Describe all solutions of Ax = b, where A = [3 5 -4 -3 -2 4 6 1 -8]Describe the general solution in parametric vector form.
Answers
The general solution of Ax = b, where A = [3 5 -4; -3 -2 4; 6 1 -8], is given by the vector:
x = (2z - 1), y = (-2z + 3), z = z
The solution can be expressed in parametric vector form as:
[x; y; z] = [2z - 1; -2z + 3; z] = z[2; -2; 1] + [-1; 3; 0]
where [2; -2; 1] is the direction vector of the line of solutions and [-1; 3; 0] is a particular solution.
To describe all solutions of Ax = b, we need to solve the system of linear equations given by the matrix equation, where A = [3 5 -4; -3 -2 4; 6 1 -8] and b is a given vector.
We can start by forming the augmented matrix [A|b] and row reducing to obtain the reduced row echelon form:
1 0 -2 | -1
0 1 2 | 3
0 0 0 | 0
The last row corresponds to the equation 0x + 0y + 0z = 0, which simplifies to 0 = 0. This equation is always true and does not provide any additional information about the variables x, y, and z.
The first two rows correspond to the equations x - 2z = -1 and y + 2z = 3. We can solve for the variables in terms of the free variable z by adding 2z to both sides:
x = 2z - 1
y = -2z + 3
Therefore, the general solution of Ax = b is given by the vector:
x = (2z - 1)
y = (-2z + 3)
z = z
We can express this in parametric vector form as:
[x; y; z] = [2z - 1; -2z + 3; z] = z[2; -2; 1] + [-1; 3; 0]
where [2; -2; 1] is the direction vector of the line of solutions and [-1; 3; 0] is a particular solution. This means that any solution of Ax = b can be obtained by taking a scalar multiple of the direction vector and adding it to the particular solution.
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Related Questions
wow lashes is a false eyelashes company. the companymade $50,000 in 2021. they have already sold enough lashes this year to make $5,500 in profit. this year, they plan to sell at least 800 more packs of lashes than the previous year. each pack of lashes makes the company $12
Answers
Answer:
whats the question
Step-by-step explanation:
what is the domain of validity for csc 0=1/sin 0
a. all real numbers
b. all real numbers except odd multiples of pi/2
c. all real numbers except even multiples of pi/2
d. all real numbers except multiples of pi
Answers
The correct answer is (b) all real numbers except odd multiples of π/2. The domain of validity for cscθ (cosecant) is restricted because cosecant is undefined when the sine of an angle is zero.
In the trigonometric identity cscθ = 1/sinθ, the denominator sinθ becomes zero at odd multiples of π/2 (such as π/2, 3π/2, 5π/2, etc.), resulting in a division by zero error. Therefore, the cosecant function is not defined for these values of θ.
For all other real numbers θ, the sine function is non-zero and well-defined, allowing us to calculate the reciprocal of the sine and determine the value of the cosecant. Hence, the domain of validity for cscθ is all real numbers except odd multiples of π/2, as stated in option (b).
It's important to note that in trigonometry, the domain of validity is determined by avoiding any values that would lead to undefined expressions or division by zero errors.
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The domain of validity for csc θ = 1/sin θ is all real numbers except multiples of π, because at these points the sine function equals zero, and division by zero is undefined.
Explanation:In mathematics, the cosecant function (csc), is defined as the reciprocal of the sine function, or 1/sinθ. The domain of a function are all the possible input values that will yield real numbers (output). For the csc function, its domain includes all real numbers except where the denominator is zero because division by zero is undefined.
In the unit circle context, sine equals zero at 0, π, 2π, ..., and the negative counterparts. Basically, these are the multiples of π. Thus, for the csc function, the domain is all real numbers except multiples of π, which matches option d in your choices.
The domain of validity for csc θ = 1/sin θ is all real numbers except multiples of π.
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90 POINTS!!!! A sequence is defined by the recursive function f(n + 1) = –10f(n). If f(1) = 1, what is f(3)? 3 –30 100 –1,000
Answers
Answer:
A sequence is a chain of numbers all related. In this case, they are related by the rule "f(n + 1) = –10f(n)". Each number is called a term. Here is what the rule in this sequence means:
Since f(n + 1) is the "next" term and f(n) is the "current" term, to get to the next term, you take the current term and multiply by -10.
When they say f(1) = 1 it means that the first term (term number 1) is 1. When they ask "What is f(3)?", they are asking, "What is the 3rd term?"
