Consider the ordered bases B = {1, x,x2} and C = {1, (x - 1), (x – 1)2} for P2. ,ت (a) Find the transition matrix from C to B. (b) Find the transition matrix from B to C. (c) Write p(x
Answers
(a) The transition matrix from basis C to basis B is {{1, 1, 1}, {-1, 0, 0}, {1, -2, 1}}.
(b) The transition matrix from basis B to basis C is {{1, -1, 1}, {1, 0, -2}, {1, 0, 1}}.
(c) To write p(x) in terms of basis C, we need to express p(x) as a linear combination of the basis vectors in C.
(a) To find the transition matrix from basis C to basis B, we need to determine how the basis vectors in C can be expressed in terms of the basis vectors in B. We write each basis vector in C as a linear combination of the basis vectors in B and form a matrix using the coefficients. The resulting transition matrix is {{1, 1, 1}, {-1, 0, 0}, {1, -2, 1}}.
(b) To find the transition matrix from basis B to basis C, we need to determine how the basis vectors in B can be expressed in terms of the basis vectors in C. We write each basis vector in B as a linear combination of the basis vectors in C and form a matrix using the coefficients. The resulting transition matrix is {{1, -1, 1}, {1, 0, -2}, {1, 0, 1}}.
(c) To write p(x) in terms of basis C, we express p(x) as a linear combination of the basis vectors in C. We determine the coefficients of the linear combination by solving a system of equations formed by equating p(x) to the linear combination of the basis vectors. The specific form of p(x) is not provided, so the exact coefficients cannot be determined without further information.
To learn more about coefficients click here:
brainly.com/question/1594145
#SPJ11
Related Questions
Cycle City charges an initial price of $15 plus $0.75 per hour for bike rentals, which is
represented by the expression 15 +0.75h.
Complete each statement to describe the terms.
The variable h represents ?
The constant 15 represents ?
The variable term 0.75h represents ?
Answers
The constant 15 represents the initial price charged by Cycle City for bike rental.
The variable term 0.75h represents the additional price charged by Cycle City for each hour of bike rental.
1238 round to the nearest 1000
Answers
Answer:
1,238.000
Step-by-step explanation:
f(x) = 3 sin(x) + 3 cos(x), 0 ≤ x ≤ 2π (a) Find the intervasl on which f is increasing and decreasin (b) Find the local minimum and maximum values of t. (c) Find the inflection points. Find the interval on which f is concave up. (Enter your answer using interval notation.) Find the interval on which f is concave down. (Enter your answer using interval notation.)
Answers
f(x) is increasing on the intervals (−∞, π/4) and (5π/4, ∞), and decreasing on the interval (π/4, 5π/4).
To determine the intervals on which f(x) = 3sin(x) + 3cos(x) is increasing and decreasing, we need to find the derivative of f(x) and examine its sign.
f'(x) = 3cos(x) - 3sin(x)
To find where f'(x) = 0, we set the derivative equal to zero and solve:
3cos(x) - 3sin(x) = 0
cos(x) - sin(x) = 0
From this equation, we can see that it is satisfied when x = π/4 and x = 5π/4.
Now, we analyze the sign of f'(x) in different intervals:
For x < π/4: f'(x) > 0, so f(x) is increasing.
For π/4 < x < 5π/4: f'(x) < 0, so f(x) is decreasing.
For x > 5π/4: f'(x) > 0, so f(x) is increasing.
Know more about derivative here:
https://brainly.com/question/30365299
#SPJ11
SOMEONE PLEASE SOLVE. EASY POINTS PLEASSSSE.
Answers
Answer:
The second one
Step-by-step explanation:
ur welcome sire or madam which ever one you are
PLEASE HELP!! ILL MARK BRAINLIEST!
click picture above, thank you
Answers
Answer:
D 12
Step-by-step explanation:
Answer:
D. 12 cm
Step-by-step explanation:
Because the sum of two sides of a triangle must always be greater than the 3rd side, 12 cannot be the third side because 5+7=12.
5)
Solve for x.
2x + 16 = 3(x - 9)
My Answer:
Answers
Answer:
Step-by-step explanation:
2x+16= 3(x-9)
2x+16= 3x-27
3x-2x^^
16= x-17
16+17
x= 33
Answer:
x=43
Remove parentheses, move the terms, collect the terms, calculate, change the signs!
could anyone help me with this?
