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notka56 [123]
2 years ago
15

Determine whether the given set of functions is linearly independent on the interval (−[infinity], [infinity]). f1(x) = x, f2(x)

= x2, f3(x) = 6x − 2x2 linearly dependent linearly independent
Mathematics
1 answer:
ziro4ka [17]2 years ago
3 0

The given set of functions are not linearly independent.

Given,

f_{1} (x) = x\\f_{2} (x) = x^{2} \\f_{3} (x) = 6x-2x^{2}

We need,

c_{1} f_{1} (x)+c_{2} f_{2} (x)+c_{3} f_{3}(x)=0

Substituting the values in equation we get,

c_{1} x+c_{2} x^{2} +c_{3} (6x-2x^{2} )=0\\

Computing the equation we get,

c_{1} x+c_{2} x^{2} +c_{3} 6x-c_{3} 2x^{2}=0

(c_{1} +6c_{3} )x+(c_{2} -2c_{3} x^{2} =0

This resolves to two equations

(c_{1} +6c_{3})x =0\\(c_{2} -2c_{3} )x^{2} =0

These will have an infinite set of solutions:

c_{1} =-6c_{3} \\c_{2} =2c_{3}

Two functions are said to be linearly independent if neither function is a constant multiple of the other.

Here, it is clear that the given functions are not linearly independent.

Learn more about linearly dependent or independent functions here:brainly.com/question/18331568

#SPJ4

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A spinner has 10 equally sized sections, 2 of which are gray and 8 of which are blue. The spinner is spun twice. What is the pro
ludmilkaskok [199]

The probability of getting grey: 2/10

The probability of getting blue: 8/10

The probability of getting blue then grey:

8/10 x 2/10

Answer 4/5

6 0
3 years ago
Take a square sheet of paper 20 cm by 20 cm, cut identical squares from each corner, and fold up the flaps to make a box (withou
iris [78.8K]

The maximum possible volume of this type of box that can be made from a 20 cm by 20 cm square of paper is 512cm³.

<h3>How to calculate the volume?</h3>

From the information, when the side of 1cm are cut, this will become an open box. The volume will be:

= 18 × 18 × 1

= 324cm³

Also, when 2cm is cut, the volume will be:

= 16 × 16 × 2

= 512cm³

Learn more about volume on:

brainly.com/question/1972490

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3 0
2 years ago
tina has 50 coins, all dimes and quarters. the value of the coins is $7.10. write a system of equations to determine how many di
Sliva [168]

Answer:

A) D + Q = 50

B) .10D + .25Q = 7.10

We multiply A) by -.10

A) -.10D - .10Q = -5 then adding this to B)

B) .10D + .25Q = 7.10

.15Q = 2.10

Quarters = 14 = 3.50

Dimes = 36 = 3.60


Step-by-step explanation:


7 0
3 years ago
PLEASE HELP ILL GIVE BRAINLIEST!!!! I AM STUMPED AS I HAVE NOT PAYED ANY ATTENTION IN CLASS PLEASE HELP ME!!!!
Svetlanka [38]

Answer:

y=\frac{-2}{3} x-15

Step-by-step explanation:

First draw a line. I will put it in an attachment so you can see the line.

Now choose to points on the line to use the slope formula.

(0,15) and (3,13).

Slope formula: \frac{y2-y1}{x2-x1}

Plug in the information needed using the two points chosen.

\frac{13-15}{3-0}=\frac{-2}{3}

The slope is \frac{-2}{3}.

Now use point-slope formula.

Point-slope formula: y-y1=m(x-x1)

y-15=\frac{-2}{3}(x-0)

y-15=\frac{-2}{3}x-0

Subtract 15 from both sides.

y=\frac{-2}{3}x-15

Hope this helps!

If not, I am sorry.

5 0
2 years ago
Can I get some help please? Show your work <br><br> Thanks!
grigory [225]
Hey Gary :) Nice to see you around

For this question, we want to use logarithmic rules to write the expression as a single logarithm.
Using the rule log_{b} ( M^{k} ) = k *  log_{b} M , we can simplify 
3log_{b} q to log_{b} ( q^{3} ) . We can also simplify 6log_{b}(v) to log_{b}( v^{6}) .

So, we have log_{b} ( q^{3} ) + log_{b}( v^{6}).

Another logarithmic rule is:
log_{b}(M*N) =  log_{b} M +  log_{b} N&#10;

Using this rule, we can use the logs we have calculated and change them to:
log_{b}( q^{3}  v^{6})

This matches answer choice A.

Hope this helps! Feel free to contact me with any questions.


4 0
3 years ago
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