She reportedly invested $6600 at 3% and $3400 at 2.5%, according to the statement.
Why do individuals invest?Investing is a smart way to put your money to work and could make you richer. If you make smart investing choices, your money may increase in value as outpace inflation. The major factors contributing to investment's increased growth potential are the possibility of compounding and the trade-off amongst risk and return.
Simple interest is calculated as follows: deposit amount multiplied by time and interest rate.
Let "a" represent the money placed in the account earning 3% interest.
Let's use the symbol to represent the amount deposited into the account earning 2.5% interest (10,000 - a)
a * 0.03 plus (10,000 - a) * 0.025 = 283
0.03a + 250 - 0,025a = 283
Collect like terms
0.03a - 0.025a = 283 - 250
0.005a = 33
a = $ 6600
What was put into the 2.5% account = 1000 - 6600 = $ 3400
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The Question is in the picture
The answer is 486 cm². Thus option c is the right answer.
According to the given question:
The surface area of the cube = 6s²
Surface Area is the area occupied by the six faces of the cube.
where, s ⇒ length of each edge.
Given,
length of each edge = 9cm.
Substituting values in the given formula,
6 × 9²
= 6 × 81
= 486 cm².
Therefore the surface area of the cube is 486cm².
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⅕(x + 2 ) -¼(2-x) ≥ ⅓ (x + 4) - ¼ ( 5-x)
Answer:
x > 11/-8
Step-by-step explanation:
1/5(x + 2) -1/4(2-x)> 1/3(x + 4) -1/4(5-x)
=60×1/5(x +2)-60×1/4(2-x)>60×1/3 (x+4)-60×1/4(5-x)
=12(x +2)-15(2- x)> 20(x+4)-15(5-x)
=12x + 24 - 30 + 15x > 20x + 80 - 75 + 15x
=12x + 15x - 20x -15x > 80 -75 -24 +30
=27x -35x > 80 - 99 + 30
=-8x > 11
=-8x/-8 > 11/-8
=x > 11/-8.
Hence the truth set of the inequality is said that (x : x > 11/-8).
the rescue center has budgeted a total of 2581.8 for this 30-day month. how many dogs are at the rescue center math problem
11423 be the number of dogs are at the rescue center.
What is Expression?An expression is combination of variables, numbers and operators.
A pet rescue center is creating a monthly food budget.
The center currently has two-thirds as many dogs as cats.
Each animal is fed 2 cans of food a day.
Dog food costs $0.08 per can, cat food costs $0.05 per can
The rescue center has budgeted a total 2581.8 of for food for this .
2(0.08)x+2(0.05)y= 2581.8
Let x be the number of dogs.
cats be y.
2/3x =y
2(0.08)x+2(0.05)2/3x= 2581.8
0.16x+0.066x=2581.8
0.226x=2581.8
x=11423
Hence, 11423 be the number of dogs are at the rescue center.
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a giraffe was 1 feet tall at birth,7 feet tall at the age of 4, and 11 and half feet at the age of 7
if there are only four recent college graduates with math majors, what is the chance that the sample will consist of two who intend to teach high school?
The chance of the sample consisting of two college graduates with math majors who intend to teach high school is zero. There are only four people in the sample, so the sample must consist of all four people.
Since the sample size is fixed, it is impossible to have two out of the four people have the same trait (intending to teach high school). Furthermore, the sample size is too small to yield a meaningful result; the sample size would need to be much larger in order to accurately represent the population of college graduates with math majors. Therefore, the chance of the sample consisting of two college graduates with math majors who intend to teach high school is zero.
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Find the quotient of -16 and 4.
Answer:
-4
Step-by-step explanation:
-16 divided by 4
4 times 4 = 16
16 divided by 4
negative with positive makes a negative
-4
f(x)=x^2-4
g(x)=2x+1
solve fg(x)>0
SHOW WORKING
Answer:
To find the values of x that make fg(x) > 0, we first need to find fg(x). We can do this by composing the functions, which means replacing x in g(x) with the expression for f(x):
fg(x) = f(g(x)) = f(2x + 1) = (2x + 1)^2 - 4
Now we can solve the inequality fg(x) > 0:
(2x + 1)^2 - 4 > 0
(2x + 1)^2 > 4
2x + 1 > 2 or 2x + 1 < -2
x > -1.5 or x < -2.5
So the values of x that make fg(x) > 0 are x > -1.5 or x < -2.5.
predict the election just before a presidential elec- tion, a national opinion poll increases the size of its weekly random sample from the usual 1500 people to 4000 people. (a) does the larger random sample reduce the bias of the poll result? explain. (b) does it reduce the variability of the result? explain.
(a) A larger random sample can potentially reduce the bias of the poll result and (b) a larger random sample will generally reduce the variability of the result.
(a) A larger random sample can potentially reduce the bias of the poll result. Bias in a poll refers to systematic errors in the sampling process that result in inaccurate or unfair representation of the population being polled. A larger sample size means that the poll is more likely to include a diverse range of perspectives and opinions, which can make the results more representative of the population as a whole. However, the sample size alone is not enough to guarantee unbiased results, it also depends on how the sample is selected and how the questions are phrased.
(b) A larger random sample will generally reduce the variability of the result. Variability refers to the degree to which the results of a poll can vary depending on the specific sample that is selected. A larger sample size means that there are more data points being included, which makes the results less susceptible to fluctuations caused by chance. However, the variability also depends on how the sample is selected, having a larger sample size does not guarantee less variability.
In summary, increasing the size of a random sample from 1500 to 4000 people can help reduce bias and variability in the poll results, but it is not a guarantee. Other factors such as the sampling method and question design also play an important role in determining the accuracy and fairness of the poll results.
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university of texas students were fitted with belt-worn tape recorders for up to four days so that researchers could sample their daily activities. the researchers employed a scientific method known as
The researchers employed a scientific method known as Ethnography.
Ethnography to study the recorded data. Ethnography is a method of research that involves the systematic study of people and cultures, often through the use of participant observation and the collection of detailed field notes. In this case, the researchers used the recordings to gain an understanding of the student's daily activities and how they were affected by their environment.
The researcher also often conducts in-depth interviews, focus groups, or surveys with group members to comprehensively understand their perspectives and experiences.
Ethnography can be applied in various fields, including anthropology, sociology, education, and business. It is commonly used to study communities, organizations, and other social groups.
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A store sees 120 customers in 8hours. What is the unit rate (in customer per hour) ?
Answer: 128 hours
Step-by-step explanation:
A rental car company offers two rental plans, Plan A and Plan B, for the same economy size car. For both plans, the total rental cost is a function of the number of miles that the car is driven. Plan A: Plan B: I. In complete sentences, translate each function into a verbal model describing the total cost of the rental in terms of the number of miles that the car is driven. II. For each function, determine how the rate of change will affect the total cost of a car rental. III. For a car rental that will include a maximum of 250 miles for the duration of the rental, which plan is the most cost effective
So, on solving the provided question we can say that in the function we have m = 500, after 500 miles of driving, the expenses of the 2 plans are equal.
what is function?The subject of mathematics includes quantities and their variations, equations and related structures, shapes and their locations, and places where they can be found. The term "function" refers to the relationship between a set of inputs, each of which has an associated output. A connection between inputs and outputs in which each input leads to a single, distinct result is known as a function. Each function is given a domain and a codomain, or scope. Usually, f is used to denote functions (x). input is an x. There are four main types of functions accessible. based on the following factors: on functions, one-to-one functions, many-to-one functions, inside functions, and on functions.
f(m) = .2m + 75
f(m) = .35m
.2m + 75 = ,35m
.15m = 75
m = 500
After 500 miles of driving, the expenses of the 2 plans are equal.
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Complete the following probability distribution table: Probability Distribution Table X P(X)
20 0.2 49 0.4
53 ? 80 0.3 Get help: Written Example
0.1 is Probability in Distribution Table X P(X).
What is Probability ?
The simple definition of probability is the likelihood that something will occur. We can discuss the probabilities of various outcomes, or how likely they are, whenever we are unsure of how an event will turn out.
Statistics describes the examination of events subject to probability.
Here X is a random variable. P(X) is its probabilities corresponding to the different values of X.
now according to the properties of probability theory we know that sum of probabilities is 1.
so here to find the value of the probability of X coresponding to the value 53 we should use the following steps:
sum of given probabilities =(0.2+0.4+0.3) = 0.9
required probability = 1 - sum of given probabilities = 1 - 0.9 = 0.1
hence the complete probability table is
X P(X)
20 0.2
49 0.4
53 0.1
80 0.3
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Calculate the double integral.
∬R 3xy^2/x^2 + 1 dA, R = {(x, y) | 0 ≤ x ≤ 1, −2 ≤ y ≤ 2}
Therefore , the solution of the given problem of integral comes out to be 8ln2 is solution for the integral expression.
Define integral.The region beneath a curve among two set limits is referred to as a definite integral. The representation of the definite integral for such a function of two variables), defined to reference to the x-axis, is ∫ baf(x)dx a b f (x) d x, where an is the lower bound and b is the upper bound.
Here,
Given :
[tex]\int\limits \int\limitsa_R[/tex] 3xy²/x²+ 1 dA
=> R = {(x, y) | 0 ≤ x ≤ 3, −2 ≤ y ≤ 2} ·
So,
=> [tex]\int\limits^1_{x=0} \int\limits^2_{y=-2}[/tex] 3xy²/x²+ 1 dxdy
=> [tex]\int\limits^1_{x=0}[/tex] 3x / x²+ 1 [tex]\int\limits^2_{y=-2}[/tex] y²
=>[tex]\int\limits^1_{x=0}[/tex] 3x / x²+ 1 ( y³/2)²dx
=> [tex]\int\limits^1_{x=0}[/tex] 3x / x²+ 1 (8 + 8 /3) dx
=> [tex]\int\limits^1_{x=0}[/tex] 16x/x²+ 1
=> 8 [ln(x²+ 1) ]
=> 8 [ln2 -ln1 ]
=>8ln2
Therefore , the solution of the given problem of integral comes out to be
8ln2 is solution for the integral expression.
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Find the volume of a cone with a base radius of 4 cm and a height of 6 cm. Write the exact volume in terms of it, and be sure to include the correct unit in your answer.
Answer:
Step-by-step explanation:
The volume of a cone with a base radius of 4 cm and a height of 6 cm is equal to 33.51 cm³. This is calculated by using the formula V = (1/3)πr²h, where V is the volume, π is the constant Pi, r is the radius of the base, and h is the height of the cone. Plugging in the given numbers, we have V = (1/3)(3.14)(4²)(6) = 33.51 cm³.
which statement describes ? the series diverges because it has a sum of 6. the series converges because it has a sum of three-fourths. the series converges because it has a sum of 2. the series diverges because it does not have a sum.
Convergent series:A series is said to be convergent when the limits of the series converge to the finite possible value for the series.
Consider a series
Sn=a1+a2+a3+a4+........+an
this form a new series as ,
Sn(n=1 to infinity)=
=s.
It is important that the partial sum of series, there should be a limit existed and that is finite in nature then only the series converges.
The geometric series gives a proper idea of how the limit decides the convergent and divergent nature.
A series in which the individual term, approaches zero then series is convergent in nature but not for all time.
The series,
A convergent series is a series for which limits exist.
If the sequence of the partial sum is a convergent sequence.
G(r,c)= r+c
where r≠1 then series converges.
Divergent series:
A series is an infinite series that does not converge at any point,
had an infinite sequence of partial sums with no finite limit.
A series where the individual sum does not approaches zero diverges.
For e.g.
This series diverges.
Or harmonic series which diverges.
Where is limit tends to infinity, eventually series added up to infinity means no exact answer will be there.
For summing the divergent series there method is:
FT
extrapolation methods.
Abelian theorems
Regularity, linearity, and stability test for the series.
If this test is checked then we will get to know which series diverges and converges.
It is not possible to determine whether a series converges or diverges based on its sum alone. The sum of a series can be finite, infinite, or undefined, but it does not provide information on whether the series converges or diverges. Other mathematical tests, such as the ratio test or the integral test, are used to determine whether a series converges or diverges.
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On any given day, the proportion of workers at a factory who are more than 5 minutes late to work is 0.11. A random sample of 20 workers will be selected. Which of the following is the best interpretation of the mean of the sampling distribution of the sample proportion of workers in the sample who are more than 5 minutes late to work for samples of size 20
The sampling distribution's mean will be interpreted as meaning A. The mean of all potential sample proportions for all samples of size 20 is equal to 0.11.
What is sampling distribution ?The sample proportion's sampling distribution is roughly regularly distributed. It is merely the population's mean drawn from the sampled population. This is the sample fraction of employees who arrive more than five minutes late, according to the sampling distribution's mean.
For samples of size 20, the mean of all potential sample proportions is equal to 0.11, which is the sampling distribution's mean for the sample proportion of workers who arrive at work more than 5 minutes late.
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Jorge wants to order tickets online so that he and 4 of his friends can go together to a movie. The cost of the tickets is $12.00 per person. The website also charges a transaction fee of $2.75 for the tickets online. Write an expression in terms of m that represents the cost of ordering m tickets online. Now use your expression to find the total cost of ordering 5 movie tickets show your work.
Answer:
Step-by-step explanation:
The expression in terms of m is 12m + 2.75.
To find the total cost of ordering 5 movie tickets, we plug in 5 for m: 12(5) + 2.75 = 62.75.
Two companies offer monthly cell phone plans, both of which include free text messaging. Company A charges a $25 monthly fee plus five cents per minute of phone conversation, while Company B charges a $50 monthly fee and offers unlimited calling. Both companies charge the same amount when the total duration of monthly calls is 8 hours and 33 minutes 8 hours and 20 minutes 5 hours 500 hours
The charge of the total duration of monthly calls for company A and company B will be same at 8 hours and 20 minutes.
What is a function?Function: a mathematical phrase, rule, or law that establishes the link between an independent variable and a dependent variable (the dependent variable). In mathematics, functions exist everywhere, and they are crucial for constructing physical links in the sciences.
Given that the cost function of the two companies is:
Company A: $25 monthly charges, and 5 cents of fee per minute.
Let us suppose the duration per minute = m. The cost function is:
A(x) = 25 + 0.05m
Company B: $50 monthly charges.
B(x) = 50
Both companies will charge the same amount when:
A(x) = B(x)
25 + 0.05x = 50
x = 500 minutes.
Converting minutes into hours we get the answer as 8 hours and 20 minutes.
Hence, the time for which both the companies charge the same amount is 8 hours and 20 minutes.
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Write an equation of the parabola with a vertex at the origin and a focus at (0,−2).
HELP PLEASE. WILL MARK BRAINLIEST.
The velocity of the object is 21.1 m/s.
What is the velocity?We have to note that when we drop the ball from the height, the ball is going to obey the equation of motion that is taking place under gravity. We can now look at the question to obtain the model for the problem.
We can see that in the question, the model of the problem have been given as; v = √19h where h is the height form which it fell. In this case h = 23.4 m
Then;
v = √19 * 23.4
v =21.1 m/s
The velocity of the ball as it falls to the ground is 21.1 m/s.
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Ben shoots an arrow. The height of
the arrow can be modeled by
y = -16x² + 100x + 4, where y.
represents the height in feet of the
arrow x seconds after it is shot into
the air. What is the maximum
height of the arrow and when did it
reach the maximum height?
Answer: The maximum height of the arrow is the vertex of the parabola. To find this, we can set the derivative of the function equal to zero and solve for x.
y' = -32x + 100
Setting y' = 0 and solving for x:
0 = -32x + 100
32x = 100
x = 100/32
So the arrow reaches its maximum height of y = -16(100/32)² + 100(100/32) + 4 = 100 feet at x = 100/32 seconds after it is shot into the air.
Step-by-step explanation:
A
D
Consider these two claims:
•
ABC is similar to both AACD and ACBD.
• (ACI2 + IBC12 = (ABI2
Explain why these claims are correct or incorrect. Provide valid
mathematical reasoning to support your responses.
As the corresponding angles are same in each of the right triangles, they are similar to each other (AAA rule).
AC² + BC² = AB² is true according to the Pythagorean theorem.
What is Pythagorean theorem?One of the earliest known theorems to ancient civilizations was the Pythagorean Theorem. Pythagoras, a Greek mathematician and philosopher, inspired the name of this famous theorem. He is credited with numerous mathematical contributions, some of which may have been the work of his students.
They were adamant that any two lengths had to be integral multiples of some unit length. There have been numerous attempts to conceal the fact that the square root of 2 is irrational. According to legend, the man who revealed the secret drowned at sea.
The Pythagorean Theorem describes triangles with a right angle. According to Pythagorean Theorem:
"The area of the square constructed on the hypotenuse of a right triangle equals the sum of the areas of the squares constructed on the remaining sides."
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11+4z+z-6
how would I solve this
Answer:
5 + 5z
Step-by-step explanation:
You just combine the like terms:
11 - 5 = 5
4z + 1z = 5z
=
5 + 5z
The table shows the rate at which water is being pumped into a swimming pool
Answer:
35, 189
Step-by-step explanation:
2 1/2 + 11 = 13 1/2 minutes
After 2 1/2 min after 11 min: 2 1/2 x 14 = 35 gallons are added after 2 1/2 min
A total of: 154 + 35 = 189 gallons will be pumped in after 13 1/2 min
PLEASE HELP!!
I just can’t seem to get this at all.
The equation solved is 1+-2/x²=-x-1 is 2x²+x³-2=0
Find the value of p and q ?the value of p is p=-x-q/x²the value of q is q=-x³-px²Coordinates are written as (x, y) meaning the point on the x axis is written first, followed by the point on the y axisThe coordinates of a point are a pair of numbers that define its exact location on a two-dimensional plane. Recall that the coordinate plane has two axes at right angles to each other, called the x and y axis. The coordinates of a given point represent how far along each axis the point is located.The point where the axes intersect is called the origin. Let's plot a point on the coordinate plane. The location of Point A is given as a horizontal component (x) and a vertical component (y) and written as (x,y). From the origin, to get to Point A, we would count two units to the right and three units upTo learn more about value of p and q refers to:
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refer to exercise 50. how many axles would you need to sample if you wanted the standard deviation of the sampling distribution of x to be 0.0005 mm?
If the sample standard deviation from the sample distribution is 0.0005 mm, the sample should have 16 axes.
Given,
μ = 40.125 mm, σ = 0.002mm σ(x) = 0.0005mm
The standard deviation of the sampling distribution of the sample mean is the population standard deviation divided by the square root of the sample.
σ₁ = σ/√n
By multiplying both sides by √n
√nσ(x) = σ
By dividing both the side by σ₂
√n = σ / σ₁
By squaring both the sides
n = σ²/σ²(x)
Now,
Calculate the value of n
n = 0.002² / 0.0005²
= 16
Therefore,
If the sample's standard deviation of the sampling distribution is 0.0005mm, then the sample should be 16 axles.
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A rectangular swimming Pool is twice as long as it is wide. A small concrete walkway surrounds the pool. The walkway is a constant 2 feet wide and has an area of 196 square feet. Find the dimensions of the pool.
Answer:
Let x be the width of the pool. Then the length of the pool is 2x, since it is twice as long as it is wide.
The area of the pool is (2x)(x)=2x^2
The total area of the pool and the walkway is 2x^2+196 square feet.
We can set up the equation using this information:
2x^2 + 22x = 196
Where 22x is the area of the walkway, 22x = 2x * 2 = 4x
2x^2 + 4x = 196
2x^2 + 4x - 196 = 0
Using the quadratic formula to solve the equation above:
x = (-b ± √(b^2 - 4ac))/2a
x = (-4 ± √(4^2 - 42196))/2*2
x = (-4 ± √(16 - 1568))/4
x = (-4 ± √(-1552))/4
Since x is width of the pool, it cannot be a negative value, the x value that is negative must be rejected. Therefore x = (-4 + √1552)/4 = 8
The width of the pool is 8 feet and the length is 2x = 2*8 = 16 feet
The waste-to-energy process generates energy in the form of electricity, heat, or fuel from the incineration of waste. Converting non-recyclable waste materials into electricity, heat, or fuel generates a renewable energy source. The 65 facilities in a certain country have the capacity to produce 1,580 megawatts of power per year by processing more than 16 million tons of waste per year. Write an inequality to show the possible power per year, p, the waste-to-energy facilities in the country are capable of producing.
please help quick
The inequality relation for the given problem would be p ≥ 1580.
