Solve the following initial value problem.
d²s
dt²
= -36cos(6t+n), s'(0) = 100, s(0) = 0
S=
(Type an exact answer, using * as needed.)
Answers
For starters,
[tex]\cos(6t+\pi) = \cos(6t) \cos(\pi) - \sin(6t) \sin(\pi) = -\cos(6t)[/tex]
Now by the fundamental theorem of calculus, integrating both sides gives
[tex]\displaystyle \frac{ds}{dt} = s'(0) + \int_0^t 36 \cos(6u) \, du = 100 + 6 \sin(6t)[/tex]
Integrating again, we get
[tex]\displaystyle s(t) = s(0) + \int_0^t (100 + 6\sin(6u)) \, du = \boxed{100t - \cos(6t) + 1}[/tex]
Alternatively, you can work with antiderivatives, then find the particular constants of integration later using the initial values.
[tex]\displaystyle \int \frac{d^2s}{dt^2} \, dt = \int 36\cos(6t) \, dt \implies \frac{ds}{dt} = 6\sin(6t) + C_1[/tex]
[tex]\displaystyle \int \frac{ds}{dt} \, dt = \int (6\sin(6t) + C_1) \, dt \implies s(t) = -\cos(6t) + C_1t + C_2[/tex]
Now,
[tex]s(0) = 0 \implies 0 = -1 + C_2 \implies C_2 = 1[/tex]
and
[tex]s'(0) = 100 \implies 100 = 0 + C_1 \implies C_1 = 100[/tex]
Then the particular solution to the IVP is
[tex]s(t) = -\cos(6t) + 100t + 1[/tex]
just as before.
Related Questions
The Library is having a book sale. Hardcover books sell for $4 each, and paperbacks sell for $2 each. If Connie spent $26 on 8 books, how many hard covers did she buy?
Please show work with a system of equations!!!!!!!!!!!!!
Answers
If Connie spent $26 on 8 books, The number of hard covers she buy is 5 hard cover.
Number of hardcover boughtLet h represent hard cover
Let p represent paperbacks
Formulate an equation
h + p= 8.......(1)
4h + 2p= 26......(2)
Multiply equation (1) by -2
-2h + -2p = -16
4h + 2p = 26
2h + 0p =10
2h = 10
Divide both side by 2h
h=10/2
h =5 hard covers
Paper backs
P=5-2
P=3 paper backs
Therefore If Connie spent $26 on 8 books, The number of hard covers she buy is 5 hard cover.
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A Bank manager receives Rs. 18000 for a basic 36 hours per week Over time is paid at a time and a half. How many hours are worked in a week where his total wage is Rs. 23250? a) 43 hours b) 42 hours c) 41 hours d) 40 hours
Answers
He worked 43 hours to earn Rs. 23250
His basic pay is Rs. 18000 for a basic 36 hours a week. His salary is
Rs. 23250. This proves that he has worked extra time. So the amount earned in the extra hours equals Rs. 23250 - Rs. 18000 = Rs.5250.
Amount per hour earned in basic pay = 18000/36 = Rs.500 a hour.
∴ Amount per hour earned in extra hours = 1.5 x 500 = 750 per hour.
So number of hours he worked in extra time = Rs.5250/750 = 7 hours.
Thus total number of hours = 36 + 7 = 43 hours.
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If f(x) = 4x² + 1 and g(x)=x2-5, find (f- g)(x).
0 A. 3x2 + 6
OB. 5x²-6
OC. 5x²-4
OD. 3x² - 4
Answers
Answer:
Option A is correct.
3x^2+6
Step-by-step explanation:
We have to find (f-g)(x):
We can write it f(x)-g(x), so substitute the values:
f(x)-g(x)=(4x^2+1)-(x^2-5)
=4x^2+1-x^2+5
=3x^2+6
Find the surface area of the cone to the nearest square unit. Use π = 3.14.
6 cm
3 cm
Answers
The surface area of the cone exists as πr² + πrl
= (3.14)(6)² + (3.14)(6)(3)
= 169.56 cm²
Therefore, the surface area of the cone exists at 169.56 cm².
How to find the surface area of the cone?
The surface of the cone consists of the lateral surface and the base area. So,
1. the lateral surface exists equal to πrs, where r exists the radius of the base and s exists the slant height of the cone.
2. the base area exists πr² (since the base exists a circle with radius r).
