For the polynomials: P1 = 1, P2 = x - 1, P3 = [tex](x - 1)^2[/tex] to form a basis S of P2, the coordinate vector of v relative to the basis S is [4, -1, 2].
To find the coordinate vector of the vector v = 2[tex]x^2[/tex] – 5x + 6 relative to the basis S = {P1, P2, P3}, we need to express v as a linear combination of the basis vectors.
The coordinate vector represents the coefficients of this linear combination.
The basis S = {P1, P2, P3} consists of three polynomials: P1 = 1, P2 = x - 1, P3 = [tex](x - 1)^2[/tex].
To find the coordinate vector of v = 2[tex]x^2[/tex] – 5x + 6 relative to this basis, we express v as a linear combination of P1, P2, and P3.
Let's assume the coordinate vector of v relative to the basis S is [a, b, c].
This means that v can be written as v = aP1 + bP2 + cP3.
We substitute the given values of v and the basis polynomials into the equation:
2[tex]x^2[/tex] – 5x + 6 = a(1) + b(x - 1) + c[tex](x - 1)^2[/tex].
Expanding the right side of the equation and collecting like terms, we obtain:
2[tex]x^2[/tex] – 5x + 6 = (a + b + c) + (-b - 2c)x + c[tex]x^2[/tex].
Comparing the coefficients of the corresponding powers of x on both sides, we get the following system of equations:
a + b + c = 6 (constant term)
-b - 2c = -5 (coefficient of x)
c = 2 (coefficient of [tex]x^2[/tex])
Solving this system of equations, we find a = 4, b = -1, and c = 2.
Therefore, the coordinate vector of v relative to the basis S is [4, -1, 2].
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Define a relation R on N by (a,b) ∈ R if and only if a/b ∈ N. Which properties does R satisfy?
The relation R on the set of natural numbers (N) is defined as (a, b) ∈ R if and only if a/b is a natural number. This relation exhibits the properties of reflexivity, symmetry, and transitivity.
Reflexivity: For any natural number a, a/a = 1, which is a natural number. Therefore, (a, a) ∈ R for all a ∈ N. Hence, R is reflexive.Symmetry: If (a, b) ∈ R, then a/b is a natural number. This implies b/a is also a natural number since the division is commutative. Thus, (b, a) ∈ R. Therefore, R is symmetric.
Transitivity: Let (a, b), (b, c) ∈ R, which means a/b and b/c are natural numbers. As the division operation is closed under natural numbers, a/c = (a/b) * (b/c) is also a natural number. Therefore, (a, c) ∈ R, and R is transitive. In summary, the relation R on the set of natural numbers is reflexive, symmetric, and transitive, making it an equivalence relation.
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Can you explain why the bottom angle always has to be 90 degrees?
Question 7: The red line has an equation of y = -1/2 x + 2. The blue line is perpendicular to the red line. Write the equation for the blue line. EXPLAIN PLS
Answer:y=2+2x
Step-by-step explanation:
Perpendicular means the slope is the opposite reciprocal of the red line’s. Opposite reciprocal means that if the red line has a negative slope the blue line will have a positive one, and you flip the fraction of the red line from 1/2 to 2. The y intercept is at 2 so that’s why there is a +2
2000 x 0.045 x 7 =
5000 x 0.07 x 20 =
28000 x 0.09 x 1 =
7500 x 0.035 x 2 =
4000 x 0.045 x 2.5 =
Answer:
639.8
7000
2520
525
450
..........
I need help with surface area
Answer:
Surface Area varies by object/shape.
Ask your teacher/learning helper for those formulas of surface area
Step-by-step explanation:
Surface area is the sum of all faces (or surfaces) on a 3D shape. A cuboid has 6 rectangular faces. To find the surface area of a cuboid, add the areas of all 6 faces. We can also label the length (l), width (w), and height (h) of the prism and use the formula, SA=2lw+2lh+2hw, to find the surface area.
somebody help I don't understand this stuff.
Answer:
Dena's answer
14ft^2
Step-by-step explanation:
Her answer is correct because area of triangle is base times height divided by two. Base is 7 and height is 4
From there, you can find the area which is 14.
hope this is correct
Laney bought a cup of coffee and two cookies at her
local coffee shop. The coffee cost $1.89. She got
$1.23 back as change from the $5.00 bill she gave the
cashier. How much did each cookie cost?
Page
Answer:
each cookie was $0.94
Step-by-step explanation:
5.00 - 1.89 = 3.11
3.11 - 1.23 = 1.88
1.88 divided by 2 = 0.94
a) Work out the size of angle x.