Answers
Answer:
93.4 cm²
Step-by-step explanation:
Area of the shaded region = area of the square - area of half of the circle
Area of the shaded region = s² + ½(πr²)
Where,
r = 6.2 cm
s = length of square = diameter of circle = 2*r = 2*6.2
s = 12.4 cm
Plug in the values
Area of the shaded region = 12.4² - ½(π × 6.2²)
= 153.76 - 60.381411
= 93.378589
≈ 93.4 cm² (nearest tenth)
josh’s favorite snack at a convenience store costs $3.47 before tax. if the tax rate is 8.3% how much would josh pay for his snack including taxes ?
Answers
Josh would pay $3.76 for his snack including taxes.
How much would josh pay for his snack including taxes?Given that; josh’s favorite snack at a convenience store costs $3.47 before tax and tax rate is 8.3%.
To determine the cost of Josh's snack including taxes, we need to add the tax amount to the original price of the snack.
First, calculate the tax amount by multiplying the original price by the tax rate:
Tax amount = 3.47 × 8.3%
Tax amount = 3.47 × 0.083
Tax amount = $0.28801
Next, we add the tax amount to the original price to find the total cost of the snack including taxes:
Total cost = Original price + Tax amount
Total cost = $3.47 + $0.28801
Total cost = $3.76
Therefore, the total cost is $3.76.
Learn about selling price, markup price and cost here: https://brainly.com/question/29511226
#SPJ1
Noah′s family travels 5.26 miles multiplied by 102 miles each day. How many miles do they travel each day?
Answers
Answer:
536.52
Step-by-step explanation:
5.26x102=536.52
y=
\,\,x^2+4x-4
x
2
+4x−4
y=
y=
\,\,x-6
x−6
Answers
A 45-foot water slide casts a 30-foot shadow.
Find the length of the shadow of a 4-foot tall child
standing nearby.
Answers
Answer:
2.666666666666666666666666 ( repeating decimal )
Step-by-step explanation:
It says a 45 foot slide casts a 30 foot shadow.
We notice that 30 is exactly 2 / 3 of 45.
A easier way to notice that is like 30 + (half of 30 which is 15)
so 30 + 15 is 45 which is exactly the height of the water slide.
The we take the 4 foot child. It is 4 foot.
Then we do 4 times 2 / 3 which we got earlier.
which will be 2.66666666666666666666666666666666666
repeating decimal don't know how to write it here
Answer:
x = 5.75ft/2.3ft
Step-by-Step:
34ft/13 \(\frac{3}{5}\) = 5.75ft/x
34x = 13 3/5 · 5.75
34x ÷ 34 = 78.2 ÷ 34
34ft/13 3/5ft = 5.75ft/2.3ft
Which quadratic expression is written in standard form? -X2 - 5x + 7 0 ) (x + 3)x (x + 4)2 x² + 2(x+3)
Answers
Because the general expression for a quadratic equation is
\(ax^2\text{ + bx + c }\)Use a known Maclaurin series to obtain a Maclaurin series for the given function. f(x) = sin (pi x/2) Find the associated radius of convergence R.
Answers
The Maclaurin series for \(\(f(x) = \sin\left(\frac{\pi x}{2}\right)\)\) is given by:
\(\[\sin\left(\frac{\pi x}{2}\right) = \frac{\pi}{2} \left(x - \frac{\left(\pi^2 x^3\right)}{2^3 \cdot 3!} + \frac{\left(\pi^4 x^5\right)}{2^5 \cdot 5!} - \frac{\left(\pi^6 x^7\right)}{2^7 \cdot 7!} + \ldots\right).\]\)
The radius of convergence, \(\(R\)\) , for this series is infinite since the series converges for all real values of \(\(x\).\)
Therefore, the Maclaurin series for \(\(f(x) = \sin\left(\frac{\pi x}{2}\right)\)\) is:
\(\[\sin\left(\frac{\pi x}{2}\right) = \frac{\pi}{2} \left(x - \frac{\left(\pi^2 x^3\right)}{2^3 \cdot 3!} + \frac{\left(\pi^4 x^5\right)}{2^5 \cdot 5!} - \frac{\left(\pi^6 x^7\right)}{2^7 \cdot 7!} + \ldots\right)\]\)
with an associated radius of convergence \(\(R = \infty\).\)
To know more about convergence visit-
brainly.com/question/31966301
#SPJ11
A recipe calls for 3 cups of sugar for every 4 pounds of fruit. How many cups of sugar are required for 10 pounds of fruit?