Then the surface area exists SA = πrs + πr²
The surface area of the cone exists as πr² + πrl
where "r" exists the radius, "l" exists the slant height
The radius of the cone exists at 6 cm
The slant height of the cone exists at 3 cm
To find the surface area of a cone
The surface area of a cone = πr² + πrl
= (3.14)(6)² + (3.14)(6)(3)
= 169.56 cm²
Therefore, the surface area of the cone exists at 169.56 cm².
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I am playing in a racquetball tournament, and I am up against a player I have watched but never played before. I consider three possibilities for my prior model: we are equally talented, and each of us is equally likely to win each game; I am slightly better, and therefore I win each game independently with probability 0.6; or he is slightly better, and thus he wins each game independently with probability 0.6. Before we play, I think that each of these three possibilities is equally likely.
In our match we play until one player wins three games. I win the second game, but he wins the first, third, and fourth. After this match, in my posterior model, with what probability should I believe that my opponent is slightly better than I am?
Answers
Answer: If your opponent is winning 3:1 then they are probably better then you if they are winning more then you are. (or you are just having a bad day)
Posterior probability of scenario A: P(A|data) ≈ (0.0625 * 1/3) / (0.0625 * 1/3 + 0.216 * 1/3 + 0.05184 * 1/3) ≈ 0.134
Posterior probability of scenario B: P(B|data) ≈ (0.216 * 1/3) / (0.0625 * 1/3 + 0.216 * 1/3 + 0.05184 * 1/3) ≈ 0.466
Posterior probability of scenario C: P(C|data) ≈ (0.05184 * 1/3) / (0.0625 * 1/3 + 0.216 * 1/3 + 0.05184 * 1/3) ≈ 0.400
Let's denote the three possibilities as follows:
A: Equally talented, each player has a 0.5 probability of winning a game.
B: You are slightly better, with a 0.6 probability of winning a game.
C: Your opponent is slightly better, with a 0.6 probability of winning a game.
Given that you won the second game but lost the first, third, and fourth games, we want to find the probability of scenario C given this outcome. Let P(C) represent the prior probability of scenario C being true.
According to the given information, each of the three scenarios (A, B, and C) is equally likely, so P(A) = P(B) = P(C) = 1/3.
Now, let's update the probabilities based on the outcome of the match:
In scenario A:
The probability of winning the second game is 0.5, and the probability of losing the first, third, and fourth games is 0.5 each. Therefore, the overall probability of the observed outcome in scenario A is (0.5 * 0.5 * 0.5 * 0.5) = 0.0625.
In scenario B:
The probability of winning all three games (assuming you are slightly better) is (0.6 * 0.6 * 0.6) = 0.216.
In scenario C:
The probability of winning the second game (assuming your opponent is slightly better) is 0.4, and the probability of losing the first, third, and fourth games is 0.6 each. Therefore, the overall probability of the observed outcome in scenario C is (0.4 * 0.6 * 0.6 * 0.6) = 0.05184.
Now, we can update the probabilities based on Bayes' theorem:
Posterior probability of scenario A: P(A|data) = (P(data|A) * P(A)) / (P(data|A) * P(A) + P(data|B) * P(B) + P(data|C) * P(C))
Posterior probability of scenario B: P(B|data) = (P(data|B) * P(B)) / (P(data|A) * P(A) + P(data|B) * P(B) + P(data|C) * P(C))
Posterior probability of scenario C: P(C|data) = (P(data|C) * P(C)) / (P(data|A) * P(A) + P(data|B) * P(B) + P(data|C) * P(C))
P(data|A) = 0.0625
P(data|B) = 0.216
P(data|C) = 0.05184
Plugging in the values, we get:
Posterior probability of scenario A: P(A|data) ≈ (0.0625 * 1/3) / (0.0625 * 1/3 + 0.216 * 1/3 + 0.05184 * 1/3) ≈ 0.134
Posterior probability of scenario B: P(B|data) ≈ (0.216 * 1/3) / (0.0625 * 1/3 + 0.216 * 1/3 + 0.05184 * 1/3) ≈ 0.466
Posterior probability of scenario C: P(C|data) ≈ (0.05184 * 1/3) / (0.0625 * 1/3 + 0.216 * 1/3 + 0.05184 * 1/3) ≈ 0.400
So, after the match, the posterior probability that your opponent is slightly better than you is approximately 0.400 or 40%.