Since term #1 is 1, then to find term #2, we multiply 1 by -10. So term #2 is -10. To find term #3, we take term #2 and multiply it by -10, so -10 x -10 = 100. So term #3 is 100
Step-by-step explanation:
Rosena had a balance of $200 in her checking account.
She withdrew $358.60 for Christmas gifts and then
deposited her paycheck of $1,450.25. What is her
ending balance?
Answers
Answer:
1291.65
Step-by-step explanation:
200-358.60=-158.60
1450.25-158.60=1291.65
The amount of money that Rosena had at the end of all deposits and credits will be $1291.65.
What is the arithmetic operator?Arithmetic operators are four basic mathematical operations in which summation, subtraction, division, and multiplication involve.,
As per the given,
Initial balance = $200
Withdrawl = -$358.60
Deposite = $1450.25
Total balance or ending balance = $200 - $358.60 + $1450.25
⇒ $1291.65
Hence "The amount of money that Rosena had at the end of all deposits and credits will be $1291.65".
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help me i need help will mark brainliest
Answers
Answer:
C
Step-by-step explanation:
i am smart
Answer: -3? i think..
Step-by-step explanation:
Forty boxes of baseballs weigh a total of 1,200 pounds. How many pounds would 4 boxes of baseballs weigh?How many pounds would 400 boxes of baseball weigh?
Answers
Answer: 4 boxes of baseballs weigh 120 pounds and 400 boxes weigh 12,000 pounds.
Step-by-step explanation:
We know that 40 boxes of baseballs weigh a total of 1,200 pounds.
So we can just that the unit rate of this by doing 1,200/40 = 30
After that we get that 1 box of baseballs weigh 30 pounds.
Next to find out how much 4 boxes of baseballs weigh we do 30 * 4 = 120 pound.
Lastly to find out how much 400 boxes of baseballs weigh we do 30 * 400 = 12,000 pounds
Given
f(x)= 2x2 + 5x - 17, find f(-1).
Answers
So here is the work:
F(-1)= 2*2 +5(-1) -17
= 4 + -5 -17
= -18
Let me know if this helped!
Answer:
Step by Step Solution:
More Icon
Reformatting the input :
Changes made to your input should not affect the solution:
(1): "x2" was replaced by "x^2".
Rearrange:
Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :
f*(x)-(2*x^2+5*x-17)=0
STEP
1
:
Equation at the end of step 1
fx - ((2x2 + 5x) - 17) = 0
STEP
2
:
Equation at the end of step 2
fx - 2x2 - 5x + 17 = 0
STEP
3
:
Solving a Single Variable Equation
3.1 Solve fx-2x2-5x+17 = 0
In this type of equations, having more than one variable (unknown), you have to specify for which variable you want the equation solved.
Step-by-step explanation:
n/−3 +5>4 Solve for this
Answers
Answer:
N<3
Step-by-step explanation:
A certain element x undergoes two successive alpha emission reactions followed by a beta emission reaction. The daughter nuclide formed is ac-230 (z=89). What is the identity of element x?
Answers
An element is a pure material made up of atoms with the same amount of protons in their nuclei. The atomic number and the mass number of the element X are 92 and 238 respectively.
What is an element?In chemistry, an element is a pure material made up of atoms with the same amount of protons in their nuclei. Chemical elements, unlike chemical compounds, cannot be broken down into simpler substances by any chemical process.
Let us consider, that z is the atomic no and A is the mass no of the parent element 'X'.
As per the question, X emits two successive alpha particles (²₁He) and one beta, i.e, particle and reached to daughter element (²³⁰₈₉Ac).
Now according to the question, we can write,
\(^A_ZX \overset{-\alpha}{\rightarrow}\ \ ^{A-4}_{Z-2}X\ +\ ^4_2He\ \ \overset{-\alpha}{\rightarrow}\ \ ^{A-8}_{Z-4}X\ +\ ^4_2He\ \ \overset{-\-\beta}{\rightarrow}\ \ ^{A-8}_{Z-3}X\ +\ ^0_{-1}He\)
We see, \(^A_ZX\) that after two α and one β of emission, we get the daughter element \(^{A-8}_{Z-3}X\). Again as given in the problem, the daughter element is \(^{230}_{89}AC\).
∴We can write-
\(^{A-8}_{Z-3}X=^{290}_{89}AC\)
comparing the two, we get,
Z-3=89
Z=92
A-8=230
A=238
Hence, the atomic number and the mass number of the element X is 92 and 238 respectively.
