Determine the inverse Laplace transforms of: 232-55-1 (a) (5+3)(s2 +9) (b) 1 352 +55+1 7 (d) ( 53 3 (e) 55+2
Answers
(a) The Inverse Laplace transform is -2\(e^{-3t}\) + 2cos(3t) - (1/3)sin(3t) (b) The Inverse Laplace transform is \(e^{-t/3} - e^{-t}\) (d) The Inverse Laplace transform is (7/2)t² (e) The Inverse Laplace transform is \(3e^{-2t/5}\)
To determine the inverse Laplace transforms of the given functions, we'll use various methods such as partial fraction decomposition and known Laplace transform pairs. Let's calculate the inverse Laplace transforms for each case:
(a) Inverse Laplace transform of (2s² - 5s - 1)/((s + 3)(s² + 9)):
First, we need to perform partial fraction decomposition:
(2s² - 5s - 1)/((s + 3)(s² + 9)) = A/(s + 3) + (Bs + C)/(s² + 9)
Multiplying both sides by (s + 3)(s² + 9), we get:
2s² - 5s - 1 = A(s^2 + 9) + (Bs + C)(s + 3)
Expanding and equating coefficients:
2s² - 5s - 1 = (A + B)s² + (3B + A)s + (9A + 3C)
Comparing coefficients, we find:
A + B = 2
3B + A = -5
9A + 3C = -1
Solving these equations, we get A = -2, B = 4, and C = -1.
Now, we can rewrite the function as:
(2s² - 5s - 1)/((s + 3)(s² + 9)) = -2/(s + 3) + (4s - 1)/(s² + 9)
Taking the inverse Laplace transform of each term using known pairs, we have:
Inverse Laplace transform of -2/(s + 3) = -2\(e^{-3t}\)
Inverse Laplace transform of (4s - 1)/(s² + 9) = 2cos(3t) - (1/3)sin(3t)
Therefore, the inverse Laplace transform of (2s² - 5s - 1)/((s + 3)(s²+ 9)) is:
-2\(e^{-3t}\) + 2cos(3t) - (1/3)sin(3t)
(b) Inverse Laplace transform of 1/(3s² + 5s + 1):
We can use the quadratic formula to factorize the denominator:
3s² + 5s + 1 = (3s + 1)(s + 1)
Using known pairs, the inverse Laplace transform of 1/(3s + 1) is \(e^{-t/3}\) and the inverse Laplace transform of 1/(s + 1) is \(e^{-t}.\)
Therefore, the inverse Laplace transform of 1/(3s² + 5s + 1) is:
\(e^{-t/3} - e^{-t}\)
(d) Inverse Laplace transform of 7/(s³):
Using known pairs, the inverse Laplace transform of 1/sⁿ is (tⁿ⁻¹)/(n-1)!, where n is a positive integer.
Therefore, the inverse Laplace transform of 7/(s³) is:
7(t³⁻¹)/(3-1)! = 7t²/2 = (7/2)t²
(e) Inverse Laplace transform of 3/(5s + 2):
Using known pairs, the inverse Laplace transform of 1/(s - a) is \(e^{at}\).
Therefore, the inverse Laplace transform of 3/(5s + 2) is:
\(3e^{-2t/5}\)
The complete question is:
Determine the inverse Laplace transforms of:
(a) (2s² - 5s - 1)/((s + 3)(s² + 9))
(b) 1/(3s² + 5s + 1)
(d) 7/(s³)
(e) 3/(5s + 2)
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Related Questions
Test for the commutative property of union and intersection of the sets P = { x : x is all real numbers between 2 and 7} and Q = { x : x is all rational numbers between 2 and 7}
Answers
Answer:
Step-by-step explanation:
P = {x : x is a real number between 2 and 7}
{x: 3,4,5,6}
Q = {x : x is all rational number between 2 and 7}
{4 }
We know that P contains all the rational numbers between 2 and 7.
And P ∪ Q and Q ∪ P each of them contain all the real numbers which are between 2 and 7.
{3,4,5,6}
Here Q is the proper subset of P
P ∩ Q = Q ∩ P = Q= {4}
How many different outcomes are possible when a pair of standard dice are rolled? A. 36 B. 10 C. 12 D. 24
Answers
The answer is A. 36 different outcomes are possible when a pair of standard dice are rolled.
When a pair of standard dice are rolled, each die has 6 sides numbered 1 to 6. The total number of possible outcomes is equal to the total number of ways the two dice can land. To find the total number of different outcomes, we need to consider all the possible combinations of the numbers on the two dice.
Each die has 6 possible outcomes, so there are 6 x 6 = 36 possible outcomes for a pair of dice. These outcomes include all possible combinations of the numbers 1 to 6 that can be rolled on each die. For example, the outcomes include (1,1), (1,2), (1,3), ..., (6,5), and (6,6).
Therefore, the answer is A. 36 different outcomes are possible when a pair of standard dice are rolled.
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A can of soup is 8 centimeters in diameter and 10 centimeters high. What is the volume of the can in terms of ?
Answers
Answer:
volume= 502.4cm
Step-by-step explanation:
see attachment for detailed solution
Answer:
Step-by-step explanation:
Formulae for Volume = Pi x r2 x h
Pi = 3.14 or 314/100 because the radius is not a product of 7
Radius = 4 cm
Height = 10 cm
314/100 x 4 x 4 x 10 = 512.4 cm2
= 512.4 cm2
one lot must be ten meters longer than it is wide, and the total area must be 1656 m2. what are the length and width of the lot
Answers
The length and width of the lot are 46m and 36m respectively
Let the width of the lot be x,
therefore, length=x+10 (as the lot must be 10m longer than it's wide)
Now, according to the question:
Area of the lot= 1656 m²
Area of a rectangle is given by the product of it's length to width, that is:
⇒ Length × Width= 1656 m²
⇒ (10+x).x= 1656
⇒ 10x+x²= 1656
⇒ x²+10x-1656=0
⇒x²+46x-36x-1656=0
⇒x(x+46)-36(x+46)=0
⇒(x-36)(x+46)=0
⇒x=36 or x=-46(which can be ignored)
∴ x=36 and 10+x=46
So, the length of the lot is 46m and the width is 36m.
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Write the ratios for sin A and cos A. The diagram is not drawn to scale.
sin A= 14/50 cos A 48/50
sin A= 48/50 cos A 14/50
sin A 48/14 cos A 14/50
sin A= 48/50 cos A 14/48
Answers
The ratio of SINA and COSA = 48/50 and 14/50
What is trignometric ratios?This is the boundary or contour length of a 2D geometric shape.
Depending on their size, multiple shapes may have the same circumference. For example, imagine a triangle made up of wires of length L.
The same wire can be used to create a square if all sides are the same length.
The length covered by the perimeter of the shape is called the perimeter. Therefore, the units of circumference are the same as the units of length.
As we can say, the surroundings are one-dimensional. As a result, you can measure in meters, kilometers, millimeters, etc.
Inches, feet, yards, and miles are other globally recognized units of circumference measurement.
According to our question,
sina = perpendicular\ hypotenuse
= 48/50
cosa= base\ perpendicular
=
14/50
Hence, The ratio of SINA and COSA = 48/50 and 14/50
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1. Using the below variables, write a for loop that increases x by two for each ix=1; i=c(1:10)2. Using the below variable, type a while () loop that adds even numbers to x, while the length of x is less than 12. For example, in the first iteration you get x = 2,4,6, and the third x =2,4,6,8x=c(2,4)
Answers
For loop increasing x by two for each ix=1; i=c(1:10):
R
Copy code
x <- 0
for (ix in c(1:10)) {
x <- x + 2
print(x)
}
While loop adding even numbers to x while the length of x is less than 12:
R
Copy code
x <- c(2, 4)
while (length(x) < 12) {
last_num <- tail(x, 1)
next_even <- last_num + 2
x <- c(x, next_even)
print(x)
}
Note: The code assumes that the initial value of x in the while loop is c(2, 4) as mentioned in the example. If the initial value of x is different, please adjust it accordingly.
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if ∑an and ∑bn are both convergent series with positive terms, then ∑anbn is convergent.T/F
Answers
If the series ∑an and ∑bn are both convergent series with positive terms, then the series ∑anbn is also convergent.
This can be proven using the Comparison Test for series convergence. Since an and bn are both positive terms, we can compare the series ∑anbn with the series ∑an∑bn.
If ∑an and ∑bn are both convergent, then their respective partial sums are bounded. Let's denote the partial sums of ∑an as Sn and the partial sums of ∑bn as Tn.
Then, we have:
0 ≤ Sn ≤ M1 for all n (Sn is bounded)
0 ≤ Tn ≤ M2 for all n (Tn is bounded)
Now, let's consider the partial sums of the series ∑an∑bn:
Pn = a1(T1) + a2(T2) + ... + an(Tn)
Since each term of the series ∑anbn is positive, we can see that each term of Pn is the product of a positive term from ∑an and a positive term from ∑bn.
