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.
Learn more about Inner Product & Norms here:https://brainly.com/question/34578319
#SPJ3
Sales at a local ice cream shop went 80% in 5 years. If 12,000 ice cream cones were sold in the current year find the number of ice cream cones sound in 5 years
By decreasing each dimension by 1 unit, the area of a rectangle decreased from 40 square feet (on the left) to 28 square feet (on the right). Find the percent decrease in area.
The percent decrease in the area of a rectangle from 40 square feet to 28 square feet is calculated by dividing the difference in areas (12 sq ft) by the original area (40 sq ft) and multiplying by 100%. The result is a 30% decrease in area.
Explanation:The percent decrease in the area of a rectangle can be found by first calculating the difference in the areas and then dividing that difference by the original area. In this case, the original area of the rectangle was 40 square feet and it decreased to 28 square feet, a difference of 12 square feet.
We use the formula for percentage change which is:
(change in value) / (original value) × 100%
Here, the change in value is the difference in areas (12 square feet) and the original value is the original area of the rectangle (40 square feet). Thus we calculate:
(12 sq ft/ 40 sq ft) * 100% = 30%
So, the percent decrease in the area of the rectangle is 30%.
Learn more about Percent Decrease here:https://brainly.com/question/8549621
#SPJ2
A suit is on sale for $154. If the original price of the suit was $440, what percent was discounted for the sale?
The Clemson Tiger Football team won the 2016 College Football National Championship. During the regular season, they won 11 games and lost 1. The data set below is the number of points by which they won (positive values) or lost (negative value) each game.
{6,6,59,19,6,46,7,3,54,−1,22,49} = {-1,3,6,6,6,7,19,22,46,49,54,59}
What is the median? ________
What is the mode? _________
What is the mean? _________
What is the 5% trimmed mean? (Round to the nearest whole number when determining the number of values to trim).
Are these averages parameters or statistics?
median is the middle value, since there is an even number, add the 2 middle numbers and divide by 2
median = 9 +17 = 26/2 = 13
mode is the number that is repeated most often
mode = 6
mean is the average of all the numbers, when added they equal 276
276/12 = 23
mean = 23
5% trimmed mean = 218 /10 = 21.8
the averages are statistics since the points of a football game can vary
What is the distance between 0.5 to -1.5
Find f`(x) for the following function. Then find f(5),f(0),f(-9).
f(x)=2x+1 (simplify)
The length of a ribbon is 3/4 meter. Sun Yi needs pieces measuring 1/3 meter for an art project. What is the greatest number of pieces measuring 1/3 meter that can be cut from the ribbon? How much ribbon will be left after Sun Yi cuts the ribbon?
Only the Fahrenheit one plz
Which of the following is true?
1.75 > 1½
0.25 ≠ ¼
0.2185 = ⅓
1.436 < 25⁄2
After converting all values to decimal form for consistent comparison, the statements '1.75 > 1½' and '1.436 < 25⁄2' are true, while the statements '0.25 ≠ ¼' and '0.2185 = ⅓' are false.
Explanation:The question is asking to compare different given values, either greater than (>), not equal to (≠), or less than (<). To do this accurately, we need to convert all numbers to a common form. In this case, it is easiest to consider everything as decimal values:
1.75 is indeed greater than 1½ (which is 1.5 in decimal), so 1.75 > 1½ is true.0.25 is equal to ¼ (which is also 0.25 in decimal), therefore 0.25 ≠ ¼ is false. 0.2185 is not equal to ⅓. ⅓ in decimal is approximately 0.333, so 0.2185 = ⅓ is false. 1.436 is less than 25/2 (which is 12.5 in decimal form), so 1.436 < 25⁄2 is true. Learn more about Decimal Comparison here:https://brainly.com/question/12970629
#SPJ11
How do I Factor 125x^3 -64
The answer is not (5x+4)(5x-4) or (5x-4)(25x^2 +15x+16)
The correct factorization would be (5x - 4)(25x^2 + 20x + 16).
The law of factoring cubes states that we use the following formula when we have two cubes being subtracted by one another.
(a - b)(a^2 + ab + b^2)
If we take the cube root of 125x^3 we get 5x, which will be our a value. If we take the cube root of 64, we get 4, which will be our b value. Then we plug in to the formula.
(5x - 4)((5x)^2 + (5x)(4) + 4^2)
(5x - 4)(25x^2 + 20x + 16)
I think the problem with your second answer is that you just did not properly multiply the 5x and the 4 to get 20x (instead you got 15x).