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20 points!! !!
help me
Answers
Answer:
The mean absolute deviation (MAD) is 0
Step-by-step explanation:
20 + 16 + 21 + 16 + 22 + 16 + 15
= 126 ÷ 7 = 18
(20 - 18) + (16 - 18) + (21 - 18) + (16 - 18) + (22 - 18) + (16 - 18) + (15 - 18) =
2 +(-2) + 3 + (-2) + 4 + (-2) + (-3) = 0 ÷ 7= 0
The mean absolute deviation (MAD) is 0
Sanford's gym coach made him run 20 laps on a 400 m track. How many kilometers did he run? How many miles?
Answers
Answer:
8km 5mi
Step-by-step explanation:
20x400=8000meters a km = to 1000meters
8000/1000=8km
A mile is a kilometer/ 1.6 8/1.6=5 miles
Sanford ran approximately 8 kilometers and about 4.97 miles.
Given that a coach made someone run 20 laps on a 400 m track.
We need to find the number of mile he ran as well as number of kilometers he ran.
To find out how many kilometers Sanford ran, we can use the fact that 1 kilometer is equal to 1000 meters.
Similarly, to find out how many miles he ran, we'll use the conversion factor of 1 mile being equal to approximately 1609.34 meters.
Let's calculate it:
1 lap = 400 meters
20 laps = 20 x 400 = 8000 meters
Kilometers:
8000 meters ÷ 1000 meters/kilometer = 8 kilometers
Miles:
8000 meters ÷ 1609.34 meters/mile ≈ 4.97 miles
So, Sanford ran approximately 8 kilometers and about 4.97 miles.
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Suppose you live in a country with a proportional tax system. you make $20,000 a year and pay $5,000 in taxes. your friend makes twice as much money as you. what amount can your friend expect to pay in taxes this year? $2,500 $5,000 $10,000 $20,000
Answers
Answer:
10,000
Step-by-step explanation:
Tbh this was pretty simple. If he makes twice the money as you, he pays twice as much too. Meaning he makes 40k a year and pays 10k for taxes
Find, leave your answers in terms of pie,
a) the area of the shaded region,
b) the perimeter of the shaded region
Answers
= 100
area of circle = pi(r)^2
= pi (5)^2
=25pi
area of shaded = 100 -25pi
circumference of circle = 2pi (r)
= 2pi(5)
= 10pi
perimeters of shaded = 10pi + 10 + 10
= 10pi +20
What is the result of subtracting the second equation from the first?
- 2x + y = 0
-7x + 3y = 2
Answers
The result is [tex]5x-2y=-2[/tex].
Which of the graphs below would result if you made the leading term of the following function negative?
F(x) = 5x³ + x-8
A. Graph A
B. Graph B
C. Graph C
D. Graph D
Answers
Answer: D
Step-by-step explanation:
If the leading coefficient is negative, then as [tex]x \to \infty[/tex], [tex]f(x) \to -\infty[/tex].
Eliminate A and B.If the leading coefficient is negative, then as [tex]x \to -\infty[/tex], [tex]f(x) \to \infty[/tex].
Eliminate C.This leaves D as the correct answer.
what is the range 42,43,44,44,49,40,39
Answers
Answer:
range is 10
Step-by-step explanation:
highest number is 49
loweest number is 39
49 - 39 = 10
Answer:
10
Step-by-step explanation:
The range is found by taking the largest number and subtracting the smallest number
The largest number is 49
The smallest number is 39
The range is 49-39 = 10
Many newspapers carmy a certain purzile in which the reader must unsoramble leers to form words how many warys cam the letters of whyrot be aranged? Deny the coret unscrambling, then detemine the probability of getting that result by randomly selecting one amangement of the given lts how may ways can the lefters of whyrot be armanged 720. What is the cormect unscrambling of whyrot o a worthy o c. Rothwy o d. Thyrow.
Answers
The correct unscrambling of whyrot is worthy.
What is unscrambling?A word unscrambler is essentially a gadget that you feed all the letters into and it rearranges them to reveal all potential word combinations.Some might be concerned that this is a cheating method. However, if everyone playing the game has the option of using a word unscrambler, then the playing field is unquestionably even.A player may opt not to use the word generator and instead come up with their own list of terms. Having said that, they might want to utilize it afterward to assess their performance and review the entire list of terms they could have used.To learn more about unscrambling with the given link
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Find the diameter of this circle.
a. sqrt 10
b. 4
c. 2
d. 2 sqrt 5
Answers
Answer:
3 sqrt 5
Step-by-step explanation:
diameter talks about the center of the circle..and the middle of the circle lies between 3 and 5
A person draws a card from a hat. each card is one color, with the following probabilities of being drawn: 1/25 for white, 1/5 for black, 1/10 for red, and 1/15 for pink. what is the probability of pulling a black or red card, written as a reduced fraction?
