1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
barxatty [35]
2 years ago
14

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, a

nd 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]).
Mathematics
1 answer:
bekas [8.4K]2 years ago
7 0

9514 1404 393

Answer:

  • (c1, c2, c3) = (-2t, 4t, t) . . . . for any value of t
  • NOT 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.)

You might be interested in
The formula that describes an object's motion is given by s=ut+1/2at^2, where s is the distance traveled, u is the initial veloc
victus00 [196]
None of the offered choices is correct.

The correct equation is
.. a = (2s -2ut)/t^2 . . . . . . . . parentheses are required
4 0
3 years ago
An electronics store makes a profit of $72 for every standard CD player sold and $90 for every portable CD sold. the managers ta
Alisiya [41]

s -> no: of standard CD players sold

p -> no: of portable CD players sold.

Profit Per Standard CD player=72$

Profit per Portable CD player =90$

Target Amount =360$

<em>I</em><em>n</em><em> </em><em>short</em><em>:</em><em> </em><em>The</em><em> </em><em>combined</em><em> </em><em>sales</em><em> </em><em>of</em><em> </em><em>Both</em><em> </em><em>the</em><em> </em><em>CD</em><em> </em><em>player</em><em>'s</em><em> </em><em>must</em><em> </em><em>exceed</em><em> </em><em>or</em><em> </em><em>atleast</em><em> </em><em>become</em><em> </em><em>equal</em><em> </em><em>to</em><em> </em><em>3</em><em>6</em><em>0</em><em>$</em><em> </em><em>to</em><em> </em><em>a</em><em>c</em><em>q</em><em>u</em><em>i</em><em>r</em><em>e</em><em> </em><em>the</em><em> </em><em>target</em><em>.</em>

<em>Thus</em><em>;</em><em> </em><em>the</em><em> </em><em>inequality</em><em> </em><em>can</em><em> </em><em>be</em><em> </em><em>stated</em><em> </em><em>as</em><em>:</em>

<em> </em><em> </em><em> </em><em> </em><em> </em><em>7</em><em>2</em><em>(</em><em>s</em><em>)</em><em> </em><em>+</em><em> </em><em>9</em><em>0</em><em>(</em><em>p</em><em>)</em><em> </em><em>≥</em><em>3</em><em>6</em><em>0</em>

<em>-</em><em>></em><em> </em><em>3</em><em>6</em><em>(</em><em>s</em><em>)</em><em> </em><em>+</em><em> </em><em>4</em><em>5</em><em>(</em><em>p</em><em>)</em><em> </em><em>≥</em><em>1</em><em>8</em><em>0</em>

<em>-</em><em>></em><em> </em><em>1</em><em>2</em><em>(</em><em>s</em><em>)</em><em> </em><em>+</em><em>1</em><em>5</em><em>(</em><em>p</em><em>)</em><em> </em><em>≥</em><em> </em><em>9</em><em>0</em>

<em> </em><em> </em><u><em>_</em><em>_</em><em>_</em><em>_</em><em>_</em><em>_</em><em>_</em><em>_</em><em>_</em><em>_</em><em>_</em><em>_</em><em>_</em><em>_</em><em>_</em></u>

<em>-</em><em>></em><u>|<em> </em><em>4</em><em>(</em><em>s</em><em>)</em><em> </em><em>+</em><em> </em><em>5</em><em>(</em><em>p</em><em>)</em><em> </em><em>≥</em><em> </em><em>3</em><em>0</em><em> </em><em> </em><em> </em><em> </em>|</u>

<em><u>Hope it helps...</u></em>

<em><u>Hope it helps...Regards;</u></em>

<em><u>Hope it helps...Regards;Leukonov/Olegion.</u></em>

8 0
3 years ago
the first few steps in solving the quadratic equation 5x2 27x = 14 − 13x by completing the square are shown. 5x2 27x = 14 − 13x
Artist 52 [7]
The best step to do next is to add 80 to both sides of equation:
5 ( x² + 8 x ) + 80 = 14 + 80
and since  80 =  5 · 16
5 ( x² + 8 x + 16 ) = 94   Answer : B ) 
After that we will continue like this:
5 ( x + 4 )² = 94 
( x + 4 )² = 18.8 ... etc
4 0
3 years ago
Read 2 more answers
What is the unit rate per year?<br>​
Darina [25.2K]

Answer:

3.6

Step-by-step explanation:

divide 36 by 10 be sure it's the easiest part

7 0
3 years ago
Read 2 more answers
I need the measure of angle 3
blsea [12.9K]

Answer:

79°

Step-by-step explanation:

Since, 101° and angle 3 are interior angles falling on the same side of transversal.

Therefore,

101 \degree + m \angle \: 3 = 180 \degree \\  \\  m \angle \: 3 = 180 \degree  -101 \degree  \\  \\ m \angle \: 3 = 79 \degree

7 0
2 years ago
Other questions:
  • The vampires play 20 games. The team won 4 more games then it lost. How many games did the vampires won
    12·2 answers
  • Arithmetic series help!!!!
    13·1 answer
  • Solve -27=19-2x for x
    6·1 answer
  • To obtain the length of an arc, what fraction is multiplied by the circumference of a circle (C = 2πr)?
    7·2 answers
  • Domain of f(x)= x+5/(x^2-1)
    14·1 answer
  • What’s this answer ? Please help!
    8·1 answer
  • Compare the two expressions
    7·1 answer
  • Solve 0= 2t^3-21t^2+ 40t
    13·1 answer
  • Please answer fast please
    15·1 answer
  • PLS help ASAP I DONT have time to answer this, it also detects if it’s right or wrong.
    7·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!