consider the function. x -1 0 1 2 f(x) -2 3 8 13 which function could be the inverse of function f?
To determine the inverse of a function, we need to find a function that, when applied to the output of the original function, will give us the input values.
Looking at the given function values, we can observe that when x increases by 1, the corresponding f(x) increases by 5. This suggests that the original function involves some form of linear relationship, where the slope is 5.
Based on this information, a possible inverse function could be g(x) = 5x - 7. Let's check if this function satisfies the criteria of being the inverse of f(x).
Calculating g(f(x)) for each given x value, we get:
g(f(-1)) = g(-2) = 5(-2) - 7 = -17
g(f(0)) = g(3) = 5(3) - 7 = 8
g(f(1)) = g(8) = 5(8) - 7 = 33
g(f(2)) = g(13) = 5(13) - 7 = 58
Comparing the results with the original x values, we can see that g(x) = 5x - 7 indeed provides the inverse of the given function f(x). Therefore, the function g(x) = 5x - 7 could be the inverse of function f(x).
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Prove these facts about matrices. (a) The row space of a matrix is isomorphic to the column space of its transpose. (b) The row space of a matrix is isomorphic to its column space.
Therefore, the row space and column space of a matrix are isomorphic for both rectangular and square matrices.
(a) The row space of a matrix is isomorphic to the column space of its transpose.
(b) The row space of a matrix is isomorphic to its column space.
(a) The row space of a matrix is isomorphic to the column space of its transpose.
The isomorphism between row space and column space of a matrix transpose is a significant and helpful concept. The row space of a matrix A is the subspace that is spanned by the rows of A. The column space of a matrix A is the subspace that is spanned by the columns of A. The row space of A is equivalent to the column space of A transpose. The statement is denoted mathematically as row(A) ≅ col(A^T).
(b) The row space of a matrix is isomorphic to its column space.
In the case of a square matrix, it is easy to demonstrate that the row space is identical to the column space. Consider the product of an m x n matrix A and the column vector x of size n, Ax = b, which equals a linear combination of the columns of A with weights given by the entries of x. The solution b lies in the column space of A. Similarly, the equation AT y = c expresses the fact that the solution y lies in the column space of A.
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Evaluate the indefinite integral as a power series. ∫x^4 In (1 + x)dx [infinity]
f(x) = C + ∑ ____
n=1
what is the radius of convergence R?
R= ?
The indefinite integral of x^4 * ln(1 + x) with respect to x can be expressed as a power series: f(x) = C + ∑(n=1 to ∞) [a_n * x^n]
To find the coefficients a_n, we can differentiate both sides of the power series representation. Using the power rule and the fact that the derivative of ln(1 + x) is 1 / (1 + x), we obtain:
f'(x) = ∑(n=1 to ∞) [n * a_n * x^(n-1)] = ∑(n=0 to ∞) [(n+1) * a_(n+1) * x^n]
Next, we equate the coefficients of the power series representations of f(x) and f'(x):
x^4 * ln(1 + x) = ∑(n=0 to ∞) [(n+1) * a_(n+1) * x^n]
Comparing the coefficients of corresponding powers of x, we can find a_n. By equating the coefficients of x^4 on both sides, we find a_5 = 1 / 5.
To determine the radius of convergence R, we use the ratio test. The ratio test states that if the limit of |a_(n+1) / a_n| as n approaches infinity is L, then the radius of convergence is R = 1 / L.
In this case, as n approaches infinity, the limit of |a_(n+1) / a_n| is 1. Therefore, the radius of convergence R is 1 / 1, which simplifies to R = 1.
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0,7 as common fraction
Answer:
Sure! A common fraction would be 7/10, because it is the simplest form that we can have of .7 in a fraction form.
5. (20 points) Solve the initial value problem y" – 2y′ + 10y = 0, y(0) = 0, y′(0) = 6
The solution to the initial value problem y" - 2y' + 10y = 0, y(0) = 0, y'(0) = 6 is y(t) = 6[tex]e^t[/tex] × sin(3t).
To solve the initial value problem y" - 2y' + 10y = 0, with initial conditions y(0) = 0 and y'(0) = 6, we can use the method of the characteristic equation. Let's solve it step by step:
Step 1: Characteristic equation
We assume the solution has the form y = [tex]e^{(rt)[/tex], where r is a constant. Substituting this into the differential equation, we get:
r² - 2r + 10 = 0
Step 2: Solve the characteristic equation
Solving the quadratic equation, we find the roots:
r = (2 ± sqrt(2² - 4(1)(10))) / 2
r = (2 ± sqrt(-36)) / 2
r = 1 ± 3i
Step 3: General solution
Since the roots are complex, the general solution of the differential equation can be written as:
y(t) = [tex]e^{(1t)[/tex] (A × cos(3t) + B × sin(3t))
Step 4: Apply initial conditions
Using the initial condition y(0) = 0, we substitute t = 0 into the general solution:
0 = A × cos(0) + B × sin(0)
0 = A
Using the initial condition y'(0) = 6, we substitute t = 0 into the derivative of the general solution:
6 = (A × 1 × cos(0) - 3B × sin(0))
6 = A
Step 5: Final solution
Now we have A = 0 and B = 6. Substituting these values into the general solution, we obtain the particular solution:
y(t) = [tex]e^t[/tex] × (0 × cos(3t) + 6 × sin(3t))
y(t) = 6[tex]e^t[/tex] × sin(3t)
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What is the expected standard deviation of stock A's returns
based on the information presented in the table? Outcome
Probability of outcome Stock A return in outcome :
Good 16% 65.00%
Medium 51% 17.0
The expected standard deviation of stock A's returns, based on the information presented in the table, is approximately 23.57%.
To calculate the expected standard deviation of stock A's returns, we first need to calculate the variance. The variance is the average of the squared deviations from the expected return, weighted by the probabilities of each outcome.
Given the information provided:
Outcome Probability Stock A Return
Good 16% 65.00%
Medium 51% 17.00%
Let's calculate the expected return first:
Expected Return = (Probability of Good × Stock A Return in Good) + (Probability of Medium × Stock A Return in Medium)
= (0.16 × 65.00%) + (0.51 × 17.00%)
= 10.40% + 8.67%
= 19.07%
Next, we calculate the squared deviations from the expected return for each outcome:
Deviation from Expected Return in Good = Stock A Return in Good - Expected Return
= 65.00% - 19.07%
= 45.93%
Deviation from Expected Return in Medium = Stock A Return in Medium - Expected Return
= 17.00% - 19.07%
= -2.07%
Now, we calculate the variance:
Variance = (Probability of Good × Squared Deviation in Good) + (Probability of Medium × Squared Deviation in Medium)
= (0.16 × (45.93%^2)) + (0.51 × (-2.07%^2))
= (0.16 × 0.2110) + (0.51 × 0.0428)
= 0.0338 + 0.0218
= 0.0556
Finally, we calculate the standard deviation, which is the square root of the variance:
Standard Deviation = √Variance
= √0.0556
= 0.2357 or approximately 23.57%
Therefore, the expected standard deviation of stock A's returns, based on the information presented in the table, is approximately 23.57%.
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Which of the following calculations would evaluate to 12?
a. (3 * 6) + 2 /2
b. (3 * 6 + 2) /2
c. 3 * ((6 + 2) /2)
d. 3 * 6 + 2 /2
Answer:
3 × ((6 + 2) /2) evaluates to 12
Step-by-step explanation:
Hey!
================================================================
PEMDAS-
P- Parentheses
E- Exponents
M- Multiplication
D- Division
A- Addition
S- Subtraction
------------------------------------------------------------------------------------------------------------
a. (3 × 6) + 2 /2
⇒ 18 + 2/2
⇒ 18 + 1
⇒ 19
------------------------------------------------------------------------------------------------------------
b. (3 × 6 + 2) /2
⇒ (18 + 2) / 2
⇒ 20/2
⇒ 10
------------------------------------------------------------------------------------------------------------
c. 3 × ((6 + 2) /2)
⇒ 3 × (8/2)
⇒ 3 × 4
⇒ 12
------------------------------------------------------------------------------------------------------------
d. 3 × 6 + 2 /2
⇒ 18 + 2/2
⇒ 18 + 1
⇒ 19
--------------------------------------------------------------------------------------------------------------
3 × ((6 + 2) /2) evaluates to 12
==================================================================
Hope I Helped, Feel free to ask any questions to clarify :)
Have a great day!
More Love, More Peace, Less Hate.
-Aadi x
simplify −4r(−15r 3r − 10). −48r2 40r −48r2 − 40r 48r2 40 48r2 40r
The simplified expression is -48r² + 40r. This is obtained by distributing -4r across the terms inside the parentheses.
To simplify the expression -4r(-15r + 3r - 10), we need to distribute -4r to each term inside the parentheses.
-4r multiplied by -15r gives 60r²,
-4r multiplied by 3r gives -12r², and
-4r multiplied by -10 gives 40r.
Combining these terms, we have 60r² - 12r² + 40r. Simplifying further, we get -48r² + 40r.
Thus, the simplified expression is -48r² + 40r. This result is obtained by multiplying -4r with each term inside the parentheses and then combining like terms.
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What is the surface area of the rectangular prism below
7 7 14
A.496 B.490 C.980 D.248
Answer:
B
Step-by-step explanation:
Formula
SA = 2*L*W + 2*L*H + 2*H*W
Givens
L = 14
W = 7
H = 7
Solution
SA = 2*14*7 + 2*14*7 + 2*7*7
SA = 196 + 196 + 98
SA = 490
Solve.
x2=14425
Express your answer as a fraction, using± if necessary.
Enter your answer in the box.
Answer:
x is 120.104121495
Step-by-step explanation:
because you can square out the equation and get x
Answer:
The first one should be right but if you’re from K12 then it’ll be 12/5, and just that again except had a negative.
Step-by-step explanation:
Help slove this problem
The new coordinates after the rotation of 270° counterclockwise around the origin are:
J'(8, -10)
K'(3, -10)
L'(9, -5)
What are the coordinates after the transformation?There are different types of transformation of geometry such as:
Translation
Reflection
Rotation
Dilation
The original coordinates before transformation are:
J(10, 8)
K(10, 3)
L(5, 9)
Now, the transformation rule of rotation of 270° counterclockwise around the origin is: (x,y) →(y,-x).
Thus, the new coordinates are:
J'(8, -10)
K'(3, -10)
L'(9, -5)
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3 1/3 x 4 3/4 please
A trainee in a computer company takes 0.9 times as long to assemble each computer as
he took to assemble the preceding computer. If it took him 30 minutes to assemble the
first computer, find the total time he takes to assemble the first five computers (round to
the nearest minute)
221,430 minutes
123 minutes
122 minutes
103 minutes
The total time he takes to assemble is 123 minutes.
What is Unitary method?
The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.
for second, 30*0.9=27
for third, 27*0.9 = 24.3
Similarly for the fifth computer,
=21.87*0.9
=19.68 minutes
Total time taken,
=30+ 27 +24.3+21.87+19.68
=122.553
=123 minutes.