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Type the correct answer in the box. Use numerals instead of words,
Consider this expression.
m2 - 71 +22
When m
= -2 and n = 5, the value of the expression is
Answers
The value of the expression is -53.
What is an expression?An expression or algebraic expression is any mathematical statement which consists of numbers, variables and an arithmetic operation between them.
Given expression
m2 - 71 +22..................(1)
m = -2 and n = 5
Substitute m = -2 and n = 5 in equation(1)
⇒ m2 - 71 +22
⇒ (-2) × 2 - 71 + 22
⇒ -4 -71 +22
⇒ -75 + 22
⇒ -53
Hence, the value of the expression is -53.
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it is important for researchers to account for attrition or loss of participants during follow-up. true or false
Answers
Answer:
The answer is TRUE
Step-by-step explanation:
It will forever be important for researchers to account for attrition or loss of participants. This helps them trace back steps.
True. It is important for researchers to account for attrition or loss of participants during follow-up as it may introduce bias and affect the validity and generalizability of the study results.
Researchers should try to minimize attrition by implementing strategies such as frequent communication with participants, offering incentives, and using follow-up methods that are less burdensome for participants. When reporting study results, researchers should also provide information on the reasons for attrition and the characteristics of those who dropped out compared to those who completed the study.
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A -10 nC charge is located at (x, y) = (1.2 cm , 0 cm).
What is the x-component of the electric field at the position (x, y) = (−4.1cm, 0 cm)?Express your answer to two significant figures and include the appropriate units.
Answers
We can use Coulomb's law to calculate the magnitude of the electric field at a distance r away from a point charge Q:
E = k * Q / r^2
where k is Coulomb's constant, Q is the charge of the point charge, and r is the distance from the point charge.
In this problem, we have a point charge Q of -10 nC located at (1.2 cm, 0 cm), and we want to find the x-component of the electric field at a distance r = 5.3 cm away at position (-4.1 cm, 0 cm).
To find the x-component of the electric field, we need to use the cosine of the angle between the electric field vector and the x-axis, which is cos(180°) = -1.
So, the x-component of the electric field at position (-4.1 cm, 0 cm) is:
E_x = - E * cos(180°) = - (k * Q / r^2) * (-1)
where k = 9 x 10^9 N*m^2/C^2 is Coulomb's constant.
Substituting the given values, we get:
E_x = - (9 x 10^9 N*m^2/C^2) * (-10 x 10^-9 C) / (0.053 m)^2
E_x ≈ -30,566.04 N/C
Rounding this to two significant figures and including the appropriate units, we get:
The x-component of the electric field is about -3.1 x 10^4 N/C (to the left).
Jamie is working at Walmart to save up enough money to buy a new phone after she broke hers. She has $100 saved up already and saves $50 a week. Write an equation that could represent this situation.
Answers
More time on the Internet: A researcher polled a sample of 1020 adults in the year 2010, asking them how many hours per week they spent on the Internet. The sample mean was 10.52 with a standard deviation of 14.76. A second sample of 1071 adults was taken in the year 2012. For this sample, the mean was 9.58 with a standard deviation of 13.33. Assume these are simple random samples from populations of adults. Can you conclude that the mean number of hours per week spent on the Internet decreased between 2010 and 2012? Let μ 1 denote the mean number of hours spent on the Internet in 2010 and μ2 denote the E a 0.10 level and the P-value method with the table. mean number of hours spent on the Internet in 2012. a. State the appropriate null and alternate hypotheses.
b. Compute the test statistic. c. How many degrees of freedom are there, using the simple method?
Answers
a. Null Hypothesis: H0: μ1 = μ2 , Alternative Hypothesis: H1: μ1 > μ2
b. Test Statistic = 1.43
c. The degrees of freedom are 2089.
a. State the appropriate null and alternate hypotheses:
The hypothesis for testing if the mean number of hours per week spent on the Internet decreased between 2010 and 2012 can be stated as follows;
Null Hypothesis: The mean number of hours spent on the Internet in 2010 and 2012 are equal or there is no significant difference in the mean numbers of hours spent per week by adults on the Internet in 2010 and 2012. H0: μ1 = μ2
Alternative Hypothesis: The mean number of hours spent on the Internet in 2010 is greater than the mean number of hours spent on the Internet in 2012. H1: μ1 > μ2
b. Compute the test statistic: To calculate the test statistic we use the formula:
Test Statistic = (x¯1 − x¯2) − (μ1 − μ2) / SE(x¯1 − x¯2)where x¯1 = 10.52, x¯2 = 9.58, μ1 and μ2 are as defined above,
SE(x¯1 − x¯2) = sqrt(s12 / n1 + s22 / n2), s1 = 14.76, n1 = 1020, s2 = 13.33 and n2 = 1071.
