The orthogonal projection of f(x) = 4x^2 - 4 onto the subspace V spanned by g(x) = x and h(x) = 1 is given by p(x) = 2x - 2/3.
What is the expression for the orthogonal projection of f(x) = 4x^2 - 4 onto the subspace V spanned by g(x) = x and h(x) = 1?To find the orthogonal projection of f(x) = 4x^2 - 4 onto the subspace V spanned by g(x) = x and h(x) = 1 in the vector space C0[0,1], we can utilize the inner product ?f,g? = ∫[0,1] 10f(x)g(x) dx. The orthogonal projection, p(x), can be obtained by calculating the inner product of f(x) with each basis function in V and scaling them accordingly.
Using the inner product, we have ?f,g? = ∫[0,1] 10f(x)g(x) dx = 10∫[0,1] (4x^2 - 4)x dx = 10∫[0,1] (4x^3 - 4x) dx = 10[(x^4/4 - 2x^2) ∣[0,1]] = 10(1/4 - 2/3) = -5/3.
Similarly, ?f,h? = ∫[0,1] 10f(x)h(x) dx = 10∫[0,1] (4x^2 - 4) dx = 10[(4x^3/3 - 4x) ∣[0,1]] = 10(4/3 - 4) = -10/3.
Next, we need to determine the inner product ?g,g? and ?h,h? to find the norms of g(x) and h(x) respectively. ?g,g? = ∫[0,1] 10g(x)g(x) dx = 10∫[0,1] x^2 dx = 10(x^3/3 ∣[0,1]) = 10/3. Similarly, ?h,h? = ∫[0,1] 10h(x)h(x) dx = 10∫[0,1] dx = 10(x ∣[0,1]) = 10.
Using the formula for the orthogonal projection, p(x) = (?f,g?/?g,g?)g(x) + (?f,h?/?h,h?)h(x), we can substitute the values we obtained:
p(x) = (-5/3)/(10/3)x + (-5/3)/(10) = (2x - 2/3).
Therefore, the orthogonal projection of f(x) = 4x^2 - 4 onto the subspace V spanned by g(x) = x and h(x) = 1 is given by p(x) = 2x - 2/3.
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Mario has 160 pizzas and is collecting two pizzas a week. Write the equation for the number of pizzas Mario has
Answer:
160+2x
Step-by-step explanation:
Answer:
Mario has after 5 weeks 170 pizzas.
Step-by-step explanation:
Each time add to the chart 2 Pizzas and move a week.
The table shows the balance of an account each year.
Years Balance
0 $40
1 $42
2 $44
3 $46
What is the interest rate of the account? What is the balance after 10 years?
Answer:
The interest rate is $2, the balance after 10 years will be $60.
Step-by-step explanation:
Each year the balance of the account increases by $2, so that would be the interest rate. After 10 years, the account will have 40 + 2 * 10 which equals $60.
Need help ASAP
Thankss + BRAINLIST only for correct answer
Answer(5,6)
Step-by-step explanation:
find the slope of the line that passes through
(-5,8) and (2,-6)
Answer:
Slope is -2
Step-by-step explanation:
Formula is y2 - y1 / x2 - x1
Hope this helps. Pls give brainliest.
1.A five - layer of cake weighs half a kilogram per layer.In each layer,the cake is decorated with icing which weighs 15g.3 candles which weighs 100g each is added.What is the total weight in kilogram of the fully decorated cake?
Answer: 2.815 kilograms
======================================================
Work Shown:
1 layer = 0.5 kg
5 layers = 5*(0.5 kg) = 2.5 kg
icing = 15 g = 15/1000 = 0.015 kg
1 candle = 100 g = 100/1000 = 0.1 kg
3 candles = 3*(0.1 kg) = 0.3 kg
------------------------
The five layers combine to 2.5 kg. On top of that we have 0.015 kg of icing, and then finally the three candles add 0.3 kg more weight.
The total weight is therefore: 2.5+0.015+0.3 = 2.815 kilograms
Is the point (3, 11) a solution for the linear equation 1/3x + y = 12? Explain.
9514 1404 393
Answer:
yes
Step-by-step explanation:
The point is on the line.
The coordinate values satisfy the equation:
1/3x + y = 12
1/3(3) + 11 = 12 . . . substitute for x and y
1 + 11 = 12 . . . . . . . true
Any point that satisfies the equation is a solution. (3, 11) is a solution.
need helpppppp
plz and thank u
5-1/10
Step-by-step explanation:
4-1/2+3/5=
9/2 + 3/5=
45/10+6/10=51/10=5-1/10
Kim got 82%, 75%, and 74% on the first 3 tests.
What grade does she need on the 4th test to have an average of 80% on all 4 tests?
A. 77%
B. 80%
O c. 85%
D. 89%
E. 100%
Answer:
C
Step-by-step explanation:
Add all percentages together, then divide by how many you added.
Answer:
C
Step-by-step explanation:
what type of polygon is this
Answer:
enneagon
Step-by-step explanation:
Guy please help me out so this is the question 3. Last Sunday, the temperature at 8:00 a.m. was -3०C. Between 8:00 a.m and 1:00 p.m., the temperature rose by 5०C. By 6:00 p.m. the temperature was 2०C colder than it was at 1:00p.m. Then, the temperature dropped 3०C each hour between 6:00 p.m. to 10:00 p.m. What was the temperature at 10:00 p.m.? I got the answer -1 is that correct?
Answer:
ayuda necesito lo mismo
Step-by-step explanation:
por favor algún voluntario
Answer:
-9C
Step-by-step explanation:
-3+5-2-3(3)=-9C
i think you made a mistake on "it got colder by 2C." If temperatures get colder, they drop, meaning you subtract it.
also, it said between the hours of 6-10pm, which is three hours, the temperature drops each hour by 3C. so, you multiply 3 to -3, and come up with -9
Find the quotient of 3 2/5 and 3 1/6 . Express your answer in simplest form.
1 5/12
95/102
1 7/95
10 23/30
Answer:
1 7/95
Step-by-step explanation:
convert the fractions into improper fractions
3 2/5 = 17/5
3 1/6 = 19/6
[tex]\frac{17}{5}[/tex] divided by [tex]\frac{19}{6}[/tex] - invert second term and multiply
so 17 * 6 = 102
5* 19 = 95
answer is 102/95, or 1 7/95
A farmer sells 8.8 kilograms of apples and pears at the farmer's market. 1 4 of this weight is apples, and the rest is pears. How many kilograms of pears did she sell at the farmer's market?
Answer: She sold 6.6kg of pears in the market.
Step-by-step explanation:
Weight of apples and pears at the farmer's market.=8.8 kilograms
Weight of apples = 1/4
which is = 1/4 x 8.8kg = 2.2 kg
Weight of Pears =Weight of apples and pears - Weight of apples
= 8.8kg- 2.2kg
= 6.6kg
A 25 m tall flagpole casts a shadow that is 10 m long. At the same time, a nearby office building casts a shadow that is 26 m long. What is the height of the building?
Answer:
kmjuhygtfcv nm,kljihuygbv njmihuygb
Step-by-step explanation:
The height of the office building is 65 meter.
What s proportionality in mathematics?
If the corresponding elements of two sequences of numbers, frequently experimental data, have a constant ratio, known as the coefficient of proportionality or proportionality constant, then the two sequences of numbers are proportional or directly proportional.
If equivalent elements in two sequences have a constant product, also known as the coefficient of proportionality, then the two sequences are inversely proportional.
The shadow of a 25 m tall flagpole casts is = 10 m.
Let the height of the office building = x m.
The shadow of a x m tall office building is = 26 m.
From theory of directly proportionality:
25 : 10 = x : 26
25/10 = x/26
x = (25/10)×26 = 65
Hence, the height of the office building is 65 meter.
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The problem is a word problem: The sum of two consecutive odd numbers is 72. find the numbers
Answer:
35 and 37
Step-by-step explanation:
consecutive ODD numbers, 35 then 37.. 35+37 = 72
0.7x-y=5.16 and 2-0.8x=0.4y round to the nearest hundredth? does anyone know this answer?
Step-by-step explanation:
What is the question? You have not stated the question.
when you go to answer this, can someone please give me the steps on how to do it, because I think I'm doing it wrong
Answer:
TUA=123
Step-by-step explanation:
so first we find <TUS in terms of x
so 180-11x-2
178-11x
so now we can use the sum of a triangle's angles which is always 180 to find the angles in triangle TUS
178-11x+5x+10+58=180
178-6x=112
take 178 from both sides
-6x=-66
x=11
so we can do 11x11+2=TUA
TUA=123
Judy made 3 pans of brownies for her friends. She cut each pan into 8 equal pieces. Her friends ate 20/8 of the brownies. What fraction of the brownies are left?
