1 point) use the inner product ⟨f,g⟩=∫10f(x)g(x)dx ⟨f,g⟩=∫01f(x)g(x)dx in the vector space c0[0,1]c0[0,1] of continuous functions on the domain [0,1][0,1] to find ⟨f,g⟩⟨f,g⟩, ‖f‖‖f‖, ‖g‖‖g‖, and the angle αf,gαf,g between f(x)f(x) and g(x)g(x) for f(x)=10x2−3 and g(x)=6x−9.
The norms and the inner product of f and g can be calculated using the given inner product definition and the knowledge that the norm of a vector (here, function) is the square root of its inner product with itself. Then, the cosine of the angle between f and g can be found by dividing their inner product by the product of their norms.
Explanation:The problem is asking us to compute certain components in the context of a vector space of continuous functions, namely inner product ⟨f,g⟩, norms ‖f‖, ‖g‖, and angle between them for f(x) and g(x). Since the functions are given as f(x)=10x^2-3 and g(x)=6x-9, these can be used in the provided inner product definition ⟨f,g⟩=∫from 0 to 1f(x)g(x)dx.
The norm of a vector, in this case, the function f or g, is the square root of the inner product of the function with itself. The cosine of the angle α between the functions f and g is given by the ratio of the inner product of f and g to the product of their norms.
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If it is known that a+b/a-b=c, find the following: 2a-2b/5a+5b
The value of (2a - 2b)/(5a + 5b) can be simplified to c.
Explanation:To find the value of (2a - 2b)/(5a + 5b) when the equation (a + b)/(a - b) = c is given, we can substitute the value of (a + b)/(a - b) with c. Rearranging the equation, we get:
(2a - 2b)/(5a + 5b) = c
Simplifying the expression, we have:
(2(a - b))/(5(a + b)) = c
So, the value of (2a - 2b)/(5a + 5b) is c.
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what factor makes the number sentence true 7x4= ( ) x7
Emily buys 240 square feet of Carpet. She can convert square feet to square yards by dividing the number of square feet by 9. How many square yards of carpet did emily buy?
at 80km/h how many seconds does it take to travel 1km
What was png company's current ratio for the year 20x1? 7.74 3.32 2.66 2.47?
Joey received a report that he scored in the 97th percentile on a national standardized reading test but in the 72nd percentile on the math portion of the test. Explain to Joey’s grandmother, who knows no statistics, what these numbers mean.
The sum of the reciprocals of two consecutive integers is -9/20. Find the two integers
which fraction is greater than 1/2 and less than 3/4
The fraction that is greater than 1/2 and less than 3/4 is 2/3. This is demonstrated by placing these fractions on a number line, where 2/3 falls between 1/2 and 3/4.
Explanation:The question is asking for a fraction that is both greater than 1/2 (or 0.5) and less than 3/4 (or 0.75). To find such fraction, we can consider fractions between these two numbers. A possible solution is 2/3 (or approximately 0.67) which is truly greater than 1/2 and less than 3/4.
Now, let's explain this visually. If you translate these fractions on a number line, 1/2 would be at the middle of the line, 3/4 would be three quarters way forward and 2/3 would be somewhere in the middle of these two fractions.
Consider the representation on a number line, 0 -> 1/2 -> 2/3 -> 3/4 -> 1. We see that 2/3 does fall in between 1/2 and 3/4.
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What is the value of mc014-1.jpg?
–6
–2
14
22
the pic is the .jpg
Answer:
Option (3) is correct.
The value of the given expression [tex]\frac{-3(7+5)}{3^2}+9(2)[/tex] is 14.
Thus, option (3) is correct.
Step-by-step explanation:
Consider the given expression in the image given,
[tex]\frac{-3(7+5)}{3^2}+9(2)[/tex]
First solve for square term in the denominator,
[tex]3^2=3 \times 3 = 9[/tex]
Expression becomes,
[tex]\frac{-3(7+5)}{9}+9(2)[/tex]
Now solve for numerator,
7 +5 = 12 and -3(12) = -36
Expression becomes,
[tex]\Rightarrow \frac{-36}{9}+9(2)[/tex]
[tex]\Rightarrow -4+9(2)[/tex]
[tex]\Rightarrow -4+18[/tex]
[tex]\Rightarrow 14[/tex]
Thus the value of the given expression [tex]\frac{-3(7+5)}{3^2}+9(2)[/tex] is 14.
Thus, option (3) is correct.