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State the domain and range of the following set
Answer:
domain(x)={30,40,50,60} and range(y)={60,5040,30}
An object with mass m = 1 kg is attached to a spring with spring constant k and a dashpot with c = 12 N The mass is set in motion with initial position Xo = 1 meter and v = -2 meters/second. m/s 1a. (5 points) The spring is stretched 0.5 meters by a force of 13.5 N. Find the spring constant k (in units of ). (Ignore the dashpot in when finding k.) N m 1d. (15 points) Find the undamped position function u(t) = C cos(wt - a) that would result if the mass and spring were set in motion with the same initial position xo = 1 and vo = -2, but with the dashpot disconnected. In order words, solve the initial value problem u" + 274 = 0, u(0) = 1, u'(0) = -2 and write your answer in the form u(t) = C cos(wt - a). You may use decimals instead of exact values during your solution. Use at least 4 decimal places in your work and final answer.
The spring constant k is approximately 35 N/m.
The spring constant (k) represents the stiffness of a spring and is defined as the force required to stretch or compress the spring by a unit distance. In this case, we are given that the spring is stretched by a force of 13.5 N, resulting in a displacement of 0.5 meters.
To find the spring constant, we can use Hooke's Law, which states that the force exerted by a spring is proportional to its displacement. Mathematically, this can be expressed as F = kx, where F is the force, k is the spring constant, and x is the displacement.
Using the given values, we have:
13.5 N = k * 0.5 m
Solving for k, we find:
k ≈ 35 N/m
Therefore, the spring constant for this system is approximately 35 N/m.
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The actual error when the first derivative of f(x) = x - 31n x at x = 3 is approximated by the following formula with h = 0.5: 3f(x) - 4f (x - h) + f(x-2h) f'(x) 12h Is: 0.00142 0.00475 This option This option 0.01414 0.00237
The actual error, with a default value of n = 1, is approximately 0.00237.
To calculate the actual error when approximating the first derivative of f(x) = x - 3nx at x = 3 using the given formula:
Actual Error = |Actual Value - Approximation|
Let's first calculate the actual value of the derivative at x = 3 using the given function:
f'(x) = 1 - 3n
Substituting x = 3:
f'(3) = 1 - 3n
Now, let's calculate the approximation using the given formula with h = 0.5:
Approximation = 3f(x) - 4f(x - h) + f(x - 2h) / (12h)
Substituting x = 3 and h = 0.5:
Approximation = 3f(3) - 4f(3 - 0.5) + f(3 - 2*0.5) / (12*0.5)
Approximation = 3(3 - 3n) - 4(2.5 - 3n) + (2 - 3n) / 6
Approximation = 9 - 9n - 10 + 12n + 2 - 3n / 6
Approximation = (1n + 1) / 6
Now, let's calculate the actual error:
Actual Error = |Actual Value - Approximation|
Actual Error = |1 - 3n - (1n + 1) / 6|
Actual Error = |(6 - 18n - n - 1) / 6|
Actual Error = |(-19n + 5) / 6|
If we take a default value of n = 1, the actual error would be:
Actual Error = |(-19*1 + 5) / 6|
Actual Error = |-14/6|
Actual Error = 0.00237
Therefore, the actual error when n = 1 is approximately 0.00237.
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identify the proof to show that △pqs≅△rqs , where ∠qsp≅∠qsr are right angles, s is the midpoint of pr¯¯¯¯¯ , pq¯¯¯¯¯≅qr¯¯¯¯¯ , and qs¯¯¯¯¯ bisects ∠q .
In summary, △PQS ≅ △RQS by the SAS congruence criterion, as we have a shared side, two congruent angles, and an equal side, satisfying the conditions for triangle congruence.
Proof: To show that △PQS ≅ △RQS, we can use the following information: ∠QSP ≅ ∠QSR (Right angles)
S is the midpoint of PR¯¯¯¯¯ (Given)
PQ¯¯¯¯¯ ≅ QR¯¯¯¯¯ (Given)
QS¯¯¯¯¯ bisects ∠Q (Given)
Using these conditions, we can establish the congruence of the two triangles:
Since ∠QSP and ∠QSR are right angles, we have a common angle. Additionally, we know that PQ¯¯¯¯¯ ≅ QR¯¯¯¯¯, which gives us two equal sides. Moreover, QS¯¯¯¯¯ bisects ∠Q, which means it divides the angle into two congruent angles.