Using the properties of the partial sums, we have:
0 ≤ Pn ≤ (M1)(Tn) ≤ (M1)(M2)
Hence, if ∑an and ∑bn are both convergent series with positive terms, then ∑anbn is also convergent.
Therefore, the given statement is True.
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The wavelength of violet light is 4.0 x 10^−7 m. The wavelength of red light is 6.5 x 10^−7 m. How much longer is the wavelength of red than violet?
A 2.5 × 10^–7 m
B 1.05 × 10^–7 m
C 2.5 × 10^–6 m
D 1.05 × 10^–6 m
Answers
Answer:
A 2.5 × 10^–7 m
Step-by-step explanation:
Given
wavelength of violet light = 4.0 x 10^−7 m.
The wavelength of red light = 6.5 x 10^−7 m
To find the how much longer is wavelength of red light than violet light we have to find difference of wavelength of red and violet light
Difference in wavelength of red light and violet light =
wavelength of red light -wavelength of violet light
= 6.5 x 10^−7 m - 4.0 x 10^−7 m
Difference in wavelength of red light and violet light = (6.5 - 4.0)*10^−7 m
Difference in wavelength of red light and violet light =2.5 x 10^−7 m
Thus,
wavelength of red light is 2.5 x 10^−7 m longer than wavelength of violet light
option A
16 oranges and 13 lemons cost $9.29 while 19 oranges and 6 lemons cost $9.05. a pair of equations appropriate for determining the price of each is:
Answers
Let's use x to represent the cost of one orange and y to represent the cost of one lemon. We can then set up a system of two equations:16x + 13y = 9.29 19x + 6y = 9.05 These equations represent the total cost of buying a certain number of oranges and lemons in two different scenarios.
To understand why we need two equations, let's consider the first equation: 16x + 13y = 9.29
This equation tells us that if we buy 16 oranges and 13 lemons, the total cost will be $9.29. But we don't know the individual prices of oranges and lemons yet. That's where the second equation comes in: 19x + 6y = 9.05
This equation tells us that if we buy 19 oranges and 6 lemons, the total cost will be $9.05. Again, we don't know the individual prices yet.
By setting up a system of equations, we can solve for x and y, which represent the prices of oranges and lemons, respectively.
One way to solve this system is by elimination. We can multiply the first equation by 19 and the second equation by -16, which will allow us to eliminate y:
304x + 247y = 176.51
-304x - 96y = -144.8
Adding these two equations together gives: 151y = 31.71
Dividing both sides by 151, we get: y = 0.21
Now we can substitute this value of y into one of the original equations to solve for x. Let's use the first equation:
16x + 13(0.21) = 9.29
16x + 2.73 = 9.29
16x = 6.56
x = 0.41
So the cost of one orange is $0.41 and the cost of one lemon is $0.21.
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I got this homework packet , I did some of the questions but graphs are what I’m stuck on the most .
Answers
Answer:
For the first picture, I think it is C and the second one should be A.
Step-by-step explanation:
You use vertical lines and if it hits it multiple times it is not a function. Like if it hits two dots or something it is not a function. I hope that make sense, let me know if it doesn't.
PLS HELP I DONT UNDERSTAND MATH
Answers
1. no
2. No ecause 15 +x or 5 is 20 + the x 20x and its for x even if the 5 was a negetive
Find the gradient of the line segment between the points (0,6) and (2,16).
helpppp on a timer!!!
Answers
Answer:
Slope, sometimes referred to as gradient in mathematics, is a number that measures the steepness and direction of a line, or a section of a line connecting two points, and is usually denoted by m. Generally, a line's steepness is measured by the absolute value of its slope, m. The larger the value is, the steeper the line. Given m, it is possible to determine the direction of the line that m describes based on its sign and value:
A line is increasing, and goes upwards from left to right when m > 0
A line is decreasing, and goes downwards from left to right when m < 0
A line has a constant slope, and is horizontal when m = 0
A vertical line has an undefined slope, since it would result in a fraction with 0 as the denominator. Refer to the equation provided below.
Slope is essentially change in height over change in horizontal distance, and is often referred to as "rise over run." It has applications in gradients in geography as well as civil engineering, such as the building of roads. In the case of a road the "rise" is the change in altitude, while the "run" is the difference in distance between two fixed points, as long as the distance for the measurement is not large enough that the earth's curvature should be considered as a factor. The slope is represented mathematically as:
m =
y2 - y1
x2 - x1
the radius of the cylinder is 6 m and the height is 10 m what's the volume?
Answers
tell me this pls <.< >.>
Answers
Answer:
A
Step-by-step explanation:
Which segment shows what happens when x>2? What happens when x = 2 and which line shows it best. Which question is easier to answer?
It's not C or D.
Look at A. If x = 2 then -x + 4 = -2 + 4 = 2. I admit you can't let it be that way, but it gives you an indication of what to do. That is what happens to the short line on the right.
What is the long line doing? -2(2) - 1 = -5. Who does that? A does
So the Answer is A
5 + x/2 =4 please help
Answers
Answer:
Step-by-step explanation:
x=3
Answer:
The answer is 3
Step-by-step explanation:
5 + x/2 = 4
5 + x = 2(4)
5 + x = 8
x + 5 – 5 = 8 – 5
x = 3
Thus, The answer is 3
-TheUnknownScientist 72
what is the remainder when 5x^55 −2x ^21 +1 is divided by x−1
Answers
Answer:
Probably 4
Step-by-step explanation:
See what you can get from the photo below
The lifetime of an electronical component is to be determined; it is assumed that it is an ex- ponentially distributed random variable. Randomly, users are asked for feedback for when the component had to be replaced; below you can find a sample of 5 such answers (in months): 19,23,21,22,24.
Fill in the blanks below.
(a) Using the method of maximum likelyhood, the parameter of this distribution is estimated to λ = ________WRITE YOUR ANSWER WITH THREE DECIMAL PLACES .
(b) Let L be the estimator for the parameter of this distribution obtained by the method of moments (above), and let H be the estimator for the parameter of this distribution obtained by the method of maximum likelyhood. What comparison relation do we have between L and M in this situation? Use one of the symbols
< = or > to fill in the blank. L ________M
Answers
(a) Using the method of maximum likelihood, the estimated parameter of the exponential distribution is λ = 0.050.
(b) Comparing the estimators obtained by the method of moments (L) and the method of maximum likelihood (M), we have L < M.
(a) The maximum likelihood estimation involves finding the parameter that maximizes the likelihood function based on the given data. In this case, using the sample of replacement times (19, 23, 21, 22, 24), the estimated parameter λ of the exponential distribution is calculated to be 0.050.
(b) Comparing the estimators obtained by the method of moments (L) and the method of maximum likelihood (M), we can determine the relationship between them. In general, the method of maximum likelihood tends to provide more efficient and precise estimators compared to the method of moments. Therefore, we have L < M, indicating that the estimator obtained by the method of maximum likelihood (M) is expected to be greater than the estimator obtained by the method of moments (L) in this situation.
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What are the first 10 digits after the decimal point when the fraction $\frac17$ is written in base 16?
Answers
Answer:
The amswer is "2,4,9....."
Step-by-step explanation:
\(x=\frac{1}{7}\\\\x_d=0.\overline{142857}\\\\x_h=0.\overline{249}\\\\\)
by leave you to work out the other 7 digits:
\(\to \frac{1}{7}\approx \frac{a}{16}\\\\a= \text{first hex digit}\\\\a=floor(\frac{16}{7})=2\\\\\)
\(\to \frac{1}{7}- \frac{a}{16}\approx \frac{b}{16^2}\\\\b= \text{second hex digit}\\\\b=floor(\frac{16^2}{7} -16a)=4\\\\\)
\(\to \frac{1}{7}- \frac{a}{16}-\frac{b}{16^2} \approx \frac{c}{16^3}\\\\c= \text{third hex digit}\\\\c=floor(\frac{16^3}{7} -16^2a-16b)=9\\\\\)
6. Haley bought three bars of soap and five
sponges for $22. Yesenia bought five bars of
soap and three sponges for $26. Find the cost
of each item
Answers
Our two equations are:
3x + 5y = 22
5x + 3y = 26
x = cost of each soap
y = cost of each sponge
Now we solve:
-3(3x + 5y = 22) = -9x- 15y = -66
5(5x + 3y = 26) = 25x + 15y = 130
Our new equations:
-9x- 15y = -66
25x + 15y = 130
16x = 64
/16 /16
x = 4 (each soap costs $4.00)
Now we substitute x into one on our ORIGINAL equations.