(08.02)Which of the following graphs best represents the solution to the pair of equations below? y = x + 1
y = −x − 1
Carrie buys 4.16 pounds of apples for 5.20 how much does 1 pound cost
Select all the solutions for the quadratic equation x2=81 . Answer Choices x=9 x=81 x=−9 x=−81
an electrician cuts a 136-ft piece of cable. one piece is 16 feet less than 3 times the length of the other piece. Find the length of each piece.
1st piece = x
2nd piece = 3x-16
x +3x-16 = 136
4x-16 = 136
4x = 152
x = 152/4 = 38
1st piece = 38 feet
2nd piece = 136 -38 = 98 feet
what is the solution of the following system? x-y=11
-x+y=-11
a4 + b4 + c4 + d4 = (a + b + c + d)4 where variables a, b, c and d can be any positive integer, negative integer or zero.
This is one of the hardest math questions ever worth 100 points and brainliest!!!
Hi there!
This set you have given is not a definitive set, therefore there is not definitive answer that can be given. It is a indefinite set, which means that any set of integers can be put in as a solution to this set. Unless there are defining quantifiers then the set and solution are both infinite.
Your friend, ASIAX
. A square picture frame occupies an area of 112 ft2 . What is the length of each side of the picture in simplified radical form? Show your work.
which of the following represents the factorization of the trinomal below
In a recent year 33.2% of all registered doctors are female. If there were 56,400 female register doctors that year, what was the total number of registered doctors?
Not sure how to start working this one out?
he ended with 16
he earned 6 for mowing the lawn, so before mowing the lawn he had 16-6 =10
he spent half on pizza and had 10 left so allowance = 10*2 = 20
he gets $20 a week for allowance
Find the z-score such that: (a) the area under the standard normal curve to its left is 0.5
193+y greater that are equal to 201 what is y
HURRY!!!!!! What is the equation of a line that passes through the point (8, −2) and is parallel to the line whose equation is 3x + 4y = 15?
A car rental agency currently has 44 cars available, 28 of which have a gps navigation system. one of the 44 cars is selected randomly. find the probability that this car
How can you decompose the composite figure to determine its area?
Answer:
D. As a semicircle, a trapezoid and two rectangles.
Step-by-step explanation:
Please find the attachment.
We have been given a composite figure. We are asked to decompose our given figure to determine its area.
Upon looking at attachment for our given composite figure, we can see that it consists one semicircle on top, one trapezoid in middle and two rectangles on bottom. So we can decompose our composite figure as a semicircle, a trapezoid and two rectangles.
Therefore, option D is the correct choice.
What is the percent increase of 36 and 63
you were to use the substitution method to solve the following system, choose the new equation after the expression equivalent to x from the second equation is substituted into the first equation. 2x − 3y = −29 x + 4y = 13
Using the substitution method, the solution to the system of linear equations is: x = -7 and y = 5.
What is the Substitution Method?The substitution method used in solving a system of linear equations involves substituting a variable for an expression into the other equation given.
Given the system:
2x − 3y = −29 - eqn. 1
x + 4y = 13 - eqn. 2
Rewrite eqn. 2
x = 13 - 4y
Substitute x = 13 - 4y into eqn. 1
2(13 - 4y) − 3y = −29
26 - 8y - 3y = -29
-11y = -29 - 26
-11y = -55
y = 5
Plug in the value of y into x = 13 - 4y:
x = 13 - 4(5)
x = -7
The solution is: x = -7 and y = 5
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To what place vaule is the number rounded 5.319 to 5.3
The average time a boulder high varsity lacrosse player plays in a game is 27 minutes with a standard deviation of 6 minutes. nolan's playing time in last week's game against fairview was 50 minutes. (a) calculate the z-score for nolan's playing time against fairview. (round your answer to 2 decimal places.)
A rectangle has side lengths of (3x+6) inches and (2x-4) inches. Write an expression to represent the perimeter of the rectangle. Then find the value of x if the perimeter is 94 inches.
Answer:
Perimeter: 2(3x+6)+ 2(2x-4)
X=9
Step-by-step explanation:
In order to create the expression you just have to remember that the perimeter of a rectangle equals 2 bases plus 2 sides, so the expression would be:
Perimeter: 2(heights)+ 2(bases)
Perimeter: 2(3x+6)+ 2(2x-4)
IN order to solve for X we just have to insert the value of perimeter, which is 94:
Perimeter: 2(3x+6)+ 2(2x-4)
94=2(3x+6)+ 2(2x-4)
94= 6x+12+4x-8
94=10x+4
94-4=10x
x=90/10
x=9
So the value of x would be 9.