A store had 888 sodas, both diet and regular. The ratio of diet sodas to regular sodas was 8:4. How many diet sodas were there?
Answer:no. I don’t understand. Where did the 12 come from
Step-by-step explanation:
identify the product and it in scientific notation. 4.7 x(6.02 x 10^23)
the product of [tex]\( 4.7 \times (6.02 \times 10^{23}) \) is \( 2.8294 \times 10^{24} \).[/tex]
Sure, let's identify the product and express it in scientific notation.
[tex]\( 4.7 \times (6.02 \times 10^{23}) \)[/tex]
To find the product, we simply multiply the two numbers:
[tex]\( 4.7 \times 6.02 \times 10^{23} \)[/tex]
First, we multiply 4.7 by 6.02:
[tex]\( 4.7 \times 6.02 = 28.294 \)[/tex]
Next, we multiply this result by [tex]\( 10^{23} \):[/tex]
[tex]\( 28.294 \times 10^{23} \)[/tex]
Now, to express this product in scientific notation, we need to adjust the decimal point so that the number is between 1 and 10:
[tex]\( 2.8294 \times 10^{24} \)[/tex]
Therefore, the product of [tex]\( 4.7 \times (6.02 \times 10^{23}) \) is \( 2.8294 \times 10^{24} \).[/tex]
1. First, we multiplied 4.7 by 6.02 to get 28.294.
2. Then, we multiplied this result by [tex]\( 10^{23} \)[/tex] to shift the decimal point 23 places to the right, resulting in[tex]\( 2.8294 \times 10^{24} \)[/tex] in scientific notation.
This method helps in handling large numbers efficiently, especially when dealing with calculations involving scientific notation and significant figures.
complete question
identify the product and it in scientific notation. 4.7 x(6.02 x 10^23)
Jana is doing an experiment. She is on a dock that is 10 feet above the surface of the water. Jana drops the weighed end of a fishing line 35 feet below the surface of the water. She reels out the line 29 feet, and then reels it back in 7 feet. What is the final distance between Jana and the end of the finishing line?
You took 500 calls in 30 days that means I took a average of
Answer:
17 calls
Step-by-step explanation:
You took 500 calls in 30 days.
We have to calculate the average calls per day.
Average calls = [tex]\frac{\text{Total calls}}{\text{total days}}[/tex]
= [tex]\frac{500}{30}[/tex]
= 16.7 ≈ 17 calls per day
That means i took an average 17 calls per day.
what is the mean of this data if necessary round your answer to the nearest tenth. please help with my homework
Rose bought 7/20 kilogram of ginger candy and 0.4 kilogram of cinnamon candy. Which did she buy more of? Explain how you know.
Answer:
Rose bought cinnamon candy more of.
Step-by-step explanation:
Rose bought ginger candy = [tex]\frac{7}{20}[/tex] kilogram
= 0.35 Kilogram
She bought cinnamon candy = 0.4 kilogram
As we know 1 kilogram = 1000 grams
0.35 kilogram = 1000 × 0.35 = 350 grams ginger candy
0.4 kilograms = 1000 × 0.4 = 400 grams cinnamon candy
Therefore, She bought cinnamon candy more.
How do i solve this equation and how did you do it
The height of Niagara falls is 182.How many yards high is Niagara falls
To convert the height of Niagara Falls from meters to yards, we multiply the given height of 182 meters by the conversion factor of 1.09361 yards per meter, which gives us approximately 199.18 yards.
Explanation:The height of Niagara Falls is provided in this question as 182. However, no units are given so let's assume this is in meters as that's a common unit for height. The conversion factor from meters to yards is approximately 1 meter = 1.09361 yards. Therefore, we multiply the given height in meters by this conversion factor to get the height in yards.
First, identify the height given in the question- here it is 182.Next, apply the conversion factor: 182 meters * 1.09361 yards/meter.Doing this multiplication gives us approximately 199.18 yards.So, Niagara Falls is approximately 199.18 yards high when converted from meters.
Learn more about Unit Conversion here:https://brainly.com/question/19420601
#SPJ12
How can you check to see if this equation is correct? 12+39=49
Answer:
By solving it.
Step-by-step explanation:
In order to see if the equation is correct, you just have to perform the operations in both sides of the inequality and then check if those are equal, that means that the equation is correct, for example if both sides of the equation give as a result 10 then the equation is correct, now let´s do it with the problem:
12+39=49
51=39
Since 51 is not equal to 39 that means that the equation is not correct.
6.24 divided by 200 equals what
Prove or disprove that the product of two irrational numbers is irrational
The product of two irrational numbers can be either rational or irrational.
The product of two irrational numbers is not always irrational. To understand this, let's consider an example and a counterexample.
Example of an Irrational Product
Take the square root of 2 (\/(2)) and the square root of 3 (\/(3)). Both of these numbers are irrational. Their product is:
\/2 × \/3 = \/6
Since \/6 cannot be expressed as a fraction of two integers (making it irrational), this is an example where the product of two irrational numbers is irrational.
Counterexample of a Rational Product
Now, consider another example with \/(2) and \/(2). Since both are irrational, their product is:
\/2 × \/2 = 2
Here, 2 is a rational number because it can be written as a fraction (2/1). Therefore, this is a counterexample where the product of two irrational numbers is rational.
In summary, the product of two irrational numbers can be either rational or irrational depending on the specific numbers involved.
PLZ HELP IM FAILING!!!!!! The linear equation y−3=4(x+5)y−3=4(x+5) y minus 3 equals . 4 open x plus 5 close is in what form.
A lawn is in the shape of a trapezoid with a height of 40 feet and bases of 60 feet and 140 feet. How many bags of fertilizer must be purchased to cover the lawn if each bag covers 1800 square feet?
Check the answer that best describes the relationship between f(x) and x. (for example if f(x) is θ(x)θ(x) check that as your answer and not o(x)o(x) or ω(x)ω(x) even though these are true also in this case.)
A school uses merit based pay for teachers. Each teacher would be given a score between 1 (Far Below Expectations) and 5 (Exceeds expectations) in the following categories. The weight of each category is included.
Content Knowledge (20%)
Lesson plans (15%)
Instruction delivery (20%)
Classroom management (15%)
Student Performance (20%)
Supplementary Responsibilities (10%)
A teacher received the following scores. What was his weighted average?
Content Knowledge = 4
Lesson plans = 3
Instruction delivery = 3
Classroom management = 5
Student Performance = 4
Supplementary Responsibilities = 2
The teacher's weighted mean is ______________.
4*0.20 = 0.8
3 *0.15 = 0.45
3*0.20 = 0.6
5 *0.15 = 0.75
4 *.20 = 0.8
2 *0.10 =0.2
0.8 + 0.45 + 0.6 +0.75 +0.8 +0.2 = 3.6
weighted mean = 3.6
The teacher's weighted mean is 3.6 out of 5.
To calculate the weighted average, you'll multiply each score by its corresponding weight, then sum up the results.
Here are the scores and their respective weights:
- Content Knowledge: 4 (score) * 0.2 (weight) = 0.8
- Lesson Plans: 3 * 0.15 = 0.45
- Instruction Delivery: 3 * 0.20 = 0.6
- Classroom Management: 5 * 0.15 = 0.75
- Student Performance: 4 * 0.20 = 0.8
- Supplementary Responsibilities: 2 * 0.10 = 0.2
Now, sum up these weighted scores:
0.8 + 0.45 + 0.6 + 0.75 + 0.8 + 0.2 = 3.6
So, the teacher's weighted mean is 3.6.
How much money should be invested at 5% interest, compounded quarterly, so that 7 years later the investment will be worth $5000? This amount is called the present value of $5000 at 5% interest.
6x+24/x^2+7x+12 simplify
if f'(2) = 3.1 and g'(2)=7.3 then the graph of f(x)+g(x) has slope 10.4 at x=2.True or false
Final answer:
The statement is true, as the slope of the graph of f(x)+g(x) at x=2 is the sum of the slopes of f and g at that point, which equals 10.4.
Explanation:
The statement is true.
In calculus, the derivative of a function at a particular point measures the rate at which the function is changing at that point. It is analogous to the slope of the tangent line to the graph of the function at that point.
When we are given that f'(2) = 3.1 and g'(2) = 7.3, these values represent the slopes of the functions f and g at x = 2, respectively.
To find the slope of f(x) + g(x) at x = 2, we simply add the slopes of f and g at that point. This is based on the rule that the derivative of the sum of two functions is the sum of their derivatives, or symbolically, (f+g)' = f' + g'.
Therefore, the slope of the graph of f(x)+g(x) at x=2 is indeed 10.4 (3.1 + 7.3).
A data set a has a mean of 7,a median 5,and a mode of 8.wich of the the numbers 7,5,and 8 must be in the data set?
For the initial value problem y' −xy = x, y(0) = 1. write down the first four nonzero terms of the series