Answer:
13/6
Step-by-step explanation: 8 pieces in 3 pan give us a total of 8/24, then minus 20/8. The writing of this equation is:
20/8- 8/24 or 8/24- 20/8 (both are good)
The common denominator here is 24 since it can divide 8 and divide itself.Since you have 24 as denominator, you'll have to reconvert the fractions above by diving 24 by their previous denominator and multiply it by their numerator:
(24/8) × 20= 60 (numerator of the 1st fraction)
(24/24) × 8= 8 (numerator of the 2nd fraction)
The new fractions are then
60/24 - 8/24= 52/24
We could stop there but since we could find an irrational fraction as an answer, why not do it
52/24 (both divided by 2)= 26/12
26/12 can still be divided so we keep going
26/12 (both divided by 2) = 13/6
13 is a prime number and therefore can be divided only by itself, and 6 cannot be divided by 13 without having a decimal answer.
13/6 is the final answer
Why are the two triangles congruent?
Answer:
becuz they look the same, theyre the same shape, AND size.. thats what makes to shapes congruent.
Step-by-step explanation:
Brainliest, pretty please? hee hee
Answer:
All three pairs of corresponding sides are equal, have the same shape and dimensions.
Step-by-step explanation:
Intro to slope-intercept form What is the y-intercept of the line represented by y = -6x – 11? Choose 1 answer: А (0, -6 B (0, -11) (-6,0) D (-11,0) Check About
pls help i suck at math
Answer:
d
Step-by-step explanation:
Please hurry I need help with this
Simplify
(x + 3)^8
(x + 3)^5
Answer:
1. Expand the expression.
x^8+24x^7+252x^6+1512x^5+5670x^4+13608x^3+20412x^2+17496x+6561
2. (x+3)^5
Use the Binomial Theorem.
x^5+5x^4⋅3+10x^3⋅3^2+10x^2⋅3^3+5x⋅3^4+3^5
Simplify each term.
x^5+15x^4+90x^3+270x^2+405x+243
Step-by-step explanation:
hope it is helpful....
Answer:
42x
Step-by-step explanation:
Which are the partial products for 8x362? Select all that apply.
Answer:
Are you guys classmates?
Jada has a stand in the marketplace where she sells ground cumin. Her weekly expenses are $300, and she sells her cumin at a fixed price per kilogram. If she sells 120 kilograms of cumin, her weekly net profit is $600.
Answer:
Step-by-step explanation:
The net profit of the marketplace is the difference between the revenue and the expenses. The revenue is the product of number of kilograms sold and the price per kilogram.
Profit = Revenue - Expenses
600 = 120x - 300
The value of x from the equation is 7.5. The answer therefore for the first question is $7.5. Then, the number of kilogram of cumin she needs to sell to cover the expenses is $300/$7.5 and that is equal to 40.
I need help ASAP! I am offering brainiest to whoever answers the question first!
Answer:
Step-by-step explanation:
1536(4)(4)=24576
Answer:1536(4)(4)=24576
Step-by-step explanation:
IS THIS RIGHT? PLS HELP
Step-by-step explanation:
yes your answer is absolutely correct ..the value of x comes out to be -1 and 7 ..
6th grade math plz help me
Grace made a dot plot showing the distances she ran each day for two weeks.
She says that she usually runs 7 miles each day because that is the distance that occurs most often.
Do you agree with Grace’s reasoning?
Use the drop-down menus to explain and show your answer.
Dot plot named as ALTDCDistances RunALTDC has number line from 1 to 7. 1 dot on 1, 3 dots on 2, 3 dots on 3, 3 dots on 4 and 4 dots on 7 are given.
The mode, which is (3,4, or 7) ,(is or is not) a typical distance for the data. The median, which is (3.5,4, or 7),(is or is not) a typical distance for the data. The mean, which is (3,4, or 7) ,(is or is not) a typical distance for the data. So, Grace’s reasoning(is or is not ) correct.
Answer:
The mode, which is 7, is not a typical distance for the data. The median, which is 3.5, is not a typical distance for the data. The mean, which is 4, is a typical distance for the data. So, Grace’s reasoning is not correct.
Pensé un número, a ese
número le sumé 15 y
obtuve como resultado 27.
¿Cuál es el número que
pensé
Answer:
si es suma tiene que ser 12+15=27
Can anyone help with this problem ?
[tex] \frac{ {m}^{11} }{ {m}^{8} } = {m}^{3} [/tex]
[tex] {m}^{11 - 8} = {m}^{3} [/tex]
When you're dividing two exponents with like bases, all you have to do is substract the exponents.
List the five ways to determine if two triangles are congruent.
Answer:
SSS (side, side, side) SSS stands for "side, side, side" and means that we have two triangles with all three sides equal. ...
SAS (side, angle, side) ...
ASA (angle, side, angle) ...
AAS (angle, angle, side) ...
HL (hypotenuse, leg)
hakim wrote an equation to represent the number of meters he would run for each kilometer, k, in a long distance race.W hat is the value of k if 1,000k =0?