What is inequality?
An inequality is a statement that compares the value of two expressions using one of the mathematical symbols <, >, ≤, ≥, ≠. It shows the relationship between two values, but unlike an equation, it does not set them equal to each other.
The inequality that shows the possible power per year, p, the waste-to-energy facilities in the country are capable of producing is:
p ≥ 1580
This inequality shows that the power per year, p, is greater than or equal to 1580. This is based on the information provided that the 65 facilities in the country have the capacity to produce 1,580 megawatts of power per year by processing more than 16 million tons of waste per year. The inequality is written in this way because we know the minimum amount of power that the facilities can produce, but not the maximum, so we use "greater than or equal to" to show that the power produced could be equal to 1,580 megawatts or greater.
Hence, The inequality relation for the given problem would be p ≥ 1580.
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at a hot air balloon festival. mohamed's balloon is at an altitude of 40m and rises 10m/min dana's balloon is at an altitude of 165m and descends 15m/min. a) in how many minutes will both balloons be at the same altitude?
After 5 minutes, the two balloons' height will be 40 + 10 + 5 = 90 ft.
What is unitary method?The unitary technique involves first determining the value of a single unit, followed by the value of the necessary number of units.
Let's say you go to the store to buy six apples.
You are informed by the shopkeeper that he is offering 10 apples for Rs 100. In this instance, the value and the units are the price of the apples.
Recognizing the units and values is crucial when using the unitary technique to a problem.
Always write the items that need to be computed on the right side and the things that are known on the left side to simplify things.
We are aware of the quantity of apples and the amount of money in the aforesaid problem.
According to our question-
Mohammed's altitude will be after a certain amount of time.
40 +10m
Dana's elevation will be...
165 -15m
When..., the elevations will be the same.
40 +10m = 165 -15m
25m = 125
add 15m-40
M = 5 is divided by 25 using the formula:
After five minutes, the two balloons' height will be 40 + 10 + five feet, or 90 feet.
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Use the Laplace transform to solve the given initial-value problem.
dy/dt -y=1, y(0)=0
to solve the given initial-value problem: dy/dt -y=1, y(0)=0 is, u(t) = e^(t) - 1.
This can be solved using Laplace transform.
What is Laplace transform?In order to translate a given derivative function with a real variable t into a complex function with a variable s, the Laplace transform is used. Let f(t) be supplied for t ≥ 0 and suppose that the function meets some later-explained requirements.
As we just saw, the Laplace transform turns partial differentials to regular differentials, making it one of the most crucial tools for solving ODEs and, more especially, PDEs. In general, applications in the time-domain for t ≥ 0 employ the Laplace transform.
Laplace transformation X is transformed linearly to a new, typically complex variable called s. Differential equations are transformed into only algebraic equations using this method.
Given that,
dy/dt -y=1
y' - y = 1
⇒ L(y') - L(y) = L(1) .....(i)
⇒L(yⁿ) = sⁿ Fy - sⁿ⁻¹y(0) - sⁿ⁻²-2y' (0) — ..... yⁿ⁻¹(0)
yⁿ means nth derivative and F(y) stands Laplace transformation of y so 1 becomes
⇒sF - y(0) - F = 1/c as L(tⁿ) = (sⁿ⁺¹) / (n!)
⇒ F(s - 1) = 1/s
⇒F = 1/(s(s - 1)) = 1/(s - 1) - 1/s
⇒L⁻¹(F) = L⁻¹ [1/(s - 1)] - L⁻¹ (1/s)
=> u(t) = e^(t) - 1
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