Answers
Answer:
7.5 cups
Step-by-step explanation:
For this you'd need to set up a ratio of 4lbs : 3 cups = 10lbs : x cups
You can turn this into an equation by turning it into a fraction, so 3/4 = x/10
Then you would solve this like a regular equation
1. 3/4 = x/10
2. 10(3/4 = x/10)
3. 10 * 3/4 = x
4. 7.5 = x
find the slope of the curve y = 6x2 6/x at the point (3, 56).
Answers
Therefore, the slope of the curve y = 6x^2 + 6/x at the point (3, 56) is 34.
Let's go through the calculation again to find the correct slope.
To find the slope of the curve at the point (3, 56), we need to take the derivative of the function y = 6x^2 + 6/x and evaluate it at x = 3.
Taking the derivative of y with respect to x, we can differentiate each term separately:
d/dx (6x^2) = 12x
d/dx (6/x) = -6/x^2
Now, combining the derivatives, we have:
y' = 12x - 6/x^2
Substituting x = 3 into the derivative expression:
y'(3) = 12(3) - 6/(3^2)
= 36 - 6/9
= 36 - 2/3
= 34 2/3
To know more about curve,
https://brainly.com/question/30176812
#SPJ11
The double number line shows that 4 pounds of tomatoes cost $14. Draw these number lines on a separate sheet of paper. Draw tick marks and write labels to show the prices of 1, 2, and 3 pounds of tomatoes. Write your answers below.
Answers
Can someone plz help me with this one problem plzzzzz I’m marking brainliest!!!
Also when you pick the graph just say 1st or 2nd graph!!!
Answers
Answer:
1st
Step-by-step explanation: i think
Plot the following ordered pairs on the same Cartesian plane for each one.
1.(2,3)
2.(0,-7)
3.(-5,9)
Answers
A graph of the given ordered pairs has been plotted as shown in the image attached below.
What is a graph?A graph can be defined as a type of chart that's commonly used to graphically represent data on both the horizontal and vertical lines of a cartesian coordinate, which are the x-axis and y-axis.
What is an ordered pair?An ordered pair can be defined as a pair of two elements that are typically written in a fixed order within parentheses as (x, y), which represents the x-axis (abscissa) and the y-axis (ordinate) on a coordinate plane.
In conclusion, a graph which represents the given ordered pairs shows a discrete function.
Read more on graphs here: brainly.com/question/4546414
#SPJ1
3 points are randomly drawn on a circle. what is the probability of them being on the same semi-circle ?
Answers
Answer:
3/4
Step-by-step explanation:
There are 3 Points A,B,C. The first point can be anywhere on the circle Let’s define it to be A. Let’s now orient the circle so that A is the top most point of the circle.Now imagine the circle to be cut in half vertically (into 2 semicircles, where A is in both semicircles) The next two points should be both clockwise or counterclockwise of point A, for the sake of counting lets choose clockwise. There is a 12∗12=1412∗12=14 probability that B and C are on the clockwise side of the semicircle. But the first point could have been A B or C so multiplying by 3 the answer is 3/4
A bank loaned out $19,000, part of it at the rate of 7% per year and the rest at 17% per year. If the interest received in one year totaled $2000, how much was loaned at 7%
Answers
Answer:
$12300
Step-by-step explanation:
You want to know the amount loaned at 7% if $19000 loaned at 7% and 17% earns $2000 in one year.
InterestThe interest on an investment P at rate r for t years is ...
I = Prt
The sum of the amounts of interest on a 7% investment of x and a 17% investment of (19000 -x) is given as 2000:
0.07x +0.17(19000 -x) = 2000
-0.10x +3230 = 2000 . . . simplify
1230 = 0.10x . . . . . . . . . . add 0.10x -2000
12300 = x . . . . . . . . . . . . divide by 0.10
The amount loaned at 7% was $12,300.
Order these numbers from least to biggest: 34.35 343.5 3.3450 3,435 34
Answers
Answer: 34.35 343.5 3.3450 3,435 34
Step-by-step explanation:
they are already in order from left to right
Answer:
The following is the order of the numbers from least to greatest:
3.3450
34
34.35
343.5
3,435
Ten deer were introduced into a protected preserve. Their expected population doubles each year. Which function represents the same relationship?
Answers
Answer:
y(t)= 10 (2)^t
Step-by-step explanation:
If t is the number of years given then the expected number can be found by
y(t)= 10 (2)^t
where t takes the value 0,1,2,3, and so on.
Putting t= 0
y(t)= 10 (2)^t
y(0)= 10 (2)^0
y(0)= 10 For the start the number of deer are 10.
