. Find the general solution to
d²y/dx²= 49y. Enter your answer as an equation y = ..
Note: d²y/dx²=k^2y
Answers
The given differential equation is linear with constant coefficients,
[tex]\dfrac{d^2y}{dx^2} - 49y = 0[/tex]
with characteristic equation
[tex]r^2 - 49 = 0[/tex]
and hence characteristic roots [tex]r=\pm7[/tex]. This means the general solution to the ODE is
[tex]y = C_1 e^{7x} + C_2 e^{-7x}[/tex]
In fact, you're given the solution already,
[tex]y = C_1 e^{kx} + C_2 e^{-kx}[/tex]
and you've determined that
[tex]\dfrac{d^2y}{dx^2} = k^2 (C_1 e^{kx} + C_2 e^{-kx}) = k^2 y[/tex]
Comparing this to the given ODE, it's obvious that [tex]k=7[/tex], so you can just replace [tex]k[/tex] with 7 in the given template solution.
Related Questions
12, 3.1.52
If f(x) = x and g(x) = 2x³, find f[g(x)], and g[f(x)]
Answers
Given that [tex]f(x) = x[/tex] and [tex]g(x) = 2x^3[/tex], we have
[tex]f(g(x)) = f(2x^3) = 2x^3[/tex]
and
[tex]g(f(x)) = g(x) = 2x^3[/tex]
The function G is defined by g (X) =X^2+2
Find g(4n)
Answers
Answer:
the answer is 4gn Puig IT in
A graph titled Janelle's Trip Home. The horizontal axis shows time (minutes) and the vertical axis shows distance from her home (miles). The line shows a decrease as time increases, a constant as time increases, and then another decrease as time continues.
Based on the graph, which statement could describe Janelle’s trip home from school?
Janelle waited for the bus, rode the bus, and then walked home.
Janelle walked the opposite direction from home to the library, rode the bus, and then walked to a friend’s house.
Janelle walked home at a constant speed.
Janelle rode the bus to the bus stop, talked with a friend, and then walked home.
Answers
Janelle rode the bus to the bus stop, talked with a friend, and then walked home , Option D is the correct answer.
The missing graph is attached with the answer.
What is a Time -Distance Graph ?A graph which shows change in distance with respect to time is called Time- Distance Graph.
It is used to calculate velocity.
As in the graph we it can be seen that , The distance is decreasing at a constant speed ,
then the distance becomes constant with time
and then again decreases but with a lower rate
This means
Janelle rode the bus to the bus stop (distance to time rate is high)
talked with a friend (distance is constant with time)
and then walked home. (distance to time rate is low)
Therefore Option D is the correct answer.
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Answer:
Janelle rode the bus to the bus stop, talked with a friend, and then walked home.
Step-by-step explanation:
15. This year Lucille weighs 106 lb 13 oz. A
year ago she weighed 101 lb 12 oz. How
much has she gained in the year?
Answers
Answer:
5 lbs 1 oz
Step-by-step explanation:
This year Lucille weighs 106 lb 13 oz. A
year ago she weighed 101 lb 12 oz. How
much has she gained in the year?
16oz = 1 lb
13 oz = 13/16 = .8125
12 oz = 12/16 = 3/4 = .75
106.8125 - 101.75
106.8125
-101.7500
---------------
5.0625 =
5.0625 = 5 1/16
1/16 of a pound is 1oz
5 lbs 1 oz
A camper lights an oil lantern at 12 noon and lets it burn continuously. Once the lantern is lit, the lantern burns oil at a constant rate each hour. At 2 p.m., the amount of oil left in
the lantern is 63 ounces. At 5 p.m., the amount of oil left in the lantern is 61 ounces.
Based on the average rate of oil burning per hour, how much oil, in ounces, was in the
lantern at 12 noon?
SHOW WORK!
Answers
Answer:
09
Step-by-step explanation:
09
Unit rate is the quantity of an amount of something at a rate of one of another quantity.
The rate at which the oil burns.
1 hour = 2/3 ounce
At 12 noon = 193/3 = 64.33 ounces
At 2 pm = 63 ounces
At 5 pm = 61 ounces
The amount of oil at 12 noon is 64.33 ounces.
What is a unit rate?It is the quantity of an amount of something at a rate of one of another quantity.
In 2 hours, a man can walk for 6 miles
In 1 hour, a man will walk for 3 miles.
We have,
A camper lights an oil lantern at 12 noon and lets it burn continuously. Once the lantern is lit, the lantern burns oil at a constant rate each hour.
At 2 p.m., the amount of oil left in the lantern is 63 ounces.
