10.1 f and g are linearly independent using the Wronskian
10.2 f₁ and g₁ belong to W
10.3 {f₁,g₁} is also linearly independent.
10.1 To show that f and g are linearly independent, we can calculate their Wronskian, which is the determinant of the matrix [f g; f' g'], where f' and g' represent the derivatives of f and g with respect to x. If the Wronskian is non-zero for all x, then f and g are linearly independent. In this case, the Wronskian of f and g is sin(x)cos(x) - cos(x)sin(x) = 0. Since the Wronskian is identically zero, f and g are linearly independent.
10.2 To show that f₁ and g₁ belong to W, we need to demonstrate that they can be expressed as linear combinations of f and g. Using the trigonometric identities, we have f₁(x) = sin(x + a) = sin(x)cos(a) + cos(x)sin(a), and g₁(x) = cos(x + a) = cos(x)cos(a) - sin(x)sin(a). These expressions show that f₁ and g₁ are linear combinations of f and g, with coefficients cos(a) and sin(a).
10.3 To prove that {f₁,g₁} is linearly independent, we can use the Wronskian again. Calculate the Wronskian of f₁ and g₁, which is (cos(x)cos(a) - sin(x)sin(a))(cos(x) - sin(a)) - (sin(x)cos(a) + cos(x)sin(a))(sin(x) - cos(a)). Simplifying this expression, we get cos²(x) - sin²(x) - cos²(a) + sin²(a), which is non-zero for all x. Therefore, the Wronskian is non-zero, indicating that f₁ and g₁ are linearly independent.
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PLEASE HELP ME FAST IM CONFUSED!
Answer: (-2,1/2) (0,0) (2,1) (4,2)
Step-by-step explanation:
plug in the number in place of X
find the coordinates of point P along the directed line segment ST so that SP to PT is the given ratio. 1. S(6,4), T(-4, -8); 1 to 3 2. S(-6, 7), 7(9,25); 2 to 3
First, we find the length of ST and multiply it by the given ratio to get the length of SP. Then, we use the midpoint formula to find the coordinates of point P.1. S(6,4), T(-4, -8); 1 to 3
Let P be the point on the directed line segment ST such that SP : PT = 1 : 3. We need to find the coordinates of P.Step 1: Find the length of ST.
Let S(x1, y1) and T(x2, y2) be the coordinates of S and T respectively. Then we can use the distance formula to find the length of ST.
d(ST) = √[(x2 - x1)² + (y2 - y1)²]
d(ST) = √[(-4 - 6)² + (-8 - 4)²]
d(ST) = √(100 + 144)
d(ST) = √244d(ST) = 2√61
Find the length of SP.We know that
SP : PT = 1 : 3. Therefore,
SP = (1/4)ST.SP = (1/4)(2√61)SP = (1/2)√61
Use the midpoint formula to find the coordinates of P.Let (x, y) be the coordinates of P. Then we can use the midpoint formula to find
(x, y).x = (1/4)(2x2 + 2x1) = (1/4)(2(-4) + 2(6)) = 1y = (1/4)(2y2 + 2y1) = (1/4)(2(-8) + 2(4)) = -1
The coordinates of P are (1, -1).
Once we have the length of SP, we can use the midpoint formula to find the coordinates of P. In the first example, we found that the coordinates of P are (1, -1) if SP : PT = 1 : 3. In the second example, we will use the same method to find the coordinates of P when S(-6, 7) and T(9, 25) are the given points, and
SP : PT = 2 : 3.
We will also find the length of ST, the length of SP, and the coordinates of P.2. S(-6, 7), T(9, 25); 2 to 3Let P be the point on the directed line segment ST such that SP : PT = 2 : 3. We need to find the coordinates of P.Step 1: Find the length of ST.Let S(x1, y1) and T(x2, y2) be the coordinates of S and T respectively. Then we can use the distance formula to find the length of ST.
d(ST) = √[(x2 - x1)² + (y2 - y1)²]
d(ST) = √[(9 - (-6))² + (25 - 7)²]
d(ST) = √(225 + 324)
d(ST) = 3√61
We know that SP : PT = 2 : 3. Therefore,
SP = (2/5)ST.SP = (2/5)(3√61)SP = (6/5)√61
Use the midpoint formula to find the coordinates of P.Let (x, y) be the coordinates of P. Then we can use the midpoint formula to find (x, y).x = (2/5)(x2 + x1) = (2/5)(9 + (-6)) = -3/5 y = (2/5)(y2 + y1) = (2/5)(25 + 7) = 16
The coordinates of P are (-3/5, 16).
To find the coordinates of point P along the directed line segment ST so that SP to PT is the given ratio, we need to find the length of ST and multiply it by the given ratio to get the length of SP. Then, we use the midpoint formula to find the coordinates of point P.
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Janey is using a recipe that calls for two Tablespoons of oil for every every 4 tablespoons create a ratio table to determine how tsp of oil she would need if she used 10 water 
in the diagram of movie theater seats, the incline of the floor, f, is parallel to the seats, s.
if m<1= 60, what is c?
if m<1= 68, what is y?
HELPPP PLEASEEE
Answer:
16. x = 40
17. y = 15
Step-by-step explanation:
16. Given that f is parallel to s, therefore by the corresponding theorem and linear pair theorem, <1 + 3x = 180°
60° + 3x = 180° (substitution)
3x = 180° - 60° (Subtraction property of equality)
3x = 120°
x = 120/3 (division property of equality)
x = 40
17. Since f and s are parallel, therefore,
m<1 = (5y - 7)° (alternate interior angles are congruent)
68° = 5y - 7 (substitution)
68 + 7 = 5y (addition property of equality)
75 = 5y
75/5 = y (division property of equality)
15 = y
The product of complex numbers (4,3) and(5,-6) is?
Answer:
The answer of this is (38,9)
Step-by-step explanation:
Answer:
38,9
Step-by-step explanation:
A plumber has a 10' piece of PVC pipe how many 9/5 foot pieces can be cut from the 10' piece
Answer:
5.55555556
Step-by-step explanation:
Hope this helps!
which of the following statements is true? question 4 options: the population mean and a sample mean for a sample selected from the population will usually be different values. the mean of the population will generally be larger than the mean of the sample selected from that population. the population mean and sample mean will always be identical. the mean of a population will always be larger than the population standard deviation.
The statement that is true among the given options is: "The population mean and a sample mean for a sample selected from the population will usually be different values." This statement accurately describes the relationship between the population mean and a sample mean.
In statistics, the population mean refers to the average value of a variable in the entire population, while a sample mean represents the average value of the variable calculated from a subset of the population (a sample). It is important to note that unless the sample is the entire population itself, the sample mean will typically differ from the population mean.
The reason for this discrepancy is due to sampling variability. When we select a sample from a population, we are observing a smaller subset of the whole, which introduces some level of randomness or uncertainty. Different samples from the same population may yield slightly different values for the sample mean.
However, as the sample size increases, the sample mean tends to converge towards the population mean.
In summary, the population mean and sample mean are generally not identical, and their values are likely to differ due to sampling variability. The sample mean provides an estimate of the population mean, and the accuracy of this estimate improves with larger sample sizes.
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Online purchasing an online video store charges $24 for each DVD shipping cost $4per order find the cost of 3 DVDs
Answer:
$76.00
Step-by-step explanation:
$24+$24+24 (3 DVDs) + $4.00 per shipping per order. = $76.00
Answer:
$76
Step-by-step explanation:
We are buying 3 DVD's at 24 dollars each
3 * 24 = 72
There is only 1 shipping charge
4
Add the costs together
72+4 = 76
The cost is 76 dollars
Find the image of A(3,7) translated using the rule (x,y)->(x-2,y+1)
Answer:
(1, 8)
Step-by-step explanation:
How can you tell if three positive numbers form a
Pythagorean triple?
Answer:
Since a Pythagorean triple is three positive integers a, b, and c such that (a^2)+(b^2)=(c^2), where a and b are the two legs, and c is the hypotenuse, first take the sum of the squares of the two legs and make an estimate. For example, 3, 4, and 5 is a Pythagorean triple since 9+16=25.
Solve for x.
−2(x+13)+9x=4
Enter your answer as a fraction in simplest form in the box.
Answer:
30/7
Step-by-step explanation:
What is the reason for each step in the solution of the equation?
-62 +72 +14=3
help plz hurry Which sentence from "Object Lesson, Part 2" most likely causes the reader to feel nervous??
He even emptied Louise's three pots of geraniums and sifted the earth.
The 41 boys and girls were buzzing and giggling now.
Feverishly he went through the remaining dollar-sized strips of comic paper.
This strip had been cut from the top of the comic sheet.
C. Feverishly he went through the remaining strips of paper
Answer:
C
Step-by-step explanation:
The key word "Feverishly", helps me determine the answer. (Also, I just took the test)
a balloon at standard pressure is placed in a cool oven at 20 degrees celsius. the balloon is removed from the oven when the internal temperature rises to 30 degrees celcius. if the volume of the balloon when It is removed from the oven is 3.75 L what is the initial volume of the balloon?
j4jrjrjttjtjtj
Step-by-step explanation:
jeejejehnnrnrnffjfjfc
Solve 2y = 3y - 20
A.20
B.-20
C.-4
D.4
Answer:
D. 4
Step-by-step explanation:
The sum of one interior and one exterior angle of a triangle is degrees.
Answer:
the oppostite
Step-by-step explanation:
Plaza Corporation purchased 70 percent of Square Company's voting common stock on January 1, 20X5, for $291,200. On that date, the noncontrolling interest had a fair value of $124,800 and the book value of Square's net assets was $380,000. The book values and fair values of Square's assets and liabilities were equal except for land that had a fair value $14,000 higher than book value. The amount attributed to goodwill as a result of the acquisition is not amortized and
In a purchase acquisition, the purchase price is allocated to the fair value of the net assets acquired. In this case, Plaza Corporation has purchased 70% of Square Company's voting common stock.
Since the noncontrolling interest in Square is 30% and has a fair value of $124,800, the implied fair value of Square Company is $178,285 ($291,200 - $124,800).The difference between the purchase price and the fair value of net assets acquired represents goodwill. The fair value of net assets acquired is $380,000 + $14,000 = $394,000. Therefore, the goodwill is $116,485 ($178,285 - $394,000).The goodwill is not amortized but is subject to impairment testing at least annually. The goodwill impairment test compares the fair value of the reporting unit, in this case, Square Company, to the carrying amount of the reporting unit, including the goodwill. If the fair value of the reporting unit is less than its carrying amount, an impairment loss is recognized, which reduces the carrying amount of the goodwill.
Based on the provided information, the amount attributed to goodwill as a result of the acquisition is $116,485. It is not amortized but is subject to impairment testing at least annually.
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Evaluate
18/29
×
4/3
Give your answer as a fraction in its simplest form.
Answer:
The answer is 24/ 29
Anthony bought a rug for his office. He made a scale drawing of the office using a scale of 1 in = 4 ft.
What is the area of the office floor not covered by the rug?
Explain and illustrate the difference between a term and a coefficient
Answer:Term is something that is being added together. Factor is something that is being multiplied together. Coefficient is a number that is being multiplied by the variable.
hope this helpppppppyuuuuuuuuu
Step-by-step explanation:
Consider the sequence 18, 15, 12, 9, 6, 3, . . . . What is f(5)?
Answer:
It is 6 because
Step-by-step explanation:
When you see 18 to go 15 its going 3 times down and when you count to 6 its the 5th number so I think it is 6.
F(5)=6
what is the LEAST possible integer value and the greatest
Answer:
hey mate I guess ur question is incomplete......after greatest what is it? plz check
Answer:
Step-by-step explanation:
-4 < x < 9
What is the right answer
The correct option is the first one, the leading coefficients are opposites.
What can we say about the leading coefficients?A general quadratic function is written as:
y = ax² + bx + c
The leading coefficient is a.
Here we have two quadratics, these are:
f(x) = ax² + bx + c
g(x) = kx² + jx + n
Notice that in the graph of (f + g)(x), we have a line instead of a quadratic, so the quadratic term is zero, this means that:
a + k = 0
a = -k
Then the leading coefficients are opposites, the correct option is the first one.
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Pet stores selling dogs for 140 and cats for $70 yesterday the store sold 28 pets and I made 3360 how many cats were sold yesterday
Answer:
8
Step-by-step explanation:
8 × $70 = $560
20 × $140= $2800
$560 + $2800 = $3360
Complete the steps to find the value of x
72°
(7x + 24)°
1) Where is the midpoint of , when A (6, 7) and B (-9, -5)?
Answer:
(−1.5,1)
Step-by-step explanation:
Finding the distance, midpoint, slope, equation and the x y-intercepts of a line passing between the two points p1 (6,7) and p2 (-9,-5)
The distance (d) between two points (x1,y1) and (x2,y2) is given by the formula
d = √ ((X2-X1)2+(Y2-Y1)2)
d = √ (-9-6)2+(-5-7)2
d = √ ((-15)2+(-12)2)
d = √ (225+144)
d = √ 369
The distance between the points is 19.2093727122985
The midpoint of two points is given by the formula
Midpoint= ((X1+X2)/2,(Y1+Y2)/2)
Find the x value of the midpoint
Xm=(X1+X2)/2
Xm=(6+-9)/2=-1.5
Find the Y value of the midpoint
Ym=(Y1+Y2)/2
Ym=(7+-5)/2=1
The midpoint is: (-1.5,1)
Answer:
(-1.5,1)
Step-by-step explanation:
the midpoint between 6 and -9 is -1.5
the midpoint between 7 and -5 is 1
(-1.5,1)
Find the first 4 terms, a10, Jamini an n≥3 n-2' and a₁5 of the sequence with the following nth term.
The sequence with the given nth term is n-2. The first four terms of the sequence are a₁ = -1, a₂ = 0, a₃ = 1, and a₄ = 2. The term a₁₀ is equal to 8, a₉ is equal to 7, and a₁₅ is equal to 13.
The given nth term of the sequence is n-2, which means that each term is obtained by subtracting 2 from the corresponding value of n.
To find the first four terms of the sequence, we substitute the values of n from 1 to 4 into the nth term expression. Thus, we have a₁ = 1-2 = -1, a₂ = 2-2 = 0, a₃ = 3-2 = 1, and a₄ = 4-2 = 2.
To find a specific term, we substitute the corresponding value of n into the nth term expression. For example, a₁₀ = 10-2 = 8, a₉ = 9-2 = 7, and a₁₅ = 15-2 = 13.
In summary, the first four terms of the sequence are a₁ = -1, a₂ = 0, a₃ = 1, and a₄ = 2. The term a₁₀ is equal to 8, a₉ is equal to 7, and a₁₅ is equal to 13.
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anybody help me? please
Answer:
0 because we can't have Repetitious x in function.
Brenda went to the store with her dad to buy snacks. They bought a box of 16 snack-size bags of chips for $7.84 and a box of 24 snack-size bags of pretzels for $12.48. How much more do pretzels cost per bag than chips?
Answer:
subtracting 7.84 from 12.48 will give 15.44 this is equal to 12 packets if you dived 12 by the price of 15.44 you will get your answer you may need to round
$0.03 pretzels cost more than cost of bag of chips.
What is Unitary Method?It is a method where we find the value of a single unit from the value of multiple units and the value of multiple units from the value of a single unit.
Steps to Use Unitary Method
First, let us make a note of the information we have. There are 5 ice-creams. 5 ice-creams cost $125.
Step 1: Let’s find the cost of 1 ice cream. In order to do that, divide the total cost of ice-creams by the total number of ice-creams. The cost of 1 ice-cream = Total cost of ice-creams/Total number of ice-creams = 125/5 = 25. Therefore, the cost of 1 ice cream is $25.
Step 2: To find the cost of 3 ice-creams, multiply the cost of 1 ice cream by the number of ice-creams. The cost of 3 ice-creams is cost of 1 ice-cream × number of ice-creams = 25 × 3 = $75. Finally, we have the cost of 3 ice-creams i.e. $75.
Given:
price of 16 snack- size bags of chips = 7.84
Cost of 1 bag of chip = 7.84 /16
= $0.49
and, price of 24 snack-size bags of pretzels = 12.48
Cost of 1 snack-size bags of pretzels = 12.48 / 24
= 0.52
Hence, by $0.03 pretzels cost more than cost of bag of chips.
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6. x2= 1
—
100
Thank you (:
Answer:
Its asking what x 2=1 it would be
Step-by-step explanation: 0.5 or 1/2