Putting t= 1
y(t)= 10 (2)^t
y(1)= 10 (2)^1
y(1)= 20 After 1 year it has doubled to 20
Putting t= 2
y(t)= 10 (2)^t
y(2)= 10 (2)^2
y(2)= 40 After 2 years it has again doubled to 40
Putting t= 3
y(t)= 10 (2)^t
y(3)= 10 (2)^3
y(3)= 80 After 3 years it has again doubled to 80
Ben and Chi are painting a room in the city recreation center. They started with 4 gallons of paint. On the first day, Ben used 14 gallon of paint and Chi used 112 gallons of paint. How many gallons of paint were left after the first day?
Group of answer choices
Answers
Wouldnt that be zero cuz they used more then they started of with?
The price of a stock decreased $2 each day for seven consecutive days.What was total change in value of the stock over the seven days?
Answers
Answer:
14$
Step-by-step explanation:
7 days
2$ each day
2×7=14$
Translate
Solve the equation.
3m= 5(m + 3)-3
HELP
Answers
Answer:
m = -6
Step-by-step explanation:
3m= 5(m + 3)-3
Distribute
3m = 5m +15 -3
Combine like terms
3m = 5m +12
Subtract 5m
3m-5m = 5m+12-5m
-2m = 12
Divide by -2
-2m/-2 = 12/-2
m = -6
say something so mean to me idc just say whats on your mind broskis
Answers
Answer:
Can grape juice be made into grapes?
Your so UGLY you turned medusa into stone.
Step-by-step explanation:
I said what was on my mind
Determine whether the graph represents a function. Explain.
Answers
Answer:
it does not represent a function
Step-by-step explanation:
it is not liner
Answer:yes
Step-by-step explanation:
each x value has one y value
If x is equal to 48 and y is equal to 12 then what is the value of x-4y?
Answers
Answer:
0
Step-by-step explanation:
48 - 4(12)
48 - 48 = 0
Answer:
The value of x - 4y would be 0.
Step-by-step explanation:
Since x is equivalent to 48, and y is equivalent to 12, you need to replace x and y with those values in order to solve the expression. \(x-4y\) = \(48 - 4 * 12\) = \(48 - 48\) = 0, so that is the correct answer.
The face of a clock is divided into 12 equal parts. The radius of the clock face is 10 inches. Assume the hands of the clock will form a central angle.
The face of a clock is divided into 12 equal parts.
Which statements about the clock are accurate? Select three options.
The central angle formed when one hand points at 1 and the other hand points at 3 is 30°.
The circumference of the clock is approximately 62.8 inches.
The minor arc measure when one hand points at 12 and the other hand points at 4 is 120°.
The length of the major arc between 3 and 10 is approximately 31.4 inches.
The length of the minor arc between 6 and 7 is approximately 5.2 inches.
Answers
The accurate statements about the clock are:
The circumference of the clock is approximately 62.8 inches.
The length of the major arc between 3 and 10 is approximately 31.4 inches.
The length of the minor arc between 6 and 7 is approximately 5.2 inches.
The circumference of the clock is approximately 62.8 inches.
The circumference of a circle is calculated using the formula C = 2πr, where r is the radius of the circle.
Given that the radius of the clock face is 10 inches, the circumference can be approximated to \(2 \times 3.14 \times 10 = 62.8\) inches.
The length of the major arc between 3 and 10 is approximately 31.4 inches. The major arc is the longer arc between two points on the circumference of a circle.
To calculate the length of an arc, we use the formula L = (θ/360) \(\times\) C, where θ is the central angle in degrees and C is the circumference of the circle.
The central angle between 3 and 10 is 210° (calculated as 10 - 3 = 7 segments \(\times\) 30° per segment).
Plugging in the values, we get L = (210/360) \(\times\) 62.8 ≈ 36.77 inches.
The length of the minor arc between 6 and 7 is approximately 5.2 inches. Similar to the previous statement, the length of an arc is calculated using the formula L = (θ/360) \(\times\) C.
The central angle between 6 and 7 is 30°, as there is one segment between them.
Plugging in the values, we get L = (30/360) \(\times\) 62.8 ≈ 5.23 inches.
The statement about the central angle formed when one hand points at 1 and the other hand points at 3 being 30° is incorrect, as the central angle between 1 and 3 is 60°.
The statement about the minor arc measure when one hand points at 12 and the other hand points at 4 being 120° is also incorrect, as the minor arc between 12 and 4 is 240°.
For similar question on minor arc.
https://brainly.com/question/28980798
#SPJ11
Answer:
b, d, and e
Step-by-step explanation:
i just did it
just some simple math fro points reward brainliest
Answers
Answer: first one is function second is not a function
Step-by-step explanation: