The solutions {sin(x), sin(x) - cos(x)} are linearly Independent since the linear combination equals zero only when all the coefficients are zero
To test the given set of solutions {sin(x), sin(x) - cos(x)} for linear independence, we can check if the linear combination of the solutions equals the zero vector only when all the coefficients are zero.
Let's consider the linear combination:
c1sin(x) + c2(sin(x) - cos(x)) = 0
Expanding this equation:
c1sin(x) + c2sin(x) - c2*cos(x) = 0
Rearranging terms:
sin(x)*(c1 + c2) - cos(x)*c2 = 0
This equation holds for all x if and only if both the coefficients of sin(x) and cos(x) are zero.
From the equation, we have:
c1 + c2 = 0
-c2 = 0
Solving this system of equations, we find that c1 = 0 and c2 = 0. This means that the only solution to the linear combination is the trivial solution, where all the coefficients are zero
Therefore, the solutions {sin(x), sin(x) - cos(x)} are linearly independent since the linear combination equals zero only when all the coefficients are zero
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The only solution to the linear combination being equal to zero is when both coefficients are zero. Hence, the given set of solutions {sin(x), sin(x) − cos(x)} is linearly independent.
To test the given set of solutions for linear independence, we need to check whether the linear combination of these solutions equals zero only when all coefficients are zero.
Let's write the linear combination of the given solutions:
c1 sin(x) + c2 (sin(x) - cos(x))
We need to find whether there exist non-zero coefficients c1 and c2 such that this linear combination equals zero for all x.
If we simplify this expression, we get:
(c1 + c2) sin(x) - c2 cos(x) = 0
For this equation to hold for all x, we must have:
c1 + c2 = 0 and c2 = 0
The second equation implies that c2 must be zero. Substituting this into the first equation, we get:
c1 = 0
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5 years ago, john was half the age he will be in 8 years. How old is he?
Answer: John is now 18 years old
Step-by-step explanation:
Let, John's age is now x years.
5 years ago, he was (x - 5) years old
In 8 years, he will be (x + 8) years old
By the given condition,
x - 5 = 1/2 (x + 8)
⇒ 2 (x - 5) = x + 8
⇒ 2x - 10 = x + 8
⇒ 2x - x = 8 + 10
⇒ x = 18
Two learners are planning to make baskets to raise money for the honors society at their school. Marcia will make baskets out of palms. Norma plans to make baskets out of pine straw. Together, they have $100 to spend on supplies.
The palm baskets cost $4 to make and will sell for $20.
The pine straw baskets cost $3 to make and will sell for $17.
The learners agree that they will each make at least 14 items. Let x represent the number of palm baskets and let y represent the number of pine straw baskets.
Answer:
3
Step-by-step explanation:
Pretty sure it is the third but sorry if im incorrect
yo 20 points! pls help me out
Answer:
the top one would be -40x+24, bottom one is x=12
Step-by-step explanation:
uwu
Answer:
a. -40x + 24
b. x = 4
Step-by-step explanation:
-8 * 5x = 40x, -8 * -3 = 24
-5 * -x = 5x
-5 * 4 = -20
40 - 20 = 20
20/5 = 4
The shadows of two vertical poles were measured at the same time to be 6m and 15m long. If the first pole is 8cm long, find the height of the second pole
Answer:
20 cm
Step-by-step explanation:
Shadow of vertical poles : 6m ; 15m
Length of poles : 8cm ; h
8cm long pole = shadow length, 6m
h cm long pole = shadow length, 15 m
Using cross multiplication :
8cm * 15 m = h cm * 6m
120 = 6h
h = 120 / 6
h = 20 cm
Height of second pole = 20cm
I need help with math here is the problem 3(2x+6)
Answer:
6x+18
Step-by-step explanation:
Step-by-step explanation:
Distribute the 3 to the 2X and 6:
3 x 2X + 6 x 3 = (3 x 2)X + 18 = 6X +18
Answer the photo below thanks
Answer:
C. 36 degrees
Step-by-step explanation:
90 + 54 = 144
180 - 144 = 36
you were correct
Please help me with this
Answer:
1) equation is set up to determine when the cost of printing at home is the same as the cost of printing at the office
2) p = 500 means that, at printing 500 pages, the costs of home versus office printing are the same
Step-by-step explanation:
Answer:
1) No, it does not represent the story.
2) It represents the number of pages.
Step-By-Step Explanation:
1) It has nothing to do with the story.
2) It says: Let p represent the number of pages
Divide 600 kg into 2 boxes so that one box has twice as much in it as the other box. How
much is in the heavier box?
Help please
Answer:
200 box 1 / 400 box 2
box 2 Step-by-step explanation:
200 + 400 = 600
Answer:
Hello asuna here
600 would be your answer
Step-by-step explanation:
Hope this helps
Need help!!!! ahaaaaaa
Answer:
Not sure if I am right but this is what I did. I have attached a picture of me solving the equation. Hope this helps, thank you !!
Answer:
Step-by-step explanation:
A,B and D
Four students are reading books with different numbers of pages. The table shows the number of pages each student has read. Drag each name to order the students from the lowest percentage of their book read to the highest percentage of their book read. Pages Read Total Number of Pages Elliot 105 175 = Elliot Frankie 165 300 Hayden 88 220 = Frankie Ruth 117 260 = Hayden = Ruth
Answer:
i think is 434.54
Step-by-step explanation:
Answer:
434.54
Step-by-step explanation:
Solve for x . Round to the nearest 100th if needed.
11/ x + 18 = 34
Answer:
x = 0.69
Step-by-step explanation:
11/x + 18 = 34
11/x = 16
11 = 16x
x = 0.6875 = 0.69
Whos your favorite character from Miraculous Ladybug?! mines Alya and of course cat noir he kinda cute
Answer:
CAT NOIR
He's cool and my cousin's fav characters LOL
Step-by-step explanation:
um, he's cool i guess?
Answer:
I like Mari and Luca bc he is rlly cute for me
6 Work out the sizes of the angles labelled rº, sº and tº.
Plzzzz help I suck at geometry
Answer:
t = 30
s = 25
r = 55
Step-by-step explanation:
Let's begin by r
r is angle in quadlitral shape, so the sum of the interior angles = 360
r = 360 - (95 +100+110) = 55
Then Now it's time for ( t )
Look at the triangle whose angles are r, 95 and t. The sum of the measures of the interior angles of triangle is 180
so t = 180 - ( 95 + r) = 180 - (95 + 55) = 30
Similarly, look at the triangle whose angles are r, s and 100
s = 180 - (100 + r) = 180 - (100 + 55) = 25
I hope you find this helpful! If you have any questions, please feel free to ask them in the comments
Help me plsssssssssssssssssssssssssssssssssss
Answer:
One inch would represent 100 miles
Answer: 1 inch is 100 miles
Step-by-step explanation:
1/4 times 4 is 1 right so 25*4=100
What is the answer to 10x2x5%20
Answer:
ITS 0
Step-by-step explanation:
3. Use distributive property to simplify
a. (-6) * [(-12) + (25)]
C. (+6) * [(-17) + (+28)]
e. (+7) * [(-12) – (+6)]
Solve this answer with solution please
Answer:
see the answersStep-by-step explanation:
to understand thisyou need to know about:PEMDAStips and formulas:orders of PEMDAS:
parenthesesexponentmultiplication ordivisionaddition orsubstractionleft to rightlet's solve:a)
remove first parentheses and add: -6×[-12+26] =-6×[14]remove third parentheses and multiply:-6×14=-84c)
remove first parentheses and add:(6)×[-17+28]=6×[11]remove third parentheses and multiply: 6×11=66e)
remove first parentheses and substract:7×[-12-(6)]=7×[-12+(-6)]=7×[-18] multiply:7×[-18]=-126please simplify √16bx⁴
Answer: 4bx^2
Step-by-step explanation:
Answer:
Hey there!
I got the answer
4bx^4
Step-by-step explanation:
All you have to do is simplify the radicand up into a product of known factors , assuming positive real numbers.
please help I have an hour to complete
Answer:
proportional
:)
need help to find X
thank you
Answer:
121
Step-by-step explanation:
Answer:
63.33 or 190/3
Step-by-step explanation:
1. vertical opposite angles are equal
2. corresponding angles some up to 180°
=> 3x - 20 + 10 = 180
=> 3x = 180+10
=> 3x = 190
=> x = 190/3
=> x = 63.333333333333333
Ron purchases $32,000 worth of stock on his brokers advice and pays his broker a 1.25% broker fee. How much did he pay his broker! Show work please !!
Graph the image of rectangle EFGH after a reflection over the line x= –1
Answer:
G (1,7)
H (2,7)
F (1,-1)
E (2,-1)
Step-by-step explanation:
The image of rectangle EFGH after a reflection over the line x = –1 will cover the points G (1,7), H (2,7), F (1,-1), and E (2,-1).
What is a translation?The process of changing the location of the image on the coordinate system will be known as the translation. A coordinate plane is a 2D plane that is formed by the intersection of two perpendicular lines known as the x-axis and y-axis.
A coordinate system in geometry is a method for determining the positions of the points by using one or more numbers or coordinates.
Given that graph the image of rectangle EFGH after a reflection over the line x= –1. Translated image of the points is attached with the answer below. The translated points are G (1,7), H (2,7), F (1,-1), and E (2,-1).
Therefore, the image of rectangle EFGH after a reflection over the line x = –1 will cover the points G (1,7), H (2,7), F (1,-1), and E (2,-1).
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Please answer please.
Answer:
Triangles are not similar.
Step-by-step explanation:
Properties of the similarity of two triangles,
1). Corresponding angles of two triangles are equal in measure.
2). Corresponding sides of the similar triangles are proportional.
From the given triangles,
- Corresponding angles of the given triangles are not equal in measure.
- Ratios of the corresponding sides,
[tex]\frac{KM}{XY}=\frac{CM}{RY}= \frac{KC}{XR}[/tex]
[tex]\frac{53}{53}= \frac{54}{53}= \frac{64}{53}[/tex]
But these ratios are not equal.
Therefore, both the triangles are not similar.
Need help ASAP giving 55 points and a branlist
Answer:
There are 54 squares on a rubix cube
Step-by-step explanation:
each side has 9 squares, and there are 6 sides, so you multiply 9x6 wich equals 54, so your answer would be
54 squares
Hope this helps! :)
A water tank holds 1,088 gallons but is leaking at a rate of 5 gallons per week. A second water tank holds
1,360 gallons but is leaking at a rate of 9 gallons per week. After how many weeks will the amount of
water in the two tanks be the same?
The amount of water in the two tanks will be the same in
weeks.
The first tank hold 1088 - 5t gallons of water after t weeks, while the seocnd tank holds 1360 - 9t gallons after t weeks.
Both tanks hold the same amount of water when
1088 - 5t = 1360 - 9t
Solve for t :
4t = 272
t = 68
So the tanks will hold the same amount of water after 68 weeks.
PLEASE HELP ASAP! What is the slope of the line graphed below?
Answer:
6/3 simply so 2 your slope is 2
Step-by-step explanation:
7x< 21 Im on khan academy so i need help
Answer:
x< 3
7x<21
Divide each term in 7x<21 by 7.
Cancel the common factor of 7.
Divide 21 by 7.
The result can be shown in multiple forms.
Inequality Form:
x< 3
Interval Notation:
(−∞, 3)
what is the error in this polynomial x²+9=(x+3)(x+3)?
Answer:
(x + 3i)(x - 3i)
Step-by-step explanation:
Wrong statement: x² + 9 = (x + 3)(x + 3)
Correct statement: x² + 9 = x² - (3i)² = (x + 3i)(x - 3i)
Solve for a.
6a−15=72
A.12
B.27
C.14 1/2
D.9 1/2
Answer:C
Step-by-step explanation:
Help a dum person out?
Answer:
150 i think i dont really understand this question either sorryyy <3
Step-by-step explanation:
bc it has to be less than 150 but the answer also has to be more than 138 so i hope that helped more than the answer i put :)
Answer:
I think It was 123
Step-by-step explanation:
Because i try to add it all four then divide it unto 5 so it was the result but I'm not sure about my answer maybe it will help :)