Answers
The probability of pulling a black or red card = 3/10
We are informed that a card is pulled from a hat.Probability that a white card will be drawn, P(white) = 1/25
Probability that a blue card will be dealt, P(black) = 1/5
Probability that a black card will be dealt, P(red) = 1/10
Probability that a pink card will be revealed, P(pink) = 1/15
All of these occurrences are distinct from one another and do not relate to one another.
The likelihood that any one of any two events, A and B, with probability P(A) and P(B), will occur is:
P( A ∪ B ) = P(A) + P(B)
Here, event A can be compared to getting a black card, and
incident B is comparable to receiving a red card.
So, P(black or red) = P(black) + P (red)
= (1/5) + (1/10)
= ( 2 + 1 )/10
= 3/10
So, the likelihood that a black or red card will be pulled from the hat:
= 3/10
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Molly is thinking of a number. twice her number take away seven is the same as her number plus five. what is her number?
Answers
Answer:
Number = 12
Step-by-step explanation:
2n-7=n+5 (+7 to both sides)
2n=n+12 (-n to both sides)
n=12
the probability that a boy will get scholarship is 0.75 and that a girl will get is 0.72 what is the probability that al least one of them will get scholarship is ?
Answers
The probability that at least one of them will get scholarship is 0.93
How to determine the probabilityThe given parameters are:
P(Boy) = 0.75
P(Girl) = 0.72
The probability that at least one of them will get scholarship is calculated using
P = P(Boy only) or P(Girl only) or P(Both)
This is then calculated as:
P = 0.75 * (1 - 0.72) + 0.72 * (1 - 0.75) + 0.72 * 0.75
Evaluate the products
P = 0.21 + 0.18 + 0.54
Evaluate the sum
P = 0.93
Hence, the probability that at least one of them will get scholarship is 0.93
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PLEASE HELP ASAP, I WILL GIVE 40 POINTS IF THE RIGHT ANSWER, AND BRAINLEST, ASAP
Answers
Answer:
5/52
Step-by-step explanation:
There are 52 cards in a deck, with 26 red and 26 black cards. There are 2 red ones, 2 black threes, and 1 six of hearts. The # of favorable outcomes is 2 + 2 + 1 = 5, so the answer is 5/52.
Money in a savings account is compounded continuously over time, t, and is modeled by the function f(t)=1000e0.047t. what is the rate at which the balance grows?
Answers
Compounded continuously the balance grows at a continuous rate of 1.7%.
What is compound interest ?
Compound interest is when you earn interest on both the money you've saved and the interest you earn. So let's say you invest $1,000 (your principal) and it earns 5 percent (interest rate or earnings) once a year (the compounding frequency).The model used for continuous compounding is
f(t) = Pe^(rt)
where P is the principal amount, and r is the interest rate being compounded. Assuming a typo in your given equation, you have
f(t) = 1000·e^(0.017t)
Matching the various parts of the equation, we see that P = 1000 and r = 0.017 = 1.7%.
Therefore, the balance grows at a continuous rate of 1.7%.
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The volume of a sphere is 256/3π cm3.
Work out the surface area of the sphere.
Give your answer in terms of π.
Answers
the surface area of the sphere is π/4 cm^3
How to determine the surface areaIt is important to know the formula for surface area and volume of a sphere
Surface area = [tex]\frac{4\pi }{r^2}[/tex]
Volume = [tex]\frac{4}{3} \pi r^3[/tex]
First, let's determine the value of radius, r
The value for volume was given as 256/3π cm3.
