Consider the following functions. f1(x) = x, f2(x) = x2, f3(x) = 2x − 4x2 g(x) = c1f1(x) + c2f2(x) + c3f3(x) Solve for c1, c2, and c3 so that g(x) = 0 on the interval (−[infinity], [infinity]). If a nontrivial solution exists, state it. (If only the trivial solution exists, enter the trivial solution {0, 0, 0}.) {c1, c2, c3} = $$ Correct: Your answer is correct. Determine whether f1, f2, f3 are linearly independent on the interval (−[infinity], [infinity]).

Answers

Answer 1

9514 1404 393

Answer:

(c1, c2, c3) = (-2t, 4t, t) . . . . for any value of tNOT linearly independent

Step-by-step explanation:

We want ...

  c1·f1(x) +c2·f2(x) +c3·f3(x) = g(x) ≡ 0

Substituting for the fn function values, we have ...

  c1·x +c2·x² +c3·(2x -4x²) ≡ 0

This resolves to two equations:

  x(c1 +2c3) = 0

  x²(c2 -4c3) = 0

These have an infinite set of solutions:

  c1 = -2c3

  c2 = 4c3

Then for any parameter t, including the "trivial" t=0, ...

  (c1, c2, c3) = (-2t, 4t, t)

__

f1, f2, f3 are NOT linearly independent. (If they were, there would be only one solution making g(x) ≡ 0.)


Related Questions

Hello, please be honest, is this correct?

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yup your right ( i’m just writing here so it lets me send it)

Answer:

Yes that is correct you got keep up good work

I need to know if 3750 is right or wrong cause I think that’s the answer

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It’s wrong.

The surface area means the area of the outside of the cube.

The area of a square is just width x height. And we are told one of the sides is 5.

A square has all equal sides. So what’s 5x5? then times that by the number of squares

I’ll put the answer in the comments

What is the domain of the graph

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Answer:

it D

Step-by-step explanation:

Is this relation a function? Justify your answer.

Answers

Answer:

Yes

Step-by-step explanation:

(I can only read the graph).

Since for each dot, a vertical line drawn through it only intersects that dot, we conclude that the relation is a function.

what's the answer???

Answers

Answer:

Step-by-step explanation:

y-4=-2(x-8)

At a diving competition, Allison scored 78.5 on her first dive. Hannah's score on her first dive was 74.65. How many more points did Allison score on her first dive than Hannah? SHOW YOUR WORK.​

Answers

If Allison scored 78.5 and Hannah scored 74.65 you’ll subtract 74.65 from 78.5 and get 3.85. That’s how many points more Allison scored

5(Y-1)=3(2Y-5)-(1-3Y)

Answers

Answer: =11/4

Step-by-step explanation:

Answer:

[tex]y = 2 \frac{3}{4} \\ [/tex]

Step-by-step explanation:

[tex]5(y - 1) = 3(2y - 5) - (1 - 3y) \\ 5y - 5 = 6y - 15 - 1 + 3y \\ 5y - 5 = 9y - 16 \\ 16 - 5 = 9y - 5y \\ 11 = 4y \\ \frac{11}{4} = y \\ 2 \frac{3}{4} = y \\ [/tex]

I'm thinking of 2 numbers. Both numbers have the same absolute value. What number must be true about the 2 numbers?

Answers

Answer: they have the same number in them for example -4 and 4

Step-by-step explanation:

La barbería El Caleño, tiene en promedio 120 clientes a la semana a
un costo actual de $6000 por corte de cabello. Se sabe que por cada incremento
de $700 en el precio, la peluquería pierde 10 clientes. ¿Cuál es el precio máximo
que puede cobrarse de modo que los ingresos semanales no sean menores que los
actuales?

Answers

Queremos maximizar el precio de tal forma que los ingresos no disminuyan.

Ese maximo precio es: $14,040.6

Sabemos que actualmente el precio es:

p = $6,000

El número de clientes es:

C = 120

Actualmente los ingresos son el producto de esos dos números, es decir:

ingresos = $6,000*120 = $720,000

Ahora sabemos que por cada incremento de $700 en el precio, el número de clientes decrece en 10.

Entonces podemos escribir el número de clientes como una ecuación lineal.

C(p) = a*p + b

tal que tenemos dos puntos en esa linea:

($6,000, 120)

($6,700, 110)

La pendiente es:

[tex]a = \frac{110 - 120}{\$6,700 - \$6,000} = \frac{-10}{\$ 700}[/tex]

Entonces tenemos:

C(p) = (-10/$700)*p + b

Sabemos que:

C($6,000) = 120 = (-10/$700)*$6,000 + b

                     120 = -85.71 + b

                     120 + 85.71 = b =

Entonces la ecuación lineal es:

C(p) = (-10/$700)*p + 205.71

Los ingresos serán dados por:

ingresos = C(p)*p = (-10/$700)*p^2 + 205.71*p

Y queremos maximizar p de tal forma que esto sea igual a lo que obtuvimos antes:

(-10/$700)*p^2 + 205.71*p = $720,000

Entonces debemos resolver la ecuación cuadratica:

(-10/$700)*p^2 + 205.71*p - $720,000 = 0.

Las soluciones son dadas por la formula de Bhaskara.

[tex]p = \frac{-205.71 \pm \sqrt{(205.71)^2 - 4*(-10/\$ 700)*\$ 720,000} }{2*(-10/\$ 700)} \\\\p = \frac{-205.71 \pm 195.45}{(-20/\$ 700)}[/tex]

La solución de maximo valor es:

p = (-205.71 - 195.45)/(-20/$700) = $14,040.6

Sí quieres aprender más, puedes leer.

https://brainly.com/question/8926135

PLEASE HELP, WILL GIVE BRAINLIEST.

Arjun's goal for this week is to drink no more than 100 grams of sugar from all of his beverages combined. The first table shows Arjun's plan for this week. Try to make a DIFFERENT plan to get close to 100 grams of sugar without going over.​

Answers

Arjun could drink 20 grams per day

OMG I NEED HELP BADLY RN


In which quadrant does the point (3 , 19) lie?

A.
Quadrant I

B.
Quadrant II

C.
Quadrant IV

D.
Quadrant III

Answers

Answer:

Quadrant I

Step-by-step explanation:

There are four quadrants that go like this.

Quadrant I = Top Right

Quadrant II = Top Left

Qudrant III = Bottom Left

Quadrant IV = Bottom Right

As long as you can graph an equation you just need to remember the quadrants.

The property tax on a house with an assessed value of $606,000 is $7070. Determine the property tax on a house with an assessed value of $810,000, assuming the same tax rate.


The property tax is $___?

Answers

Answer:

9450

Step-by-step explanation:

.........................


Find the unit price in dollars per ounce).
A 24-ounce can of pineapple for $1.08
PLS PLS HELPME ASAP

Answers

Answer:

$0.05 per ounce

Step-by-step explanation:

To find the price in dollars per ounce, divide the price by the number of ounces.

[tex]\frac{1.08}{24}[/tex] = $0.045 per ounce = $0.05 per ounce

Which problem could the bar diagram represent

Answers

ANSWER: is there a picture for the question?

Step-by-step explanation:

what is the slope between these 2 points?
(-4,5) and (2,1)

-3/4
-2/3
3/8
-1/5

Answers

Answer:

b

Step-by-step explanation:

y2-y1/x2-x1

memorize this formula so you always know slope for 2 points given.

y is the second number in parentheses.

whichever you choose as y2 or y1, the x values will match those numbers as well.

(y2-y1) = (1-5)

(x2-x1) = (2+4)

(-4)/6

-2/3

solve pls Brainliest

Answers

Answer:

25

Step-by-step explanation:

155-180=25 degrees

Answer:

x = 25°

Step-by-step explanation:

=
Find the slope of the graph of — 4x + 2y = 10 by
rewriting the equation in slope-intercept form.

Answers

Answer:

multiply by -1

Step-by-step explanation:

Slope intercept form : y = mx + b

-4x + 2y  =  10                  Solve the equation for y

+4x        = +4x    

    2y = 4x + 10

      y = 4x/2 + 10/2           Divide all terms by 2

    multiply by -1                   Simply

What is the area of a circle with a diameter of 10cm (used 3.14)

Answers

Answer:

78.5

Step-by-step explanation:

A=[tex]pie[/tex]r^2

A=3.14 times 5^2

A=3.14 times 25

A= 78.5

Jesus Loves You!!!

78.5 is the correct answer

use the distributive law to factor.
16m + 6n

Answers

Using the distributive law to factor, the expression becomes 16m + 6n = 2(8m + 3n)

GIven three integers A, B and C, according to the distributive property;

A(B+C) = AB + BC

Given the expression 16m + 6n

First, we need to get the factors of both terms

16m = 2 * 8 * m

6n = 2 * 3 * n

From both factors, we can see that 2 is common to both of them. Hence using the distributive law to factor, the expression becomes;

16m + 6n = 2(8m + 3n)

Learn more here: https://brainly.com/question/2118428

helppppppppppp please

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The answer would be 6

Answer:

6

.......

.

...........

6846 is shared equally between 7 people how much does each person get?​

Answers

Answer:

978

explanation is a calculator

HELP ME SOLVEEEE !!!!!

Answers

Answer:

y=2

Step-by-step explanation:

y+7=9(y-1)

y+7=9y-9

y-9y=-9-7

-8y=-16

y=2

>> Answer

_________

[tex] \: [/tex]

[tex] \frac{1}{3} (y + 7) = 3(y - 1)[/tex]

[tex] \frac{y + 7}3 = 3(y - 1) [/tex]

[tex]y + 7 = 9(y - 1)[/tex]

[tex]y + 7 = 9y - 9[/tex]

[tex]y - 9y = - 9 - 7[/tex]

[tex] - 8y = - 16[/tex]

y = 2

which quanity is proportional to 5/25

Answers

Answer:

1/5

Step-by-step explanation:

BAKERY Rolls are being prepared to go to grocery stores, Divide 72 rolls
into 2 groups so the ratio is 3 to 5,

Answers

Answer:

27:45

Step-by-step explanation:

The ratio is 3:5, so the total is 8. 72/8 is 9. 9*3 is 27, and 9*5 is 45, so the two groups consist of 27 and 45 BAKERY Rolls.

Can someone pls help me Pls

Answers

8/9 * 1/7 is 8/63 sooo yeah

Answer:

8/63

Step-by-step explanation:

(1/7)×(8/9)=8/63

yep

Which fraction has a repeating decimal as its decimal expansion?

Answers

3/11

.2727272727… the 27 just repeats forever

What is a multiplication table

Answers

Answer:

a table of products of two factors especially the integers 1 to 12 have a nice day

Step-by-step explanation:

:)

This is a multiplication table, it’s on the back of every composition book. It’s hard for me to explain but it shows you the answer of what the number you’re trying to multiple will come out to. For example the 3 on the top and the 5 on the left comes out the 15

what is the greatest common factor of 15v to 3rd power and 12v to the 2nd power?

Answers

Answer:

Step-by-step explanation:

the great common factor is 3 =5v over 4 in a fraction

can anyone heelp me pls

Answers

Answer:

I think it's b.

Step-by-step explanation:

b. ,. ....

The area of the table should be
10 ft2. You want the length of the table to be 1 ft shorter than twice its width.
What should the dimensions of the table be?

Answers

Answer: width : 2.5 ft. and length : 4 ft.

Step-by-step explanation:

The area = W × L

[tex]10=W(2W-1)[/tex]

[tex]10=2W^{2} -W[/tex]

[tex]0 = 2W^{2}-W-10[/tex]

[tex]0=(2W-5)(W+2)[/tex]

W = 2.5 and -2

You can't use -2 so

[tex]L = 2(2.5)-1[/tex]

[tex]L = 4[/tex]

please give me a brainliest answer

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