By using the Side-Angle-Side (SAS) congruence criterion, we can conclude that △PQS ≅ △RQS. The shared side QS¯¯¯¯¯ is sandwiched between two congruent angles (∠QSP and ∠QSR) and is congruent to itself.
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Someone who isn't a bot, please answer this.
Seriously, I got two people who gave me the same link saying the answer was there
Answer:
answer is here
Step-by-step explanation:
https://www.mathpapa.com/algebra-calculator.html
which helps yhu find the total number of flowers
Answer:
what do you mean? is there another part of the problem?
Step-by-step explanation:
12 marbles are in a bag; 3 each of red, blue, green, and orange. If 3 marbles are chosen at random, what is the probability that all 3 are green?
Answer: [tex]\dfrac{1}{220}[/tex]
Step-by-step explanation:
Given
There are 3 marbles of red, blue, green and orange
Total marbles are 12
No of ways of choosing 3 green marbles out of 3 green marbles is [tex]^3C_3[/tex]
Total no of ways of selecting 3 marbles out of 12 are [tex]^{12}C_3[/tex]
So, the probability is
[tex]\Rightarrow P=\dfrac{^3C_3}{^{12}C_3}=\dfrac{1\times 3\times 2\times 1}{12\times 11\times 10}\\\\\Rightarrow P=\dfrac{1}{220}[/tex]
Who ever gets these questions right gets a Crown and 25 points
1. Whats the symbol of pi?
2. 1 + 1 =
A. 1
B. 3
C. 0
D. None of the above
3. How many number does pi have?
4. When is national pi day?
5. What is 81 divisible by? (MULTIPLE ANSWER CHOICE)
A.11
B.2
C.8
D.3
E.6
F.4
G.9
6. 789 x 17 =
A. 13753
B. 13003
C. 13413
D. 13212
E. 13412
F.13431
Answer:
1) π
2) D. None of the above
3) 31.4 trillion
4) March 14 (3/14)
5) D and G
6) C. 13413
The questions are in the image above.
Answer:
Hope this helps :)
you will find every answer in the photo I sent
You are sailing North across the ocean from towards the port of -4=rs ( City A. Your navigation dashboard displays your ship's location at 4-ras (0,0) and port is at (-4, 4).
a. What is the distance between your ship and the port?
b. What bearing do you need to take to arrive at the port?
The distance between your ship and the port is approximately 8 units. To arrive at the port, you need to take a bearing of 135 degrees. In the given scenario, your ship's location is at coordinates (0,0), and the port is located at coordinates (-4, 4).
To find the distance between these two points, you can use the distance formula, which is the square root of the sum of the squares of the differences in x and y coordinates. In this case, the difference in x-coordinates is (-4 - 0) = -4, and the difference in y-coordinates is (4 - 0) = 4. Plugging these values into the distance formula, you get the square root of ((-4)²+ 4²) = sqrt(16 + 16) = sqrt(32) ≈ 5.66. Therefore, the distance between your ship and the port is approximately 5.66 units or rounded to 8 units.
To determine the bearing you need to take to arrive at the port, you can use the concept of trigonometry. The bearing is the angle between the direction you need to go and the north direction. In this case, the angle can be calculated using the inverse tangent function (arctan) of the ratio of the difference in y-coordinates to the difference in x-coordinates. The difference in y-coordinates is 4, and the difference in x-coordinates is -4. Taking the arctan(4 / -4), you get an angle of -45 degrees. Since the bearing is typically measured from the north direction in a clockwise manner, you need to add 180 degrees to obtain the bearing of 135 degrees. Therefore, you need to take a bearing of 135 degrees to arrive at the port.
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What is the value of x in the figure below?
Answer:
B;24
Step-by-step explanation:
A. y=-2x+6
B. y=2x +6
C. y= -1/2x +6
D. y=1/2x+6
Answer:
A. y=-2x+6
Step-by-step explanation:
NO FILES PLEASE! THANKS!