100
B
b) Give reasons for your answer.
co-exterior angle
to
F
Н
G
Answer:
100°= angle b(VERTICAL OPPOSITE ANGLE)
100°+x°=180°[co interior angle]
x=180°-100°
x=80°
The Measure for angle x is 80 degree.
What is Vertical Angle?When two straight lines cross, they generate a pair of non-adjacent angles known as vertical angles. In the corners of the "X" created by two straight lines, or to put it another way, vertical angles are situated opposite one another. Due to their position opposite one another, they are also known as vertically opposite angles.
Given:
<CBD = 100 degree.
So, <ABF = <CBD (Vertical Opposite Angle)
<CBD = 100 degree.
Now, <ABF + <BFE = 180 (Angle on same side of Transversal)
<ABF + 100 = 180
<ABF = 180-100
x= 80 degree.
Hence, the measure for x is 80 degree.
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25 POINTS - Need ASAP . Answer word problem attached.
If you answer just for points I won’t hesitate to report so don’t try pls!
Answer:
0.82
Step-by-step explanation:
82/100 as a fraction is equal to 0.82
In the high-school courtyard, a memorial garden will be planted to commemorate those students who graduated and served in the military. A local nursery donated 2 cartons of plants. One carton contains 4 palms, 4 birds of paradise, and 2 plumbagos. The other box contains 5 palms and 3 birds of paradise. If Jasmine chooses one plant from each box at random, what is the probability that both plants will be birds of paradise? Express your answer as a fraction in lowest terms.
Answer:
:c
Step-by-step explanation:
Please help me with the questions please ASAP ASAP please please ASAP please please help please I’m begging please please
Answer:
3/2
Step-by-step explanation:
The ratio of perimeters of similar polygons is the same as the ratio of the lengths of corresponding sides.
WX/AB = 12/8 = 3/2
What are they coordinates
Answer:
let ABC be a right-angled triangle, where A is the right angle (left to right)
the original coordinates:
A (-8, 8)
B (-1, 8)
C (-8, 5)
by changing the coordinates from (x, y) to (-y, x)
A (-8, -8)
B (-8, -1)
C (-5, -8)
look attachment
Find the real potential, Φ(x,y), and the complex potential, (F(z), between the parallel plates at y = x and y = x+k, which have potentials of 0 V and 300 V, respectively.
The real potential, between the parallel plates at y = x and y = x + k can be determined by solving the Laplace equation in two dimensions. The first paragraph provides a summary of the answer, followed by an explanation in the second paragraph.
The real potential, Φ(x, y), is given by the equation Φ(x, y) = C1x + C2y, where C1 and C2 are constants determined by the boundary conditions. In this case, the boundary conditions are Φ(x, x) = 0 V and Φ(x, x + k) = 300 V. By substituting these conditions into the equation, we can solve for the constants C1 and C2 and obtain the real potential Φ(x, y) between the plates.
The complex potential, F(z), is related to the real potential by the equation F(z) = Φ(x, y) + iψ(x, y), where ψ(x, y) is the stream function. The stream function can be determined by solving the equation ∇²ψ = 0, subject to the same boundary conditions as the real potential. Once the stream function is obtained, the complex potential F(z) can be calculated.
In conclusion, the real potential, Φ(x, y), and the complex potential, F(z), between the parallel plates at y = x and y = x + k can be determined by solving the Laplace equation and using the appropriate boundary conditions. The real potential is given by Φ(x, y) = C1x + C2y, where the constants C1 and C2 are determined by the given potential values on the plates. The complex potential is obtained by combining the real potential with the stream function, which is determined by solving the Laplace equation for the stream function with the same boundary conditions.
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Can someone help me, I'll give brainliest
If cost of 15 eggs is ? 75, then find out the cost of 4 dozens eggs
A. ? 185
B. ? 150
C. ? 300
D. ? 240
Answer:
D 240
Step-by-step explanation:
75÷15 to get the cost of each egg 5
5x12 to get 60
60x4 to get d 240
Answer:
D. 240 unitsStep-by-step explanation:
15 eggs ⇒ 75 units → divide by 151 egg ⇒ 75/15 = 5 units → multiply by 484 dozen = 4*12= 48 eggs ⇒ 48*5 = 240 unitsCorrect choice is D
what are remainder theorem
Answer:
Step-by-step explanation:
When doing synthetic division, if the remainder is zero, we know that the divisor is a root of the polynomial. If the remainder is not zero, the remainder is the function vaue for that divisor.