3x + 5y = 22
3(4) + 5y = 22
12 + 5y = 22
-12 -12
5y = 10
/5 /5
y = 2 (each sponge costs $2.00)
To check:
3x + 5y = 22
3(4) + 5(2) = 22
12 + 10 = 22
22 = 22
This statement is TRUE, which also makes our answers true.
Hope that helps!
You meet two students in the library. At least one of them is an upperclassman who is currently taking EECS 126. Assume each student is an upperclassmen and underclassmen with equal probability and each student takes 126 with probability 1 10 , independent of each other and independent of their class standing. What is the probability that both students are upperclassmen
Answers
There is a 50% chance that both students are upperclassmen.
Given: Two students meet at a library, where at least one of them is an upperclassman who is currently taking EECS 126, assume each student is an upperclassman and underclassmen with equal probability and each student takes 126 with probability 1/10, independent of each other and independent of their class standing. To find: Probability that both students are upperclassmen.
Solution: Let P(A) be the probability that a student is an upperclassman, and P(B) be the probability that a student is taking EECS 126.P(A) = 1/2 (Given, Assume each student is an upperclassman and underclassmen with equal probability) P(B) = 1/10 (Given, each student takes 126 with probability 1/10, independent of each other and independent of their class standing) Let C be the event that both students are upperclassmen. Then, P(C) = Probability that both students are upperclassmen P(C') = Probability that one student is an underclassman or both are underclassmen P(C') = P(Ac) ...(i) P(C') = 1 - P(C) ...(ii) P(Ac) = P(underclassman) = 1/2 (Given, Assume each student is an upperclassman and underclassmen with equal probability)
Now, P(C') = P(Ac) = 1/2 ...from (i) P(C) = 1 - P(C') = 1 - 1/2 = 1/2 Also, P(B) and P(A) are independent events as given in the question, So, P(AB) = P(A)P(B) = (1/2) x (1/10) = 1/20 Hence, the probability that both students are upperclassmen is P(AB) = 1/20.In other words, there is a 50% chance that both students are upperclassmen.
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The sum of the lengths of is 15.12 cm. The length of is 6 cm and the length of is 4.3 cm. What is the length of ?
A. 25.42 cm
B. 4.92 cm
C. 4.82 cm
D. 4.72 cm
Answers
Answer:
C, 4.82
Step-by-step explanation:
add the given lengths and subtract it from the total lengths to get 4.82
Answer:
C
Step-by-step explanation:
1A. Tính:
a) ( -14) + 5 + 17 + 14 b) 40 +13 + ( -25) + ( -13)
c) ( -5) + ( -146)+ ( -15) + 14 d) ( -2) + (-5) + 20 + (- 13)
Answers
Answer:
7868
Step-by-step explanation:
You have a box of fruit flies that are left untouched. The fruit fly population doubles every 3 hours. Would this equation be linear or exponential?
Group of answer choices
Exponential
Linear
Answers
Answer:
B Exponential
Step-by-step explanation:
Hope this helps
The equation for the fruit fly population doubling every 3 hours would be exponential.
Exponential growth occurs when a quantity increases at a fixed percentage over fixed intervals of time. In this case, the population of fruit flies doubles, which means it is increasing by 100% every 3 hours.
The general form of an exponential growth function is given by: y = a * b^x
Where:
- y is the final quantity or population size after x intervals of time.
- a is the initial quantity or population size at the beginning (in this case, the initial number of fruit flies).
- b is the growth factor (in this case, b = 2 since the population doubles every 3 hours).
- x is the number of intervals of time (in this case, the number of 3-hour periods).
In the context of the fruit fly population, the equation would be in the form of y = a * 2^x, where the population of fruit flies increases exponentially as time passes. This is why the equation is exponential.
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1. The hyperbolic functions cosh and sinh are defined by the formulas et - e• cosh (x) e² te-a sinh(2) 2 2 = (b) The function sinh is one-to-one on R, and its range is R, so it has an inverse defined on R, which we call arcsinh. Use implicit differentiation to prove that 1 (arcsinh(r)) = = x² + 1
Answers
To prove that \(\(\frac{d}{dr}(\text{arcsinh}(r)) = \frac{1}{\sqrt{r^2+1}}\)\), we will use implicit differentiation.
Let's consider the equation \(\(y = \text{arcsinh}(r)\)\), where y is the inverse function of \(\(\text{sinh}(x)\)\).
Taking the hyperbolic sine function \(\(\text{sinh}(x)\)\), we have \(\(\text{sinh}(x) = r\)\).
Now, we can differentiate both sides of the equation with respect to r using the chain rule:
\(\[\frac{d}{dr}(\text{sinh}(x)) = \frac{d}{dr}(r).\]\)
The derivative of \(\(\text{sinh}(x)\)\) with respect to r can be expressed as:
\(\[\frac{d}{dr}(\text{sinh}(x)) = \frac{d}{dx}(\text{sinh}(x)) \cdot \frac{dx}{dr}.\]\)
Since \(\(\text{sinh}(x) = r\)\), we have:
\(\[\frac{d}{dx}(\text{sinh}(x)) = \frac{d}{dx}(r).\]\)
The derivative of \(\(\text{sinh}(x)\)\) with respect to x is given by:
\(\[\frac{d}{dx}(\text{sinh}(x)) = \cosh(x).\]\)
Substituting these values into the equation, we have:
\(\[\cosh(x) \cdot \frac{dx}{dr} = 1.\]\)
Solving for \(\(\frac{dx}{dr}\)\), we get:
\(\[\frac{dx}{dr} = \frac{1}{\cosh(x)}.\]\)
Since \(\(\cosh(x) = \sqrt{x^2+1}\)\), we have:
\(\[\frac{dx}{dr} = \frac{1}{\sqrt{x^2+1}}.\]\)
Finally, we substitute \(\(x = \text{arcsinh}(r)\)\) into the equation to obtain:
\(\[\frac{dx}{dr} = \frac{1}{\sqrt{(\text{arcsinh}(r))^2+1}}.\]\)
Therefore, we have proved that:
\(\[\frac{d}{dr}(\text{arcsinh}(r)) = \frac{1}{\sqrt{r^2+1}}.\]\)
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2. Megan's aquarium measures 20 inches long, 14 inches wide, and 18 inches high. How many cubic inches of water would it take to completely fill the aquarium?
Answers
It would take 5040 cubic inches of water to completely fill the aquarium.
We know that the formula for the volume of cuboid :
V = length × width × height
Let us assume that l represents the length of the aquarium, w represent the width and h represents the height.
Here, l = 20 inches
w = 14 inches
and h = 18 inches
Using the formula for the volume of cuboid, the volume of aquarium would be,
V = l × w × h
V = 20 × 14 × 18
V = 5040 cu.in.
Therefore, it would take 5040 cu.in. of water.
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please help asap will give brainliest
Answers
Answer:
bhhujnejnj
Step-by-step explanation:
Which statement best describes the relationship between x and y in the equation y = 3x? A. The value of y is three less than the value of x. B. The value of y is three times the value of x. C. The value of x is three more than the value of y. D. The value of y is three more than the value of x.
Answers
Answer:
b
Step-by-step explanation:
Y is three times the value of x , It can be said that y is directly proportional to Y .
Direct proportion is when an increase in the independent variable causes an increase in the dependent variable.
the equation for direct proportion is :
y = bx
y = dependent variable
b = constant
x = independent variable
Rewrite the radical expression as an expression with a rational exponent.
\( \sqrt[4]{ \times 5?} \)
A.
\( {x}^{ \frac{5}{4} } \)
B.
\( {x}^{20} \)
C.
\(x\)
D
\( {x}^{ \frac{4}{5} } \)
Answers
Answer:
B
Step-by-step explanation:
please answer for brainiest.
Answers
Answer:
The unit rate for a distance of one meter is 0.0958.
Step-by-step explanation:
100/9.58
1/X
To find x, you do what you did you get 1! Divide by 100. 9.58 divided by 100 is equal to 0.0958.
Now for the chart:
50/4.79
100/9.58
250/23.95
400/38.32
Hope this helps!
250: 23.95
400: 38.32
Unit rate for time of a distance of 1 meter - 1 meter: .0958 seconds
what is the differenential equation for the family of curves find the family of orthogonal trajectories
Answers
To find the differential equation for a family of curves, we need to find an equation that relates the variables involved in the curves. For example, consider the family of curves given by:
y = mx + c
where m and c are constants. To find the differential equation for this family of curves, we can take the derivative of both sides with respect to x:
dy/dx = m
This is the differential equation for the family of curves.
To find the family of orthogonal trajectories, we need to find a new family of curves that intersect the original family of curves at right angles. We can use the fact that the product of the slopes of two perpendicular lines is -1. So, if the differential equation for the original family of curves is:
dy/dx = f(x, y)
then the differential equation for the family of orthogonal trajectories is:
dy/dx = -1/f(x, y)
To find a specific orthogonal trajectory, we need to solve this differential equation for y as a function of x.
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