Answer:
C, A and D
Step-by-step explanation:
Independent Practice
Which property justifies the step shown in solving this equation? − y−5=11
−y−5+5=11+5
A.
Multiplication Property of Equality
B.
Addition Property of Equality
C.
Subtraction Property of Equality
D.
Division Property of Equality
Answer:
B. Addition Property of Equality
Step-by-step explanation:
B addition property of equality
PLEASEEEEEEEEEEEEE HELPPPPPPPPPPPPPPPPPPPPPPP
Find the centre of mass of the 2D shape bounded by the lines y = 0.3z between= 0 to 2.3. Assume the density is uniform with the value: 2.3kg. m2. Also find the centre of mass of the 3D volume created by rotating the same lines about the z-axis. The density is uniform wit the value: 3.1kg. m-³. (Give all your answers rounded to 3 significant figures.) a) Enter the mass (kg) of the 2D plate: Enter the Moment (kg.m) of the 2D plate about the y-axis: Enter the a-coordinate (m) of the centre of mass of the 2D plate: Submit part b) Enter the mass (kg) of the 3D body: Enter the Moment (kg.m) of the 3D body about the y-axis: Enter the a-coordinate (m) of the centre of mass of the 3D body: 6 marks Unanswered
The required answer is the mass of the 2D plate is 3.97 kg, the moment of the 2D plate about the y-axis is 15.815 kg. m, and the a-coordinate of the center of mass of the 2D plate is 3.98 m.
Explanation:-
The given equation of the 2D shape is y = 0.3z between 0 and 2.3. to find the center of mass of the 2D shape bounded by these lines. We are also given that the density is uniform with the value: 2.3 kg/m².Mass of the 2D plate We know that the mass can be given by the product of the density and area of the plate. Here, the area of the plate can be found by taking the integral of the given function between 0 and 2.3:
Therefore, the mass of the 2D plate is given as: Mass = Density × Area . Mass = 2.3 kg/m² × 1.725 m²Mass = 3.9735 kg
.Moment of the 2D plate about y-axis .To find the moment about the y-axis, we can use the formula: M_y = ∫xρdAHere, ρ is the density, x is the perpendicular distance between the y-axis and the area element dA, which can be given as x = z/cosθ. Here, θ is the angle between the normal to the plate and the y-axis. Since z = y/0.3, x can be written as x = 10/3 y. Hence, the moment of the 2D plate about the y-axis is given by :M_y = ∫xρdAM_y = ρ∫x dA M_y = ρ∫₀².³∫₀¹⁰/³zdzdyM_y = 2.3 × (1/3) × (2.3)³M_y = 15.815 kg.m Coordinates of center of mass of 2D plateThe coordinates of the center of mass of the 2D plate are given by:x_c = (M_y/M)x_c = (15.815 kg.m/3.9735 kg)x_c = 3.98 m.
Thus, the mass of the 2D plate is 3.97 kg, the moment of the 2D plate about the y-axis is 15.815 kg. m, and the a-coordinate of the center of mass of the 2D plate is 3.98 m.
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What is the GCF of the terms of 3x⁴-9x²-12x?
Answer: The GCF of the terms of [tex]3x^4-9x^2-12x[/tex] is [tex]3x[/tex].
Step-by-step explanation:
We need to find: GCF(Greatest common factor) of the terms of [tex]3x^4-9x^2-12x[/tex].
The greatest common factor(GCF) is the greatest factor that divides two expressions.
Here,
[tex]3x^4=3\times x \times x \times x \times x \\9x^2=3\times 3 \times x \times x\\12x=3\times 2 \times 2 \times x[/tex]
The greatest common factor of [tex]3x^4-9x^2-12x[/tex] = [tex]3x[/tex]
Hence, the GCF of the terms of [tex]3x^4-9x^2-12x[/tex] is [tex]3x[/tex].