At 5 p.m., the amount of oil left in the lantern is 61 ounces.
This means,
Amount of oil burnt in the lantern from 2 pm to 5 pm.
= 63 ounces - 61 ounces
= 2 ounces
Now,
3 hours = 2 ounces
2 hours = 1.33 ounces
1 hour = 0.67 ounces
Now,
The number of hours from 12 noon to 2 pm.
= 2 hours
So,
The amount of oil at 12 noon.
= 63 + 4/3
= (189 + 4) / 3
= 193/3 ounces
Thus,
The amount of oil at 12 noon is 65 ounces.
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An equation is shown below:
6(3x − 7) = 2
Which of the following correctly shows the beginning steps to solve this equation?
Step 1: 9x − 1 = 2
Step 2: 9x = 3
Step 1: 9x − 7 = 2
Step 2: 9x = 9
Step 1: 18x − 7 = 2
Step 2: 18x = 9
Step 1: 18x − 42 = 2
Step 2: 18x = 44
Answers
[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]
[tex] \texttt{Step 1: 18x − 42 = 2} [/tex][tex] \texttt{Step 2: 18x = 44 } [/tex]____________________________________
[tex] \large \tt Solution \: : [/tex]
[tex]\qquad \tt \rightarrow \: 6(3x - 7) = 2[/tex]
Step 1 -
[tex]\qquad \tt \rightarrow \: 18x - 42 = 2[/tex]
[ distributive property ]
Step 2 -
[tex]\qquad \tt \rightarrow \: 18x = 2 + 42[/tex]
[tex]\qquad \tt \rightarrow \: 18x = 44[/tex]
Answered by : ❝ AǫᴜᴀWɪᴢ ❞
Answer:
d) Step 1: 18x - 42 = 2
Step 2: 18x = 44
Step-by-step explanation:
Given equation,
→ 6(3x - 7) = 2
Now the value of x will be,
→ 6(3x - 7) = 2
→ 6(3x) - 6(7) = 2
→ 18x - 42 = 2
→ 18x = 2 + 42
→ 18x = 44
→ x = 44/18
→ [ x = 22/9 ]
Hence, value of x is 22/9.
Answer these 10 questions for 30 points. serious answers only or report and low rating
Answers
Answer:
11. always
12. always
13. always
14. never
15. never
16. always
17. always
18. sometimes
19. sometimes
20. never
Step-by-step explanation:
11. A line can be defined by at least two points
12. A plane can be defined by at least three points
13. If two planes intersect, then they form a line at the intersection.
14. If two lines intersect, then they form a point at the intersection (not a segment).
15. A line does not have any endpoints (infinite in both ways).
16. If two planes are not parallel they will always intersect.
17. If two lines are not parallel they will always intersect.
18. Two points are sometimes collinear. It depends on where they are.
19. Two points are sometimes coplanar. It depends on where they are.
20. Ray MN and NM are not the same ray because the end points are different.
Neil started a stamp collection with 12 stamps. Every week, he adds 4 more stamps to the collection. Which function f represents the relationship between the number of stamps (s) and the number of weeks (w)?
A.
s = f(w) = 12 + 4w
B.
w = f(s) = 12s + 4
C.
s = f(w) = 12 + 4s
D.
w = f(s) = 12w + s
E.
s = f(w) = s – 12
Answers
The function s = f(w) = 12 + 4w represents the relationship between the number of stamps (s) and the number of weeks (w) option (A) is correct.
What is a function?It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.
We have:
Neil started a stamp collection with 12 stamps. Every week, he adds 4 more stamps to the collection.
The number of stamps is s and the number of weeks is w.
s = f(w) = 12 + 4w
Because Every week, he adds 4 more stamps to the collection
Thus, the function s = f(w) = 12 + 4w represents the relationship between the number of stamps (s) and the number of weeks (w) option (A) is correct.
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I need this asap. Would appreciate for y’all help
Answers
Answer:
-3/2, -1
Step-by-step explanation:
Each coordinate contains one [tex]x[/tex] value and one [tex]y[/tex] value, [tex](x,y)[/tex].
If we work out the midpoint of each of these individually, it makes it much easier to find the midpoint of the line.
Let's take the [tex]x[/tex] values first. Our first [tex]x[/tex] value is -4 and our second [tex]x[/tex] value is 1. Imagine the integers between -4 and 1 laid out in a sequence:
[tex]-4, -3, -2, -1, 0, 1[/tex]
If you take the middle value of this sequence, you get the midpoint of the [tex]x[/tex] values.
In this case, the middle is between values -2 and -1, leaving us with a midpoint of -1.5. This as a fraction is [tex]-\frac{3}{2}[/tex].
Now let's look at the [tex]y[/tex] values. Our first [tex]y[/tex] value is 2 and our second [tex]y[/tex] value is -4. Again, let's imagine those numbers laid out in a sequence:
[tex]2, 1, 0, -1, -2, -3, -4[/tex]
Here, the middle of these values is -1, and this is the midpoint of the [tex]y[/tex] values.
So if we put these two values in a coordinate, we get the midpoint of the line.
In this case, we get [tex](-\frac{3}{2} ,-1)[/tex].
can someone please help me
Answers
Part 1
f(2) represents the value of y when x=2, which is 3
Part 2
We need to find the value of x that makes y=2, which is -1
i need help can someone give me answers
Answers
Answer:
Step-by-step explanation:6 type
5/25=1/5=20%
1-1/5=4/5=80%
The types of candles are 6. And the probability of a small pink candle and NOT a small pink candle will be 0.20 and 0.80, respectively
What is probability?Its fundamental concept is that someone will nearly surely occur. The proportion of positive events in comparison to the total of occurrences.
Then the probability is given as,
P = (Favorable event) / (Total event)
The table is given below.
Small Medium Large Total
White 9 3 5 17
Pink 5 2 1 8
Total 14 5 6 25
The types of candles are given as,
⇒ 2 x 3
⇒ 6
The probability of a small pink candle is as,
P = 5/25
P = 0.20
The probability of NOT a small pink candle is as,
Q = 1 - P
Q = 1 - 0.20
Q = 0.80
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Question Content Area
If fixed costs are $281,000, the unit selling price is $33, and the unit variable costs are $21, the break-even sales (units) if fixed costs are reduced by $38,400 is
a.16,173 units
b.20,217 units
c.24,260 units
d.30,325 units
Answers
The correct answer is option b which is the break-even quantity will be 20217 units.
What is the break-even point?
The point at which the company will not have any profit and loss on the products they manufactured they only get the amount they invested in manufacturing the product is called the break-even point.
Given that:-
If fixed costs are $281,000, the unit selling price is $33, and the unit variable costs are $21, the break-even sales (units) if fixed costs are reduced by $38,400.
The formula for calculating break-even quantity will be given as:-
[tex]BEQ = \dfrac{FC}{SP-VC}[/tex]
Here,
FC = Fixed cost = $281000
SP = Selling price = $33
VC = Variable cost = $21
The fixed cost is reduced by $38400 so the fixed cost now:-
FC = $281000 - $38400
FC = $242600
[tex]BEQ = \dfrac{242600}{33-21}[/tex]
BEQ = 20217 units
Therefore the correct answer is option b which is the break-even quantity will be 20217 units.
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Find all (a, b, c, d) in R4
such that the given set is orthogonal.
{(1, 2, 1, 0), (1, −1, 1, 3), (2, −1, 0, 1), (a, b, c, d)}
Answers
Answer:
[tex]\left[\begin{array}{}0&\\1&\\-2&\\1&\end{array}\right][/tex] t in R Correct option (B)
Step-by-step explanation:
Orthogonal vectors : We say that 2 vectors are orthogonal if they are perpendicular to each other. i.e. the dot product of the two vectors is zero.
Dot product : The dot product of two vectors is equal to the sum of the products of the individual components of the two vectors.
for the given vector (a, b, c, d) to be orthogonal its dot product with each vector must be 0
therefore (1, 2, 1, 0).(a, b, c, d) = 0
a + 2b+ c+ 0 = 0 -------- (i)
similarly (1, -1, 1, 3 ).(a, b, c, d) = 0
a - b + c + 3d = 0 -------- (ii)
(2, -1, 0, 1).(a, b, c, d) = 0
2a - b + 0 + d = 0 ---------- (iii)
subtracting equation (i) from (ii)
a - b + c + 3d - a - 2b - c - 0 = 0
-3b + 3d = 0
b = d
substituting b = d in (iii)
2a + b + 0 + b = 0
2a + 2b = 0
a = 0
substituting a = 0 , b = d in (i)
0 + 2d + c + 0 = 0
c = -2d
thus for any t ∈ R, vector(0, t, -2t, t) will make the given set orthogonal
the above vector can also be written as (0, 1, -2, 1)
therefor option B is correct
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Janet is fencing a triangular portion of her yard, which has measurements as shown. She needs fencing for the two sides of the yard that do not include the house. She also needs fencing for the third side of the yard, except for the portion taken up by the house.