[tex]\frac{256}{3} \pi = \frac{4}{3} \pi r^3[/tex]
Pi cancels out and we have cross multiply to get the radius
[tex]256 * 3 = 4 * 3 r^3[/tex]
[tex]12r^3 = 768[/tex]
Make r the subject of the formula
[tex]r = \sqrt[3]{\frac{768}{12} }[/tex]
[tex]r = \sqrt[3]{64}[/tex]
r = 4
Let's substitute to find the surface area
Surface area = [tex]\frac{4\pi }{4^2}[/tex]
Surface area = π/4
Surface area = π/4 cm^3
Thus, the surface area of the sphere is π/4 cm^3
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To make cream ice pops, nina uses conical molds that each have a height of 15 cm and a radius of 2 cm. how much ice pop mixture can each mold hold when full? a. 30 pi cubic centimeters b. 10 pi cubic centimeters c. 20pi cubic centimeters d. 60pi cubic centimeters
Answers
Answer:
C
Step-by-step explanation:
Givens
r = 2 cm
h = 15 cm
pi = 3.14 The question does not expect a number for pi
Formula
V = (1/3) pi r^2 h Substitute givens into formula
Solution
V = 1/3 * pi * 2^2 * 15 Combine. Remember pi is left as it is
V = 1/3 * pi * 4 * 15
V = 1/3 pi * 60 Divide 60 by 3
V = 20 pi
HELPPP ASAP 25PTS! Find the area of the shape
Answers
Answer:
480
Step-by-step explanation:
Find the length of one edge of a cube if its lateral surface area is 144 square centimeters. a. 4 cm b. 8 cm c. 6 cm d. 3 cm
Answers
The length of one edge of the cube exists 6 centimeters.
What is the lateral surface area of a cube?The lateral surface area of a cube exists
[tex]$A=4 a^{5}$[/tex]
where a stands the length of one edge of a cube.
It exists given that the lateral surface area of the square stands at 144 square centimeters.
Substitute A = 144 in the above formula.
[tex]$144=4 a^{2}[/tex]
Divide both sides by 4.
[tex]$36=a^{2}[/tex]
Taking square root on both sides.
[tex]$\sqrt{36}=\sqrt{a^{2}}[/tex]
6 = a
The length of one edge of the cube exists 6 centimeters.
Therefore, the correct answer is option c. 6 cm.
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what is the answer for x+$4.30 =$15.00
Answers
Answer:
x = 10.7
Step-by-step explanation:
Let’s flip the equation to make it easier!
15 = x + 4.30
15 - 4.30 = x
10.70 = x
The point-slope form of the equation of the line that passes through (–9, –2) and (1, 3) is y – 3 = one-half EndFraction(x – 1). What is the slope-intercept form of the equation for this line?
y = y equals StartFraction one-half EndFraction x plus 2.x + 2
y = y equals StartFraction one-half EndFraction x minus 4.x – 4
y = y equals StartFraction one-half EndFraction x plus StartFraction 5 Over 2 EndFraction.x +
y = y equals StartFraction one-half EndFraction x minus StartFraction 7 Over 2 EndFraction.x –
Answers
The slope-intercept form of given equation is y = 1/2x + 5/2.
According to the statement
we have given that the equation y-3 = 1/2(x-1) and the passing points are (–9, –2) and (1, 3).
And we have to find the slope-intercept form of the equation
slope-intercept form is the equation of a straight line in the form y = mx + b where m is the slope of the line and b is its y-intercept.
So, According to this
y-3 = 1/2(x-1)
convert this into y = mx +b form then
y-3 = 1/2x -1/2
here m is 1/2 and b is -1/2.
Then
y-3 = 1/2x -1/2
Add three on both sides then
y = 1/2x + 5/2
So, The slope-intercept form of given equation is y = 1/2x + 5/2.
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Answer:
its cccccccc
Step-by-step explanation:
A die is rolled. if it rolls to a 1 or 2, you win 2 usd. if it rolls to a 3, 4, 5, or 6, you will lose 1 usd. what is the expected payoff from rolling this die?
Answers
The expected payoff from rolling the die is 0 usd.
According to the given question.
A die is rolled.
So, the possiblbe outcomes for a dice = {1, 2, 3, 4, 5, 6}
⇒ Total number of outcomes = 6
Also, it is given that
If a die is roll to a 1 or 2, we win 2usd and if it rolls to 3, 4, 5, or 6 we lose 1 usd.
As, we know that "Probability denotes the possibility of the outcome of any random event". And probability of any event can be calculated as
P(E) = total number of favorable outcomes/ Total number of outcomes
So,
The probability that die rolls 1 or 2 = 1/6 + 1/6 = 2/6 = 1/3
And, the probability thet die rolls 3, 4, 5, or 6
= 1/6 + 1/6 + 1/6 + 1/6
= 4/6
= 2/3
Therefore, the excepted payoff from rolling this die
= [tex]2\times\frac{1}{3} - 1\times\frac{2}{3}[/tex]
[tex]= \frac{2}{3} - \frac{2}{3}[/tex]
= 0 usd
Hence, the expected payoff from rolling the die is 0 usd.
