Use the inner product〈f,g〉=∫10f(x)g(x)dxin the vector space C0[0,1] of continuous functions on the domain [0,1] to find 〈f,g〉, ∥f∥, ∥g∥, and the angle αf,g between f(x) and g(x) forf(x)=−10x2−6 and g(x)=−9x−4.〈f,g〉= ,∥f∥= ,∥g∥= ,αf,g .
Answers
Answer:
a) <f,g> = 2605/3
b) ∥f∥ = 960
c) ∥g∥ = 790
d) α = 90
Explanation
a) We calculate <f,g> using the definition of the inner product:
b) How
∥f∥ = <f,f> then:
∥f∥ =
c)
∥g∥ = <g,g>
∥g∥ =
d) Angle between f and g
<f,g> = ∥f∥∥g∥cosα
Thus
Final answer:
The answer to this problem involves applying integrals, norms, and concepts of angles between vectors to the functions f(x) and g(x). The INNER PRODUCT is the integral of the products of the two functions, the norms are the square roots of the inner products of the functions with themselves, and the angle between the functions is calculated using the dot product and norms.
Explanation:
To find the inner product 〈f,g〉, the norms ∥f∥ and ∥g∥, and the angle αf,g between the functions f(x)=−10x2−6 and g(x)=−9x−4, we'll apply concepts from vector calculus. The inner product (also known as the dot product) is the integral from 0 to 1 of the products of the two functions. The norm of a function is the square root of the inner product of the function with itself. The angle between two vectors in a Vector Space, in this case the space of continuous functions C0[0,1], is given by cos(α) = 〈f,g〉/( ∥f∥∙ ∥g∥). Integrating and solving these equations will give us the desired values.
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Answer:
Step-by-step explanation:
In order to resolve correctly this combined calculation, we need to resolve it in order:
First, the operation in parenthesis. Secondly, the powers. Then multiplications and divisions, and after all, substraction and adittion.
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represents the total number of Bluefin Tuna, y in the tank.
Answers
Answer:
Y=4Z
Step-by-step explanation:
SHE ORDERED 63 MEDIUM SHIRTS
AND 27 LARGE SHIRTS, WHAT WAS
THE RATIO OF MEDIUM TO LARGE
SHIRTS?
Answers
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Provide your answer below:
inches
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Content attribution
The area of a triangular painting is 50 in.² the base is 20 inches what is the height
Answers
The height of the triangle is 5 inches.
Area of the triangle:
The region occupied by a triangle within its sides is known as the area of the triangle. The area of a triangle can be calculated by the calculating product of the base and height of the triangle with a half i.e 1/2. The formula for the area of the triangle is given by
Area of triangle = (1/2) × base × height
Here we have
Area of the triangle = 50 in²
The base of the triangle, b = 20 inches
As we know,
Area of the triangle = 1/2 (base × height)
From the given data,
=> 50 = 1/2 (20 × height)
Multiply by 2 on both sides
=> 100 = (20 × height)
Divided by 20 into both sides
=> 100/20 = (20 × height)/20
=> 5 = height
=> height = 5 in
Therefore,
The height of the triangle is 5 inches.
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8 = 3x + 5
Please help
Answers
Answer:
-3x+13
Step-by-step explanation:
Group like terms
=-3x+8+5
Add the numbers 8+5=13
-3x+13
Best answer gets brainliest.
Answers
Answer:
no x=4.5
Step-by-step explanation: