened with a balance of $2800
earning 4.25% simple interest. What will be the
balance in the account in 30 years?
Answers
Answer:
The simple interest in the account will be $3570 and the total amount including principle and simple Interest will be $6370Step-by-step explanation:
firstly ,
Given That
principal(p)=$2800
Rate(R)=4.25%
Time(T)=30 years
now , we have from formula
simple interest (S.I)= P × T ×R / 100
= (2800×30×4.25) / 100
= $3570
Therefore , Simple Interest in 30 years will be $3570
now , we know
Amount(A) = Principal (P) + Interest (I)
= $2800 + $3570
= $ 6370
Therefore the simple interest in 30 years will be $3570 and the total amount in the bank will be $6370 .
The distance around the earth (circumference) is 4.0074 x 10° centimeters.
Write this in decimal form.
Answers
Answer:
4007400000
You move the decimal place to the right 9 places.
Step-by-step explanation:
The required distance around the earth (circumference) in standard form is 40,074,000,000.
What is a number system?A number system is described as a procedure of organizing to express digits. It is the mathematical notation for representing the numbers of a given set by using numbers or other characters in a uniform method. It delivers a special exhibit of every digit and defines the arithmetic structure.
Here,
The number 4.0074 x 10¹⁰ means 4.0074 multiplied by 10 to the power of 10. To convert this number to standard form, we simply need to move the decimal point 10 places to the right.
So the answer in standard form is:
40,074,000,000
Thus, the required distance around the earth (circumference) in standard form is 40,074,000,000.
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Find the value of p for which the polynomial x3 + 4x²-px-18 is exactly divisible by x-2. Hence factories the polynomial
Answers
Solution in da attachment!! :)
what is the value of x when y= -1
Answers
Answer:
x=+1
Step-by-step explanation:
the value of x will be positive 1 for we will take x=0 y=-1 where we inter change the values to be x=y-1=0
Remember, we always want to draw our image first. Figure 26. Line TV with midpoint U. Segment lengths has been appropriately labeled. Since we know is the midpoint, we can say Answer substituting in our values for each we get: Answer Solve for We now want to solve for . Answer Answer Solve for , , and This is just the first part of our question. Now we need to find , , and . Lets start with and . We know that so let’s substitute that in. Answer Answer We will do the same for . From our knowledge of midpoint, we know that should equal , however let’s do the math just to confirm. We know that so let’s substitute that in. Answer Answer Using the segment addition postulate we know: Answer
Answers
The blanks in each statement about the line segment should be completed as shown below.
How to fill in the blanks about the line segment?Since we know U is the midpoint, we can say TU=8x + 11 substituting in our values for each we get:
8x + 11 = 12x - 1
Solve for x
We now want to solve for x.
−4x+11=−1
−4x = -12
x= 3
Solve for TU, UV, and TV
This is just the first part of our question. Now we need to find TU, UV, and TV. Lets start with TU and UV.
TU=8x+11 We know that x=3 so let’s substitute that in.
TU=8(3)+11
TU= 35
We will do the same for UV. From our knowledge of midpoint, we know that TU should equal UV, however let’s do the math just to confirm.
UV=12x−1 We know that x=3 so let’s substitute that in.
UV=12(3)−1
UV= 35
Based on the segment addition postulate, we have:
TU+UV=TV
35+35=TV
TV= 70
Find the detailed calculations below;
TU = UV
8x + 11 = 12x - 1
8x + 11 - 11 = 12x - 1 - 11
8x = 12x - 12
8x - 12x = 12x - 12 - 12x
-4x = -12
x = 3
By using the substitution method to substitute the value of x into the expression for TU, we have:
TU = 8x + 11
TU = 8(3) + 11
TU = 24 + 11
TU = 35
By applying the transitive property of equality, we have:
UV = TU and TU = 15, then UV = 35
By applying the segment addition postulate, we have:
TV = TU + UV
TV = 35 + 35
TV = 70
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In Exercises 33-38, find the distance from the point to the line.
33. (0, 0, 12); x = 41, y=-21, z=21
34. (0, 0, 0); x=5+ 31, y=5+41, z=-3-5t
35. (2, 1, 3); x = 2 + 21, y=1+61, z=3
36. (2. 1,-1); x = 2t, y = 1 + 21, z=21
37. (3,-1,4): x=4-1, y=3+21, z=-5+31
38. (-1.4,3); x = 10+ 4t, y=-3, z=41
Answers
The distance from the point (0, 0, 12) to the line x = 41, y = -21, z = 21 is 21 units.
What is the distance between (0, 0, 12) and the line x = 41, y = -21, z = 21?The given question asks for the distance between a point and a line in each exercise. In this particular exercise (Exercise 33), the point is (0, 0, 12), and the line is represented by the equations x = 41, y = -21, z = 21.
To find the distance between a point and a line, we can use the formula derived from the concept of vector projection. The formula states that the distance between a point P and a line L is equal to the magnitude of the vector projection of the vector from a point on the line to the point P onto the direction vector of the line.
In this case, the direction vector of the line is (1, -1, 0). We can choose any point on the line to calculate the distance, so let's consider the point (41, -21, 21) on the line. The vector from this point to the given point P is (-41, 21, -9).
Next, we calculate the dot product of this vector and the direction vector of the line:
(-41, 21, -9) · (1, -1, 0) = (-41) + (-21) + (0) = -62.
The magnitude of the direction vector is √(1^2 + (-1)^2 + 0^2) = √2.
Finally, we can find the distance by dividing the absolute value of the dot product by the magnitude of the direction vector:
Distance = |(-62)| / √2 = 62 / √2 = 21√2 ≈ 29.7 units.
Therefore, the distance from the point (0, 0, 12) to the line x = 41, y = -21, z = 21 is approximately 29.7 units.
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when the base-$b$ number $11011 b$ is multiplied by $b-1$, then $1001 b$ is added, what is the result (written in base $b$)?
Answers
we express the result in base $b$: $b^5 - 2b^4 + 3b^3 - 2b^2 + 2b^1 + b^0$ (written in base $b$)
To find the result when the base-$b$ number $11011_b$ is multiplied by $b-1$ and then $1001_b$ is added, we can follow these steps:
Step 1: Multiply $11011_b$ by $b-1$.
Step 2: Add $1001_b$ to the result from step 1.
Step 3: Express the final result in base $b$.
To perform the multiplication, we can expand $11011_b$ as $1 \cdot b^4 + 1 \cdot b^3 + 0 \cdot b^2 + 1 \cdot b^1 + 1 \cdot b^0$.
Now, we can distribute $b-1$ to each term:
$(1 \cdot b^4 + 1 \cdot b^3 + 0 \cdot b^2 + 1 \cdot b^1 + 1 \cdot b^0) \cdot (b-1)$
Expanding this expression, we get:
$(b^4 - b^3 + b^2 - b^1 + b^0) \cdot (b-1)$
Simplifying further, we get:
$b^5 - b^4 + b^3 - b^2 + b^1 - b^4 + b^3 - b^2 + b^1 - b^0$
Combining like terms, we have:
$b^5 - 2b^4 + 2b^3 - 2b^2 + 2b^1 - b^0$
Now, we can add $1001_b$ to this result:
$(b^5 - 2b^4 + 2b^3 - 2b^2 + 2b^1 - b^0) + (1 \cdot b^3 + 0 \cdot b^2 + 0 \cdot b^1 + 1 \cdot b^0)$
Simplifying further, we get:
$b^5 - 2b^4 + 3b^3 - 2b^2 + 2b^1 + b^0$
Finally, we express the result in base $b$:
$b^5 - 2b^4 + 3b^3 - 2b^2 + 2b^1 + b^0$ (written in base $b$)
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Find the value of k and yz if y is between x and z. x y = 3 k − 2 , y z = 7 k 4 , x z = 4 k 38
Answers
Considering that y is between x and z, we have that:
The value of k is of k = 6.The length of yz is 46 units.How to find the value of k and of yz?We consider that y is between x and z, hence the length of the segment is given by:
xz = xy + yz
The separate lengths are given as follows:
xz = 4k + 38.xy = 3k - 2.yz = 7k + 4.Hence:
4k + 38 = 3k - 2 + 7k + 4.
4k + 38 = 10k + 2
6k = 36
k = 6.
Hence the length of yz is given by:
yz = 7k + 4 = 7(6) + 4 = 42 + 4 = 46 units.
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I need a answer fast thanks!
Answers
Answer:
Chart:
x y
-6 11
3 5
15 -3
-12 15
Step-by-step explanation:
The only things you can plug in are the domain {-12, -6, 3, 15}
Plug in the domain into equation to find y.
-6 :
y = -2/3 (-6) +7
y = +47
y=11
(-6,11)
3:
y = -2/3 (3) +7
y = -2 +7
y = 5
(3, 5)
15:
y = -2/3 (15) +7
y = -10 +7
y = -3
(15 , -3)
-12:
y = -2/3 (-12) +7
y = 8 + 7
y= 15
(-12,15)
Answer:
1) 11
2) 3
3) -3
4) -12
Step-by-step explanation:
eq(1):
\(y = \frac{-2}{3} x + 7\\\\y - 7 = \frac{-2}{3} x\\\\x = (y - 7)\frac{-3}{2} \\\\x = (7-y)\frac{3}{2} ---eq(2)\)
1) x = -6
sub in eq(1)
\(y = \frac{-2}{3} (-6) + 7\\\\y = \frac{12}{3} + 7\\\\y = 4+7\\\\y = 11\)
2) y = 5
sub in eq(2)
\(x = (7-5)\frac{3}{2} \\\\x = 3\)
3) x = 15
sub in eq(1)
\(y = \frac{-2}{3} 15 + 7\\\\y = \frac{-30}{3} +7\\\\y = -10 + 7\\\\y = -3\)
4)
sub in eq(2)
\(x = (7-15)\frac{3}{2} \\\\x = -8\frac{3}{2}\\ \\x = -12\)
What is the Roman number of 500 and 1000?
Answers
Answer:
500=D 100=M
Step-by-step explanation:
I hope that helps :D
(7 × 8) − (35 + 12) − (2 × 2) =
Answers
Answer:
5
Step-by-step explanation:
(7 × 8) − (35 + 12) − (2 × 2)
Solve the operations in the brackets
(56) − (47) − (4)
Subtract
9 − 4
5
I hope this helps!
Jana is a caterer . She's making lasagna cupcakes and Gorgonzola onion tarts for a party ,and only has a limited time to finish . She already has all her fillings ready and just needs to assemble and bake the appetizers . It takes 10 minutes to assemble each pan of lasagna cupcakes . It takes 15 minutes to roll out the Gorgonzola onion tarts and fill each pan . She has a maximum of 2 hours to assemble the appetizers . Next she needs to bake the appetizers . Each pan of lasagna cupcakes takes 20 minutes to bake . Each pan of Gorgonzola tarts takes 6 minutes to bake . She has 60 minutes to bake the appetizers . What system of inequalities that models this scenario ? CHECK ALL THAT APPLY . Also how would those inequalities look graphed ?
Answers
Answer::
\(\begin{gathered} 20x+6y\le60 \\ 10x+15y\le120 \\ x\ge0 \\ y\ge0 \end{gathered}\)Explanation:
Let the number of lasagna cupcakes made = x
Let the number of Gorgonzola onion tarts made = y
0. It takes ,10 minutes, to assemble each pan of lasagna cupcakes.
,1. It takes ,15 minutes, to roll out the Gorgonzola onion tarts and fill each pan.
,2. She has a maximum of ,2 hours (120 minutes), to assemble the appetizers.
These translate to the inequality:
\(10x+15y\le120\)0. Each pan of lasagna cupcakes takes 20 minutes to bake.
,1. Each pan of Gorgonzola tarts takes 6 minutes to bake.
,2. She has 60 minutes to bake the appetizers.
These translate to the inequality:
\(20x+6y\le60\)Since she must bake either lasagna cupcakes or Gorgonzola tarts, we have that:
\(\begin{gathered} x\ge0 \\ y\ge0 \end{gathered}\)So the system of inequalities is:
\(\begin{gathered} 20x+6y\le60 \\ 10x+15y\le120 \\ x\ge0 \\ y\ge0 \end{gathered}\)The graph that bests represents this scenario is:
You get 10 points❄️ Plz plz plz is math
Answers
explanation:
Do you find this with synthetic and long divison?
Answers
Answer:
p=-2
Step-by-step explanation:
we can solve by both methods
if it is divisible by x-1,then remainder is zero.
i solve by synthetic division.
x-1=0,x=1
1 | 1 -1 p 2
| 1 0 p
_________
1 0 p |2+p
Here 2+p is remainder.
p+2=0
p=-2
Which statement about equations and expressions is true? An example of an equation is 4. 5 x = 13. 2 because it shows that two expressions are equal. An example of an expression is 4. 5 x = 13. 2 because it shows that two equations are equal. An example of an equation is 4. 5 x = 13. 2 because it is a mathematical phrase represented by numbers, a variable, and operations. An example of an expression is 4. 5 x = 13. 2 because it is a mathematical phrase represented by numbers, a variable, and operations.
Answers
An example of an equation is 4.5 x = 13.2 because it shows that two expressions are equal.
What is the difference between an expression and an equation?We can say that an expression is a random combination of numbers, variables, functions, etc.
For example, 3x - 2 is an expression.
While on the other hand, an equation means that two different expressions are connected to each other by an equal sign in between, For example, 3x - 2 = 5 + x is an equation.
Based on the above examples, we can say that:
An example of an equation is 4.5 x = 13.2 because it shows that two expressions are equal.
Therefore, An example of an equation is 4.5 x = 13.2 because it shows that two expressions are equal.
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Omar thinks of a two digit number it is a factor of 78 it is a prime number what is his number
Answers
Factors of 78 are:
1,2,3,6,13,26,39,78.
13 is the prime two-digit number.
Answer:
\(13\)
Step-by-step explanation:
First write the factors of 78
\(1 \: \: 3 \: \: 6 \: \: 13 \: \: 26 \: \: 39 \: \: 78\)
Now write the prime number that you can see above
\(3 \: \: \: 13\)
Now write the two digit number ( prime number) that you can see above
\(13\)
Slope of -3,2 need help
Answers
Answer:
I think the answer is 2/-3
Step-by-step explanation:
-3/2
x y
Rise/Run
The slope of the line who passes through the points (-1, 2) and (3,-2) is
Answers
Connor has made deposits of $125.00 into his savings account at the end of every three months for 15 years. If interest is 10% per annum compounded monthly and he leaves the accumulated balance for another 5 years, what would be the balance in his account then?
Answers
You can calculate the balance in Connor's account after 15 years of regular deposits and an additional 5 years of accumulation.
To calculate the balance in Connor's account after 15 years of regular deposits and an additional 5 years of accumulation with 10% interest compounded monthly, we can break down the problem into two parts:
Calculate the accumulated balance after 15 years of regular deposits:
We can use the formula for the future value of a regular deposit:
FV = P * ((1 + r/n)^(nt) - 1) / (r/n)
where:
FV is the future value (accumulated balance)
P is the regular deposit amount
r is the interest rate per period (10% per annum in this case)
n is the number of compounding periods per year (12 for monthly compounding)
t is the number of years
P = $125.00 (regular deposit amount)
r = 10% = 0.10 (interest rate per period)
n = 12 (number of compounding periods per year)
t = 15 (number of years)
Plugging the values into the formula:
FV = $125 * ((1 + 0.10/12)^(12*15) - 1) / (0.10/12)
Calculating the expression on the right-hand side gives us the accumulated balance after 15 years of regular deposits.
Calculate the balance after an additional 5 years of accumulation:
To calculate the balance after 5 years of accumulation with monthly compounding, we can use the compound interest formula:
FV = P * (1 + r/n)^(nt)
where:
FV is the future value (balance after accumulation)
P is the initial principal (accumulated balance after 15 years)
r is the interest rate per period (10% per annum in this case)
n is the number of compounding periods per year (12 for monthly compounding)
t is the number of years
Given the accumulated balance after 15 years from the previous calculation, we can plug in the values:
P = (accumulated balance after 15 years)
r = 10% = 0.10 (interest rate per period)
n = 12 (number of compounding periods per year)
t = 5 (number of years)
Plugging the values into the formula, we can calculate the balance after an additional 5 years of accumulation.
By following these steps, you can calculate the balance in Connor's account after 15 years of regular deposits and an additional 5 years of accumulation.
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Find the domain for the rational function f of x equals quantity x plus 4 over quantity 3 times x minus 5. negative infinity to negative five thirds and negative five thirds to infinity negative infinity to five thirds and five thirds to infinity (−∞, −4)( −4, ∞) (−∞, 4)(4, ∞)
Answers
Answer:
(-∞, 5/3) and (5/3,∞)
Step-by-step explanation:
f(x) = (x+4)/ (3x-5)
The domain is the values that x can be
We have one discontinuity or value the x cannot be
The denominator cannot be zero
3x-5 ≠0
3x≠5
x ≠5/3
The domain is all real numbers but x = 5/3
(-∞, 5/3) and (5/3,∞)
Find the equation of the line passing through the given point and parallel to the given line.
(-1, 2), 2y = 6x + 13
Answers
The equation of the line passing through the given point and parallel to the given line (-1, 2), 2y = 6x + 13 will be y=3x+3.
What is a straight line?A straight line is a combination of endless points joined on both sides of the point.
The slope 'm' of any straight line is given by:
A linear equation has the form y = mx + b in the slope-intercept format. X and Y are the variables in the equation. The values m and b represent the line's slope (m) and the value of y when x is 0.
\(\rm m =\dfrac{y_2-y_1}{x_2-x_1}\)
It is given that, the equation of the line passing through the given point and parallel to the given line.(-1, 2), 2y = 6x + 13
The slope of the given line is,
2y = 6x + 13
y=3x+13/2
m=3
The equation of the line passing through the (-1, 2) and slope equal to 3 is,
y-2=3(x+1)
y-2=3x+1
y=3x+3
Thus, the equation of the line passing through the given point and parallel to the given line (-1, 2), 2y = 6x + 13 will be y=3x+3.
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Verify that the Mean Value Theorem can be applied to the function f(x) = x^4/5 on the interval (0,32). Then find the value of e in the interval that satisfies the conclusion of the Mean Value Theorem. Enter the exact answer
Answers
The value of e in the interval (0,32) that satisfies the conclusion of the Mean Value Theorem is e = 2^-20.
To verify that the Mean Value Theorem can be applied to f(x) = x^4/5 on the interval (0,32), we need to check whether the function is continuous on the closed interval [0,32] and differentiable on the open interval (0,32).
First, let's check if the function is continuous on the closed interval [0,32]. Since f(x) is a polynomial function with positive exponents, it is continuous everywhere, including at x = 0 and x = 32. Therefore, f(x) is continuous on the closed interval [0,32].
Next, let's check if the function is differentiable on the open interval (0,32). We can use the power rule of differentiation to find that f'(x) = (4/5)x^-1/5 = 4x^-1/5/5. This derivative exists and is continuous for all x in the open interval (0,32). Hence, f(x) is differentiable on the open interval (0,32).
Since f(x) is continuous on the closed interval [0,32] and differentiable on the open interval (0,32), we can apply the Mean Value Theorem. By the theorem, there exists at least one value e in the open interval (0,32) such that:
f'(e) = (f(32) - f(0))/(32 - 0)
Plugging in the values of f(x) and f'(x) we found earlier, we get:
4e^-1/5/5 = (32^4/5 - 0)/(32 - 0)
Simplifying this equation, we get:
4e^-1/5 = 1024/5
Dividing both sides by 4 and raising to the 5th power, we get:
e = (1024/5/4)^-5 = 2^-20
Therefore, the value of e in the interval (0,32) that satisfies the conclusion of the Mean Value Theorem is e = 2^-20.
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Which expression below does not give the area of this figure?
a
b
c(a+b)
(a+b)c
ab + ac
ac + bc
Answers
Answer:
Step-by-step explanation:
Ab + ac
The two general approaches to forecasting are: Multiple Choice mathematical and statistical. historical and associative. judgmental and qualitative. precise and approximation. qualitative and quantitative.
Answers
Qualitative forecasting involves using subjective judgments ,The two general approaches to forecasting are qualitative and quantitative.
Qualitative forecasting involves using subjective judgments, opinions, and expert knowledge to predict future outcomes. This approach relies on qualitative data, such as market trends, customer preferences, and industry insights. It is often used when historical data or quantitative models are not available or not reliable. Qualitative forecasting methods include market research, surveys, expert opinions, and Delphi technique.
Quantitative forecasting, on the other hand, involves using mathematical and statistical models to analyze historical data and identify patterns and trends. This approach relies on quantitative data, such as sales figures, financial data, and market statistics. Quantitative forecasting methods include time series analysis, regression analysis, moving averages, exponential smoothing, and econometric models.
Both qualitative and quantitative approaches have their strengths and limitations, and the choice of approach depends on the nature of the problem, available data, and the expertise and resources of the forecaster. Often, a combination of both approaches is used to achieve more accurate and reliable forecasts.
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The two general approaches to forecasting are judgmental and qualitative, and mathematical and statistical. Judgmental and qualitative forecasting involves subjective factors such as experience and intuition. Mathematical and statistical forecasting relies on historical data and quantitative analysis.
Explanation:The two general approaches to forecasting are judgmental and qualitative, and mathematical and statistical.
Judgmental and qualitative: This approach involves relying on expert opinions and subjective judgment to make forecasts. It is based on subjective factors such as experience, intuition, and personal insights.
Mathematical and statistical: This approach involves using mathematical models and statistical techniques to make forecasts. It relies on historical data and quantitative analysis to predict future outcomes.
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(3x - 6)(3x + 2)
Answer (in Standard Form) =
a =
b =
c =
Answers
Answer:
9x²+12x+12
a = 9
b = 12
c = 12
Step-by-step explanation:
Factor
9x²+6x-18x-12
9x²-12x-12
a = 9
b = 12
c = 12
the diagram shows triangle PQR. PSR is a straight line. Size of angle SQR 3:1. Work out the size of angle PSQ
Answers
The value of the size of angle PSQ of the given triangle is; 61°
What us the missing angle of the triangle?From the given triangle ΔPQR, we see that;
m∠QPS = 65°
m∠PRQ = 43°
Now, it is clear that Line PSR is a straight line divided in the ratio;
size of angle PQS : size of angle SQR = 3:1
m∠PQS : m∠SQR = 3:1
Thus, since sum of angles in a triangle is 180°, then we say that;
∠PQR = 180° - (∠QPS + ∠PRQ)
Plugging in the relevant values;
∠PQR = 180° - (65° + 43°)
∠PQR = 72°
Using the concept of angle addition postulate, we have that;
∠PQR = m∠PQS + m∠SQR
Since m∠PQS : m∠SQR = 3:1, then we have;
m∠PQS = 3 × m∠SQR
Thus;
∠PQR = (3 × m∠SQR) + m∠SQR
∠PQR = 4 × m∠SQR
4 × m∠SQR = ∠PQR
4 × m∠SQR = 72°
m∠SQR = 72°/4
m∠SQR = 18°
m∠PQS = 3 × m∠SQR
m∠PQS = 3 × 18°
m∠PQS = 54°
Finally;
∠PSQ = 180° - (65° + 54°)
∠PSQ = 61°
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It is nonsensical to talk about the direction of specific differences in ANOVA because it is a(n) ______ test. Group of answer choices omnibus monobus multibus octobus
Answers
It is nonsensical to talk about the direction of specific differences in ANOVA because it is an omnibus test.
An omnibus test is a statistical test that evaluates whether there is a difference between groups or conditions, without specifying which groups or conditions differ from each other. In the case of ANOVA (Analysis of Variance), it tests whether the means of two or more groups are equal or not. However, it does not tell us which specific groups are different from each other.
Instead, to identify the specific group differences, post-hoc tests such as Tukey's test, Bonferroni's test, or Scheffe's test can be used. These tests compare the means of each group and identify which groups differ significantly from each other.
Therefore, talking about the direction of specific differences in ANOVA is nonsensical because ANOVA does not provide information about which groups differ from each other. It only tells us whether there is a significant difference between groups or not.
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\({[x,y]:y=\frac{x}{x-8}]\)
Answers
PLEASE HELP ASAP!!!!!
Answers
Answer:
9<✓88<10
Step-by-step explanation:
✓88 = 9.38083