Using the above values we have:
Test Statistic = (10.52 - 9.58) - (0) / sqrt(14.76²/1020 + 13.33²/1071) = 1.43
c. The degrees of freedom can be calculated
using the formula:
df = n1 + n2 - 2
where n1 and n2 are as defined above.
Using the above values we have:
df = 1020 + 1071 - 2 = 2089
Therefore, the degrees of freedom are 2089.
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Please help solve this problem
Answers
Answer:
120m/s
Step-by-step explanation:
v-? (speed)
s-5400m(travel)
t-45s(time)
v=s/t
v=5400/45
v=120m/s
Given the equations and the table below, what is the first x-value when the y-value of equation 2 is greater than the y-value of equation 1 after the functions first intersect?Equation 1: f(x)=5x^3Equation 2: f(x)=2x+3A: x=14B: x=7C: x=17D: x=12
Answers
From what I explained in the session before, the x value must be between 10 and 15, so only 2 options are viable, 14 and 12. Let's evaluate each of them
\(\begin{gathered} f(x)=5x^3 \\ f(12)=5(12)^3 \\ f(12)=5(1728) \\ f(12)=8640 \\ \\ f(x)=2^x+3 \\ f(12)=2^{(12)}+3 \\ f(12)=4096\text{ +3 = 4099} \end{gathered}\)So, 12 is not the answer. Let's evaluate 14
\(\begin{gathered} f(x)=5x^3 \\ f(14)=5(14)^3 \\ f(14)=5(2744) \\ f(14)=13720 \\ \\ f(x)=2^x+3 \\ f(14)=2^{14}+3 \\ f(14)=16384+3 \\ f(14)=16387 \end{gathered}\)So, x = 14 is the correct answer
help me out i will give brainlist
Answers
Answer:
no
Step-by-step explanation:
0.06 = \(\frac{6}{100}\) ← that is 6 books out of 100
she requires to have 60 out of 100 , that is
\(\frac{60}{100}\) = 0.6
(a) 11³ x 11=11
11³
||³ + x = || 2
Answers
Step-by-step explanation:
I suspect you mean
11³ × 11 = ?
11³ ÷ 11 = ?
11³ × 11 = 11⁴
11³ ÷ 11 = 11²
why ?
11³ = 11×11×11
11³ × 11 = 11×11×11 × 11 = 11×11×11×11 = 11⁴
11³ ÷ 11 = 11×11×11 / 11 = 11×11 × 1 = 11×11 = 11²
One equation in a system of equations with no solution is y=-20 +5.
Which equation could be the second equation in the system?
Answers
Answer:
the answerr is i9 dont know haha bum
Step-by-step explanation:
hahay
Answer:
B. 2x + y = 8
Step-by-step explanation:
y = -2x + 5 matches with 2x + y = 8, as they have same slope of "-2".
There you go, it is the second equation with y = -2x + 5.
PLEASE ANSWER FAST!IM TIMED——————————What is the sum of the fractions? Use the number line to help find the answer.
3
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6
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4
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Kk
Answers
In an ideal transformer, use the relationship between primary and secondary emfs E1 and E2. and primary and secondary currents I1 and I2 to prove that primary power E1I1 is equal to the negative secondary power −E2I2. (2) Show that if the inductance is given as L=Niϕ, it can also be expressed as L=ℜN2.
Answers
The inductance L can be expressed as L = ℜN^2, which is an alternative representation of the inductance equation.
To prove that the primary power E1I1 is equal to the negative secondary power -E2I2 in an ideal transformer, we start by considering the relationship between the primary and secondary emfs and currents.
The primary emfs (E1) is related to the secondary emf (E2) by the turns ratio of the transformer, denoted as a. Therefore, we can write E2 = aE1.
Similarly, the primary current (I1) is related to the secondary current (I2) by the inverse of the turn ratio, which can be written as I2 = (1/a)I1.
Now, let's consider the power in the primary and secondary circuits. The power in the primary circuit is given by P1 = E1I1, and the power in the secondary circuit is given by P2 = E2I2.