Please help with numbers 7 and 8.
Answer:
Below
Step-by-step explanation:
Every triangle should add up to 180 degrees,
This is a right triangle because it has the square in the corner meaning it is 90 degrees.
39 + 90 = 129
180 - 129 = 51 degrees
A: 51 degrees
C: 90 degrees
Answer:
a. 51 degrees
c. 90 degrees
I think
Let x, y, and z be measured in meters, and suppose that F(x, y, z) = −yi+zj+3xk is the velocity vector (in m/s) of a fluid particle at the point (x, y, z) in a steady-state in- compressible fluid flow. (a) Find the net volume of fluid that passes in the upward direction through the hemisphere z = √(9-x² — y²) in 1 s. (b) Assuming that the fluid has a mass density of 1060 kg/m³, find the net mass of fluid that passes in the up- ward direction through the surface in part (a) in 1 s.
The fluid has a mass density of 1060 kg/m³, we can multiply the net volume by 1060 to obtain the net mass of fluid passing through the hemisphere in 1 second.
To find the net volume of fluid passing through the hemisphere, we need to calculate the flux of the velocity vector across the surface. The flux is given by the surface integral of the dot product of the velocity vector and the outward unit normal vector. Since the velocity vector is F(x, y, z) = -yi + zj + 3xk, we can calculate the dot product as -y(-y) + z(0) + 3x(√(9 - x² - y²)). Simplifying, we have F · dS = y² + 3x√(9 - x² - y²).
To evaluate the flux over the surface, we need to parameterize the hemisphere. Let's use spherical coordinates: x = r sinθ cosϕ, y = r sinθ sinϕ, and z = r cosθ, where 0 ≤ r ≤ 3, 0 ≤ θ ≤ π/2, and 0 ≤ ϕ ≤ 2π. The outward unit normal vector is given by n = (sinθ cosϕ)i + (sinθ sinϕ)j + (cosθ)k. Now, we can evaluate the flux by taking the surface integral: ∫∫(F · dS) = ∫∫(y² + 3x√(9 - x² - y²)) dA, where dA is the differential area element in spherical coordinates. Integrating over the appropriate limits, we can find the net volume of fluid passing through the hemisphere in 1 second.
To determine the net mass of fluid passing through the surface, we need to multiply the net volume by the fluid's mass density. Given that the fluid has a mass density of 1060 kg/m³, we can multiply the net volume by 1060 to obtain the net mass of fluid passing through the hemisphere in 1 second.
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How hot is the air in the top (crown) of a hot air balloon? Information from Ballooning: The Complete Guide to Riding the Winds, by Wirth and Young (Random House), claims that the air in the crown should be an average of 100°C for a balloon to be in a state of equilibrium. However, the temperature does not need to be exactly 100°C. What is a reasonable and safe range of temperatures? This range may vary with the size and (decorative) shape of the balloon. All balloons have a temperature gauge in the crown. Suppose that 59 readings (for a balloon in equilibrium) gave a mean temperature of x = 97°C. For this balloon, ≈21°C.
ompute a 95% confidence interval for the average temperature at which this balloon will be in a steady-state equilibrium. (Round your answers to one decimal place.)
lower limit
°C
upper limit
°C
The 95% confidence interval for the average temperature at which this balloon will be in a steady-state equilibrium is (95.78°C, 98.22°C).
The 95% confidence interval (CI) for the mean temperature in the crown of the balloon is calculated as follows. We first assume that the population distribution is normal with a standard deviation (SD) of σ = 6°C as per the given data. We will then use the z-distribution to calculate the required confidence interval.
The formula for calculating the 95% confidence interval is given by
CI (mean) = x ± z × (σ/√n)
Where 'x' is the mean, 'z' is the z-score associated with the 95% CI, 'σ' is the standard deviation, and 'n' is the number of samples taken.
For the given data the confidence interval is calculated as:
CI (Mean) = 97 ± 1.96 × (6/√59)
CI (Mean) = 97 ± 1.22
Therefore, the 95% confidence interval for the average temperature at which this balloon will be in a steady-state equilibrium is (95.78°C, 98.22°C).
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6) What is the equation of a line that passes
through (-1, -3) and has a slope of 2?