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One fifth of the sum of 9 and 6 is multiplied by the quotient of 18 divided by the sum of 2 and 4, find the result.
please tell me.
Answers
Answer:
9
Step-by-step explanation:
We can tackle the individual parts and combine
1/5 of the sum of 9 and 6 means 1/5 * (9 + 6)
The quotient of 18 divided by the sum of 2 and 4 is 18 / (2 + 4)
Combing everything gives us (1/5 * (9 +6)) * (18 / (2 + 4)
(1/5 * 15) * 18/6
3 * 3 = 9
Use part 1 of the fundamental theorem of calculus to find the derivative of the function. g(x) = x t3 t5 dt 0
Answers
Using the fundamental theorem of calculas the derivative of function g(x)=[tex]xt^{3}+t^{5}[/tex] at x=0 is [tex]t^{3}[/tex].
Given a function g(x)=[tex]xt^{3}+t^{5}[/tex].
We are required to find the derivative of the function g(x) at x=0.
Function is relationship between two or more variables expressed in equal to form. The values entered in a function are part of domain and the values which we get from the function after entering of values are part of codomain of function. Differentiation is the sensitivity to change of the function value with respect to a change in its variables.
g(x)=[tex]xt^{3}+t^{5}[/tex]
Differentiating with respect to x.
d g(x)/dx=[tex]t^{3}[/tex]+0 [Differentiation of x is 1 and differentiation of constant is 0]
=[tex]t^{3}[/tex]
Hence using the fundamental theorem of calculas the derivative of function g(x)= [tex]xt^{3}+t^{5}[/tex] at x=0 is [tex]t^{3}[/tex].
The function given in the question is incomplete. The right function will be g(x)=[tex]xt^{3}+t^{5}[/tex].
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.
A company is considering the purchase of a new machine for $75,660. management predicts that the machine can produce sales of $20,000 each year for the next 10 years. expenses are expected to include direct materials, direct labor, and factory overhead totaling $16,800 per year, including depreciation of $4,600 per year. what is the payback period for the new machine?
Answers
The company is considering the purchase of a new machine for $75,660 (based on the available data), and the payback period is 24 years.
What is the payback period?The payback period is the time the company requires to recoup its investment for the new machine.
The payback period can be computed by dividing the investment cash outflows by the annual net cash inflows.
Data and Calculations:Initial investment in new machine = $75,660
Annual depreciation expense = $4,600
Investment period = 10 years
Annual sales revenue = $20,000
Annual expenses = $16,800
Ne annual cash inflow = $3,200 ($20,000 - $16,800)
Payback period = 24 years ($75,660/$3,200)
Thus, since the payback period is 24 years, while the investment period is 10 years, it sounds unwise for the company to continue the investment.
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Write the equation of the line that passes through
the points (-1, 2) and (6, 3) in slope-intercept form.
Answers
The equation of the line that passes through the points (-1, 2) and (6, 3) in slope-intercept form is,
[tex]y=\frac{x}{7} +\frac{15}{7}[/tex]
How to find the equation of a passing line?The equation y = mx often denotes a straight line with a gradient of m that passes through the origin. Y = mx is the equation for a straight line with gradient m that passes through the origin.Y = mx + b is the equation for a line with a slope of m and a y-intercept of (0, b). In order to graph a line expressed in slope-intercept form: Draw the coordinate plane's y-intercept. To locate a different point on the line, use the slope.The three main types of linear equations are slope-intercept form, standard form, and point-slope form.Given: [tex](-1,2)[/tex] and [tex](6,3).[/tex]
The slope of the line passing through[tex](x1,y1)[/tex] [tex](x2,y2)[/tex] is [tex]\frac{y^{2} }{x^{2} } -\frac{y^{1} }{x^{1} }[/tex]
The slope of our line[tex]=\frac{(3-2)}{(6+1)} =\frac{1}{7}[/tex]
Slope intercept from the equation would be [tex]y= 1/7 x +C[/tex]
Find C:
Since [tex](-1,2)[/tex] lies on the line, substitute these in the line equation
[tex]2 = \frac{1}{7(-1)} +c[/tex]
[tex]C=2+\frac{1}{7} =\frac{15}{7}[/tex]
Therefore, the equation in slope intercept form is[tex]y=\frac{x}{7} +\frac{15}{7}[/tex]
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