Substituting the expressions for E2 and I2, we have P2 = (aE1)(1/a)I1, which simplifies to P2 = E1I1.
Therefore, we can conclude that the primary power E1I1 is equal to the negative secondary power -E2I2.
Regarding the expression of inductance, given as L = NiΦ, where N is the number of turns and Φ is the magnetic flux, we can further simplify it.
We know that the magnetic flux Φ is related to the current I by the inductance L, i.e., Φ = LI. Substituting this into the previous expression, we have L = NLI.
Since L is a scalar quantity, we can express it as L = ℜN^2, where ℜ is a constant that depends on the physical properties of the transformer.
Therefore, the inductance L can be expressed as L = ℜN^2, which is an alternative representation of the inductance equation.
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Can someone help me, please?
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PLEEEEASE HURRY!!!!!!!!
FIGURE ABCD IS REFLECTED ABOUT THE Y-AXIS TO OBTAIN FIGURE A'B'C'D
WHICH STATEMENT BEST DESCRIBES THE RELATIONSHIP BETWEEN THE TWO FIGURES?
A: FIGURE ABCD IS SIMILAR TO FIGURE A'B'C'D
B: FIGURE ABCD IS BIGGER THAN A'B'C'D
C: THE MEASURE OF ANGLE D IS EQUAL TO MEASURE OF ANGLE A'
D: THE MEASURE OF ANGLE D IS EQUAL TO MEASURE OF ANGLE B'
Answers
Answer:
pretty sure A
Step-by-step explanation:
Which of the following export pricing strategy does NOT consider fixed costs in setting price for export? a. Flexible cost-plus method b. Incremental pricing c. Standard worldwide price d. Rigid cost-plus method
Answers
b. Incremental pricing is correct answer.
Incremental pricing is a pricing strategy that focuses on covering only the variable costs associated with exporting a product. It does not take into account fixed costs such as overhead expenses or other costs that are not directly related to the production and export of the product.
On the other hand, the other options mentioned do consider fixed costs in setting the price for export:
a. Flexible cost-plus method: This method considers both variable costs and fixed costs, and adds a markup or profit margin to determine the export price.
c. Standard worldwide price: This strategy sets a uniform price for the product across different markets, taking into account both variable and fixed costs.
d. Rigid cost-plus method: Similar to the flexible cost-plus method, this approach includes both variable and fixed costs in setting the price for export.
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Solve the following equation: 3.3+4x=-6.9x+6.6
Round your answer to the nearest tenth.
Answers
The solution to the equation 3.3 + 4x = -6.9x + 6.6, rounded to the nearest tenth, is x ≈ 0.3.
To solve the equation 3.3 + 4x = -6.9x + 6.6, we need to isolate the variable x on one side of the equation.
First, let's simplify the equation by combining like terms:
3.3 + 4x = -6.9x + 6.6
Next, let's move the variable terms (4x and -6.9x) to one side and the constant terms (3.3 and 6.6) to the other side:
4x + 6.9x = 6.6 - 3.3
Combine the x terms on the left side:
10.9x = 3.3
Now, divide both sides of the equation by 10.9 to solve for x:
x = 3.3 / 10.9
Using a calculator, we can find the decimal approximation of x:
x ≈ 0.3028
Rounding to the nearest tenth, the solution to the equation is x ≈ 0.3.
In summary, the solution to the equation 3.3 + 4x = -6.9x + 6.6, rounded to the nearest tenth, is x ≈ 0.3.
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(PLEASE HELP) Reflect (-5,1) in the x axis followed by the y axis.
Answers
Answer:
(-5, -1)
Step-by-step explanation:
Find the slope of the line that passes through (2, 3) and (7,9).
Answers
Answer:
1.2
Step-by-step explanation:
the slope is 1.2
full formula is y=6/5x+1.2
solve for x, 2^2=128
Answers
Answer:
x=32
Step-by-step explanation:
Ice cream sandwiches are wrapped in white paper before they are put in a box to be sold. How many ice cream sandwiches can be wrapped with 500 square inches of paper?
Answers
Answer:
9.6
Step-by-step explanation:
Which of the following is a true statement about perfect squares?
A: 6 dot 6 equals 36.
B:12 dot 12 equals 2 left-parenthesis 12 right-parenthesis.
C:18 is a perfect square.
D:50 is a perfect square.
Answers
Answer:
A. 6 dot 6 equals 36.
Step-by-step explanation:
Hope this helps :)