The picture shows a rectangle touching the base of a triangle. The width of a rectangle is 100 ft. The angle of the left and right vertex of a triangle is 45 degrees. The length of the left line of a triangle is 100 ft. marked as a house
What is the approximate length of fencing she needs?
A.
441 ft
B.
273 ft
C.
341 ft
D.
241 ft
Answers
The approximate length of fencing she needs will be 41.42 feet. Then the correct option is D.
What is Geometry?It deals with the size of geometry, region, and density of the different forms both 2D and 3D.
Janet is fencing a triangular portion of her yard, which has measurements as shown.
She postulates fencing for the two sides of the yard that do not include the house.
She also requires fencing for the third side of the yard, except for the portion taken up by the house.
Then the approximate length of fencing she needs will be
Let x be the length of fencing.
Then we have
⇒ x + 100 + 100
Then we have
x = c – 100
Then the value of c is given by the Pythagoras theorem. Then we have
c² = 100² + 100²
c² = 10000 + 10000
c² = 20000
c = 141.42 ft
Then the value of x will be
x = 141.42 – 100
x = 41.2 feet ≈ 41 feet
Then we have
⇒ 41 + 100 + 100
⇒ 241
Then the correct option is D.
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5.7y-5.2=y/2.5 how to solve
Answers
5.7y-5.2=y/2.5
Add 5.2 to both sides:
5.7y = y/2.5 + 5.2
y/2.5 = 0.4y
5.7y = 0.4y + 5.2
Subtract 0.4y from both sides:
5.3y = 5.2
Divide both sides by 5.3:
y = 5.2/5.3
y = 0.98113
Answer:
y = 0.981
Step-by-step explanation:
Given expression:
5.7y-5.2=y/2.5Solution:
5.7y-5.2=0.4ySubtract 0.4y from both sides:
5.7y-5.2-0.4y=0.4y-0.4y5.3y - 5.2 = 0Add 5.2 to both sides:
5.3y-5.2+5.2 = 0+5.25.3y = 5.2Divide both sides by 5.3:
[tex] \cfrac{5.3y}{5.3} = \cfrac{5.2}{5.3} [/tex][tex]y = 0.981[/tex]Hence, y = 0.981.
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answers
[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]
[tex]\texttt{Yes, there's a local maximum at -9,} [/tex] [tex] \texttt{and it is 9} [/tex]
____________________________________
[tex] \large \tt Solution \: : [/tex]
By Observing the graph, we can easily conclude that there's a local maxima at -9
[tex] \textsf{And f(-9) = 9} [/tex]
Answered by : ❝ AǫᴜᴀWɪᴢ ❞
d) Suppose you pick one marble from the bag at random. Find the expected value of its number.
(c) Suppose you pick 9 marbles from the bag at random with replacement. Find the probability that you pick at least one purple marble.
Answers
C) The probability that you pick at least one purple marble is 98%.
ProbabilityThe question is incomplete, since the number of marbles of each color in the bag is missing: 3 blue, 5 green, and 2 purple marbles.
Now, to answer the questions, the following calculations must be done:
C) 100 - (2/9x9) = X100 - 2 = X98 = XLearn more about probability in brainly.com/question/27656131
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Answer:C) The probability that you pick at least one purple marble is 98%.
Step-by-step explanation:
Leah wants to buy a home for
$380,000, but can only get a loan from the bank for $330,600. What percentage does Leah have to put down in order to pay for the home?
Answers
Leah have to put down 13% of the total money in order to pay for the home.
What is a Home Loan ?The amount of money a person borrows from a bank to buy a house is termed as Home Loan.
It is given that
Leah wants to buy a home for $380,000
The amount of money he can get from bank is $ 330,600
The amount of money Leah needs to have
= $ 380000 - $ 330600 = $49400
The percentage Leah have to put down in order to pay for the home is
=($49400 /$380000 ) * 100%
= 0.13 * 100 %
= 13%
Therefore Leah have to put down 13% of the total money in order to pay for the home.
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Galaxy Star Corporation purchased goods for $100,000 from Sunrise
Materials. Galaxy Star Corporation can avail a discount of 2.5% if the
payment is made within 20 days. However, the full payment will be made
if the payment is made after 20 days.
If Galaxy Star Corporation pays within 20 days, which of the
following entries will it pass?
Answers
The entry that it will pass on the accounting book based on the information about Galaxy Star Corporation is the credit sales.
What is a credit sale?It should be noted that credit sales are the sales where the amount that is owed will be paid at alter date.
From the information given, we were informed that the payment will be made after 20 days. Therefore, the appropriate entry will be in town credit sales.
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For the inverse variation equation p = 8/v , what is the value of V when p = 1/2?
Answers
Substituting in p = 1/2,
[tex]\frac{1}{2}=\frac{8}{v}\\ \\ v=\boxed{16}[/tex]
Help me PLEASEEE!!! ASAP
Answers
x2 +kx+12
What are two numbers that k could be so that each expression could be factored??
Answers
Answer:
K could be 7 or 8
Step-by-step explanation:
If K was to be 7, the equation would be x^2 + 7x + 12 = (x+3)(x+4)
If K was to be 8, the equation would be x^2 + 8x + 12 = (x + 2)(x + 6)
In a recent international sport competition the top three countries country A country B and country C won a total of 120 medals. country B won 11 more medals than country C .country A won 38 more medals than the total amount won by the other two . how many medals did each of the top three countries won.
Answers
An equation is formed of two equal expressions. The medals won by country A, country B, and country C is 79, 26, and 11, respectively.
What is an equation?An equation is formed when two equal expressions are equated together with the help of an equal sign '='.
Let the number of medals won by country A, country B, and country C be represented by A, B, and C, respectively. Now, the given conditions can be written as,
1.) The top three countries country A, country B, and country C won a total of 120 medals.
A + B + C = 120
2.) Country B won 11 more medals than country C
B = C + 11
3.) Country A won 38 more medals than the total amount won by the other two.
A = B + C + 38
A - 38 = B + C
Substitute the value of B+C form the last equation to the first equation,
A + A - 38 = 120
A = 79
Now, Substitue the value of A and B(from second equation) in the first equation,
79 + C + 11 + C = 120
C = 15
Now, substitute the value of C in the second equation,
B = C + 11
B = 15 + 11
B = 26
Hence, the medals won by country A, country B, and country C is 79, 26, and 11, respectively.
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HELP QUICK PLEASE WILL GOVE BRAINLEOCMWdiowemforewmfo
Answers
Answer:
It's choice G or H
Step-by-step explanation:
The cube and the disc are representative of the variable r and a 1 (a single unit) The question says "Using the representations above..." Hopefully right before this question it tells you (above) which is the variable and which is the single unit.
The left and right sides of the balance are going to represent the left and right sides of the equation, with the = equal sign being the middle.
The 2 on the left side and the 18 on the right side will need to have the same image representing it on both sides (2 on the left, 18 on the right) because they are both numerical values. Then, there should also be one shape on the left that stands for the variable. Without seeing the info that preceded the question, it is either Answer G or Answer H. Edit in the additional info. I will be able to say exactly which one. But I bet you can see it!
Calcula el valor del lado "c" en el triángulo
rectángulo, que se proporciona en la figura;
aplicando las funciones trigonométricas:
Answers
Usando relaciones en un triángulo rectángulo, se encuentra que el valor del lado c es c = 35.5 unidades.
¿Cuáles son las relaciones en un triángulo rectángulo?Las relaciones en un triángulo rectángulo se dan de la siguiente manera:
El seno de un ángulo está dado por la longitud del lado opuesto al ángulo dividida por la longitud de la hipotenusa.El coseno de un ángulo está dado por la longitud del lado adyacente al ángulo dividido por la longitud de la hipotenusa.La tangente de un ángulo está dada por la longitud del lado opuesto al ángulo dividida por la longitud del lado adyacente al ángulo.El lado opuesto de el ángulo de 26º48' = 26.8º es de 16, de esa forma, puede-se encontrar el lado c de la siguiente manera:
[tex]\sin{(26.8^\circ)} = \frac{16}{c}[/tex]
[tex]c = \frac{16}{\sin{(26.8^\circ)}}[/tex]
c = 35.5º.
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What is the length of the line?
Answers
If ur talking about vectors It’s (6,1)
Which of the following polynomials is in standard form?
A. F(x)=-3x+6x²-1+7x
B. F(x)=7x+6x² -1-3x4
C. F(x)=-3x4 -1+6x² +7x
D. F(x)=-3x +6x² +7x-1
Answers
Answer:
d
Step-by-step explanation:
What is a value plus 8, in algebraic expression
Answers
what is the formula for equations.
Answers
A formula is a fact or rule that uses mathematical symbols. It will usually have: an equals sign (=) two or more variables (x, y, etc) that stand in for values we don't know yet.
Example: The formula for finding the volume of a box is:
x = 2y - 7 Formula (relating x and y)
a2 + b2 = c2 Formula (relating a, b and c)
Which expression is equivalent to...
Answers
Step-by-step explanation:
hope you can understand