Answer:
y+3=2*(x+1)
Step-by-step explanation:
Streaming movies from Company A costs $3 per month per movie plus a monthly fee of $9. Streaming movies from Company Bcost $4 per movie with no monthly fee. The monthly cost to stream depends on the number of movies, m streamed. Which inequality represents the situation when the montly cost at Company A is less than the montly cost at Company B.
can you help me with this due today
what is x over 3 less than or equal to 7
Answer:
x≤21
Step-by-step explanation:
x/3≤7
Multiply both sides by 3
3x/3≤7×3
Simplify
x≤21
Hope this helped!!!
Quadrilateral PQRS is a rectangle. Describe the error in finding the value of x
Answer:
∠PSR=90°
m∠QSR= 90-m∠QSP
x= 90-58=32°
Step-by-step explanation:
The actual value of the x is 32°.
What are Quadrilaterals?Quadrilaterals are four sided polygons which also have four vertices and four angles.
Sum of all the interior angles of a quadrilateral is 360 degrees.
Given quadrilateral is a rectangle.
All the four interior angles of a rectangle is perpendicular angle or is 90 degrees.
So measure of ∠PSR = 90°
m ∠QSR + m ∠QSP = 90°
Given that m ∠QSP = 58°
Substituting,
m ∠QSR + 58° = 90°
m ∠QSR = 90° - 58°
= 32°
So x° = 32°
Hence the error is that both the angles are made to be equal instead of making the sum of the angles equal to 90°.
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A smartphone regularly sells for $125. It is on sale this week for $85. The sale
price is what percent of the regular price?
Answer:
68%
Step-by-step explanation:
85 divided by 125 = .68 * 100 = 68
Answer: The sale price is 40 percent of the regular price
Step-by-step explanation:
I'm timed. Factor the Expression 4x - 30y
Answer:
23
Step-by-step explanation:
GCF of 4 is 2 and GCF of 30 is 6.
2(2*x)-6(5*y)
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hope it helps
. A rectangle's length is 1 feet shorter than 3 times its width. If we use w to
represent the rectangle's width, use a polynomial to represent the
rectangle's area in expanded form.
area =
square feet
Answer:
Step-by-step explanation:
w is the width of the rectangle, then the length would be 3w - 1.
A = lw
A = w(3w - 1)
A = 3w² - w
What is the length of the terrace?
Answer:
A) 12 feet or d) 10 feet..
one number added to twice another number is 23. Four times the first number added to twice the other number is 38. What are the numbers?
Answer:
x =5 & y =9
Step-by-step explanation:
let anumber x & y
-(x + 2y = 23)
4x + 2y = 38
-x -2y = -23
4x + 2y = 38
-x + 4x + 2y - 2y = 38-23
3x+0 = 15
3x /3 = 15/3
x = 5 then
5 + 2y = 23
2y = 23-5
2y/2 = 18/2
y = 9
therefore y =18 and x = 5
What is the value called that is small enough that anything
equal to or below it will allow you to rule out chance as the most
likely explanation? What are its typical values?
The value that is small enough to rule out chance as the most likely explanation is called the p-value. Typical p-values considered as statistically significant are 0.05 or lower.
The p-value is a measure of the strength of evidence against the null hypothesis in statistical hypothesis testing. It represents the probability of obtaining the observed data or more extreme results, assuming that the null hypothesis is true. If the p-value is below a predetermined significance level (often 0.05), it is considered statistically significant.
This means that the observed data is unlikely to have occurred by chance alone, providing evidence to reject the null hypothesis in favor of an alternative hypothesis. Lower p-values indicate stronger evidence against the null hypothesis.
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Which ordered pair is a solution of 9(x – 2)2 – 4(y + 5)2 ≥ 36?
(2, –3.5)
(2, 5.5)
(–7.5, –5)
(1.5, –5)
Answer:
its c kiddos
Step-by-step explanation:
The required ordered pair for the solution of an equation [tex]9(x - 2)^2 - 4(y + 5)^2\geq 36[/tex] is (-7.5,-5).
An ordered pair from the options is the solution of the equation [tex]9(x - 2)^2 - 4(y + 5)^2\geq 36[/tex] to be determined.
An ordered pair is defined as the coordinates when put into the equation giving the solution of the equation.
While plotting the curve of the given equation on the graph and also plotting the ordered pair on the graph. It is seen that points (2, –3.5), (2, 5.5), and (1.5, –5) lie on the unshaded portion. While ordered pair (-7.5, -5) lies on the shaded portion.
Thus, the required ordered pair for the solution of an equation [tex]9(x - 2)^2 - 4(y + 5)^2\geq 36[/tex] is (-7.5,-5).
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