We would like to know the velocity of the block when it reaches some position x. Finding this requires an integration. However, acceleration is defined as a derivative with respect to time, which leads to integrals with respect to time, but the force is given as a function of position. To get around this, use the chain rule to find an alternative definition for the acceleration ax that can be written in terms of vx and dx/ dx.
Answers
Answer:
An alternative definition for the acceleration ax that can be written in terms of \(v_x\) and \(\frac{dv_x}{dx}\) is \(a_x=v_x \frac{dv_x}{dx}\)
Step-by-step explanation:
We know that :
\(a_x=\frac{dv_x}{dt}\)
Now we are supposed to find an alternative definition for the acceleration ax that can be written in terms of \(v_x\) and \(\frac{dv_x}{dx}\)
So, We will use chain rule over here :
\(a_x=\frac{dv_x}{dt}\\a_x=\frac{dv_x}{dt} \times \frac{dx}{dx}\\a_x=\frac{dv_x}{dx} \times \frac{dx}{dt}\\a_x=\frac{dv_x}{dx} \times \frac{dx}{dt} [\frac{dx}{dt}=v_x]\\a_x=\frac{dv_x}{dx} \times v_x\\a_x=v_x\frac{dv_x}{dx}\)
Hence an alternative definition for the acceleration ax that can be written in terms of \(v_x\) and \(\frac{dv_x}{dx}\) is \(a_x=v_x \frac{dv_x}{dx}\)
The alternative definition for the acceleration ax that can be written in terms of vx and dx/ dx is \(a_x = v_x \frac{dv_x}{dx}\)
Chain rule:Here we used the chain rule:
It is the basic method for differentiating a composite function. Here the first factor on the right, Df(g(x)), represents that the derivative of f(x) is first found and then x, wherever it arises, is replaced by the function g(x).
So,
\(a_x = \frac{dv_x}{dt}\\\\ = \frac{dv_x}{dt} \times \frac{dx}{dx}\\\\= \frac{dv_x}{dx} \times \frac{dx}{dt}\\\\ = \frac{dv_x}{dx} \times \frac{dx}{dt} (\frac{dx}{dt} = v_x)\\\\ = \frac{dv_x}{dx} \times v_x\\\\= v_x\frac{dv_x}{dx}\)
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Related Questions
4/7+2/3=??
Please explain to :)
Answers
Answer: 1 5/21
Step-by-step explanation: change 4/7 into 12/21 and 2/3 into 14/21. Now that you have a common denominator, add the numerators. 26/21. Simplify into 1 5/21
The school media specialist has catalogue 2/3 of the new books in a shipment. If she has catalogued 52 books, what is the total number of books in the shipment?
Answers
Answer:
78 Books
Step-by-step explanation:
To answer the problem divide 52 by 2, then take the answer(26) and multiply by 3 which leads you to the 78.
What is an equation of the line that passes through the points (-2, 1)(−2,1) and (-6, -5)(−6,−5)?
Answers
Answer:
ind the slope of the original line and use the point-slope formula y − y 1 = m ( x − x 1 )
to find the line parallel to x + 4y = 28 .
Step-by-step explanation:
what is -2 x 3 i do not understand this and this is my last problem
Answers
Answer:
-6
Step-by-step explanation:
if they were both positive numbers, it would be 6. But when you multiply a negative by a positive, the answer is negative.
Answer:
-6
Step-by-step explanation:
When you multiply a positive number by another positive number, you will always get a positive number as your answer. Same thing for negative. If you multiply a negative by a negative, you will always get a positive. However, when you multiply a negative by a positive, you will always get a negative number.
Since you know this, you can multiply 2 by 3, which is 6. Because 2 is negative and 3 is positive, you know that the answer must be negative. Therefore, you add the negative symbol to 6, giving you -6.
I hope this isn't too confusing. Please let me know if you have any more questions. Good luck!
What is the product of 14.5 and 8.32
Answers
Answer:
120.64
Step-by-step explanation:
The answer is 120.64 because 14.5 multiplied by 8.32 is 120.64
P.S Can I have brainliest?
Compute the missing x and y values so that each ordered pair will satisfy the given equation y=2x+4
Answers
The missing ordered pairs that satisfy the equation y = 2x + 4 are (3, 10) and (2, 8).
The equation given is y = 2x + 4. To compute the missing x and y values, we need to substitute the given ordered pairs into the equation and solve for the missing variable.
Let's assume we have an ordered pair (x, y) that satisfies the equation y = 2x + 4.
For example, let's say one missing value is x = 3. We can substitute this into the equation:
y = 2(3) + 4
y = 6 + 4
y = 10
So, the missing ordered pair is (3, 10).
Similarly, if another missing value is y = 8, we can substitute this into the equation and solve for x:
8 = 2x + 4
4 = 2x
x = 2
So, the missing ordered pair is (2, 8).
In summary, the missing x and y values that satisfy the equation y = 2x + 4 are (3, 10) and (2, 8).
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Every 2 centimeters on a floor plan represents
meters of the house. The dining room is 8 cm by
10 cm on the floor plan, and the bedroom is 6cm by10cm on the floor plan. If installing tile costs $34
per square meter and installing carpet costs $21 per
square meter, how much would it cost to install tile
in the dining room and install carpet in the bedroom?
Show your work.
Answers
Given statement solution is :- It would cost $680 to install tile in the dining room and $315 to install carpet in the bedroom.
To find the cost of installing tile in the dining room and carpet in the bedroom, we need to calculate the areas of both rooms first.
Given:
Every 2 centimeters on the floor plan represents 1 meter of the house.
Dining Room:
On the floor plan, the dining room is 8 cm by 10 cm.
Converting this to meters, the dimensions of the dining room are 8 cm / 2 = 4 meters by 10 cm / 2 = 5 meters.
The area of the dining room is 4 meters * 5 meters = 20 square meters.
Bedroom:
On the floor plan, the bedroom is 6 cm by 10 cm.
Converting this to meters, the dimensions of the bedroom are 6 cm / 2 = 3 meters by 10 cm / 2 = 5 meters.
The area of the bedroom is 3 meters * 5 meters = 15 square meters.
Now, let's calculate the costs.
Cost of Tile:
The cost of installing tile is $34 per square meter.
The area of the dining room is 20 square meters.
Therefore, the cost of installing tile in the dining room is 20 square meters * $34/square meter = $680.
Cost of Carpet:
The cost of installing carpet is $21 per square meter.
The area of the bedroom is 15 square meters.
Therefore, the cost of installing carpet in the bedroom is 15 square meters * $21/square meter = $315.
Therefore, it would cost $680 to install tile in the dining room and $315 to install carpet in the bedroom.
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Víctor has 2 times as many trophies as Dean. Together ,víctor and Dean have 27 trophies does víctor have?
Answers
Answer:
Victor has 18 trophies
Step-by-step explanation:
Let's set up "let statements"
Let d = Dean's trophies
Since Victor has 2 times as many trophies as Dean, we can set up a let statement for Victor like this...
Let 2d = Victor's trophies
Now we can set up an equation! Since we know Dean and Victor have 27 trophies altogether...our equation has to involve addition...
2d + d = 27
Combine like terms...(2d and d)
3d = 27
Divide 3 on both sides to isolate the variable "d"
3d ÷ 3 = d
27 ÷ 3 = 9
So...
d = 9
That means Dean has 9 trophies. But we are not done yet because we need to figure out how many trophies Victor has. Since Victor has 2 times the number of trophies as Dean we can do...
2 · 9 = 18
Therefore, Victor has 18 trophies!
Hope this helps :)
Increase 2,400 by 5%
Answers
Increasing 2400 by 5% gives us 2520
we can increase the value by using the formula:
\(initial value+ percentage increase *initial value\) = increased percentage
in the aforementioned question we have
initial value = 2400
percentage increase = 5%
thus we can find out the increased percentage by:
2400 + 2400 X (5/100)
=2400 + 120
=2520
the value by which 2400 is increased is 120
to arrive at the increased value which is 2520
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Which expressions are equivalent?
1. 3x-7y and -7y+3x
2. 3x-7y and 7y-3x
3. 3x-7y and 3y-7x
4. 3x-7y and-3y+7x
Answers
Answer:
1. 3x-7y and -7y+3x
Step-by-step explanation:
1. 3x -7y and -7y +3x
This is correct because the terms remain unchanged. The -7y stays a -7y and the positive 3x stays a positive 3x.
2. 3x -7y and 7y -3x
This is not correct because the signs of the 3x and 7y switch. For the expressions to be equivalent, the signs must remain unchanged.
3. 3x -7y and 3y -7x
This is not correct because the variables of the 3 and 7 switched. The variables need to stay the same, for the expressions to be equivalent.
4. 3x-7 and -3y+7x
This is not correct because both the variables and the signs of the expressions changed. Both the signs and variables would need to stay the same in order to be equivalent.
The machinery in a cereal plant fills 350 g boxes of cereal. The specifications for the machinery permit for a certain amount of fill tolerance. It is found that the weights of filled cereal boxes are normally distributed with a mean of 350 g and a standard deviation of 4 g. What is the probability that a box of cereal is under filled by 5 g or more?
Answers
There is approximately an 89.44% probability that a box of cereal is underfilled by 5 g or more.
To find the probability that a box of cereal is underfilled by 5 g or more, we need to calculate the probability of obtaining a weight measurement below 345 g.
First, we can standardize the problem by using the z-score formula:
z = (x - μ) / σ
Where:
x = the weight value we want to find the probability for (345 g in this case)
μ = the mean weight (350 g)
σ = the standard deviation (4 g)
Substituting the values into the formula:
z = (345 - 350) / 4 = -1.25
Next, we can find the probability associated with this z-score using a standard normal distribution table or a statistical calculator.
The probability of obtaining a z-score less than -1.25 is approximately 0.1056.
However, we are interested in the probability of underfilling by 5 g or more, which means we need to find the complement of this probability.
The probability of underfilling by 5 g or more is 1 - 0.1056 = 0.8944, or approximately 89.44%.
Therefore, there is approximately an 89.44% probability that a box of cereal is underfilled by 5 g or more.
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slope is 2
y intercept is 0
equation is y = 2x
THANKS
0 freee points
Answers
Answer:
what
Step-by-step explanation:
Answer:
do you need help???
Step-by-step explanation:
Pre calculus Log26x = 1 + 2 log2y1 + log6x = log6 (15y- 25)
Answers
Hello there. To solve this simultaneous equation, we'll have to remember some properties about logarithms.
Given the equations:
\(\begin{gathered} \log _2(6x)=1+2\log _2(y) \\ 1+\log _6(x)+\log _6(15y-25) \end{gathered}\)First, we'll transform those ones into logarithms applying the following rule in reverse:
\(\log _a(a)=1\)Thus, we get:
\(\log _2(6x)=\log _2(2)+2\log _2(y)\)For the first equation; Now, apply the power and product rules in reverse:
\(\begin{gathered} \log _c(a^b)=b\cdot\log _c(a) \\ \log _c(ab)=\log _c(a)+\log _c(b) \end{gathered}\)In order to obtain:
\(\log _2(6x)=\log _2(2)+\log _2(y^2)=\log _2(2y^2)\)Since both logarithms have the same base, the expressions inside them must be equal as well, therefore:
\(\begin{gathered} 6x=2y^2 \\ \\ y^2=3x \end{gathered}\)Now, going for the second equation, we'll apply the same three rules as before:
\(\begin{gathered} 1+\log _6(x)=\log _6(15y-25) \\ \log _6(6)+\log _6(x)=\log _6(15y-25) \\ \log _6(6x)=\log _6(15y-25) \\ 6x=15y-25 \end{gathered}\)The thing is that we can plug in 6x as y², found on the first equation, to get a quadratic equation for y:
\(2y^2=15y-25\)Subtract 15y-25 on both sides of the equation
\(2y^2-15y+25=0\)Using the quadratic formula, we take the roots of the equation:
\(y=\frac{15\pm\sqrt[]{225-4\cdot2\cdot25}}{2\cdot2}=\frac{15\pm\sqrt[]{25}}{4}=\frac{15\pm5}{4}\)So we have two possible roots:
y = (15 - 5)/4 = 10/4 = 5/2 or y = (15 + 5)/4 = 20/4 = 5.
Plugging in this value in the first equation, we solve for x:
\(\begin{gathered} 6x=2\cdot\mleft(\frac{5}{2}\mright)^2 \\ 6x=2\cdot\frac{25}{4} \\ x=\frac{25}{12} \end{gathered}\)Or
\(\begin{gathered} 6x=2\cdot5^2 \\ 6x=2\cdot25=50 \\ x=\frac{25}{3} \end{gathered}\)The pair of solutions are:
\(\begin{gathered} (x,y)=\mleft(\frac{25}{3},5\mright) \\ (x,y)=\left(\frac{25}{12},\frac{5}{2}\right) \end{gathered}\)You can plug this into any of the equations and see if they truly satisfy them as an exercise.
A quality control engineer Is interested in the mean length of sheet insulation being cut automatically by machine. It is known that the standard deviation in the cutting length that this machine produces is 0.15 feet. A sample of 70 cut sheets yields a mean length of 12.14 feet. This sample will be used to obtain a confidence interval for the mean length cut by machine. Referring to problem statement, the Z value to use in obtaining the 99% confidence interval is approximately .A.1.645B. 1.96C.3.23D.2.58
Answers
Answer:
D.2.58
Step-by-step explanation:
We have that to find our \(\alpha\) level, that is the subtraction of 1 by the confidence interval divided by 2. So:
\(\alpha = \frac{1 - 0.99}{2} = 0.005\)
Now, we have to find z in the Ztable as such z has a pvalue of \(1 - \alpha\).
That is z with a pvalue of \(1 - 0.005 = 0.995\), so Z = 2.58.
The answer is given by option D.
- 30 = 12 – 6r
Pls help
Answers
Answer: r = 7
Step-by-step explanation:
Subtract 12 from both sides to isolate the r variable. You have -42 = -6r. Divide both sides by -6 to get r by itself and you get r = 7. Verify by substituting 7 as the r value and solving the equation.
Answer:
r=7
Step-by-step explanation:
First subtract 12 from both sides
Now you have -42=-6r
Next divide each side by -6
Now you have 7=r
And that is your answer
If 18 pound of fertilizer covers 25 square feet of ground, how much fertilizer, in pounds, is needed to cover 1 square foot of ground?
Answers
Answer:
you need exactly 0.72 fertilizer but since its pounds, you round up so the answer is 1 pound.
Step-by-step explanation:
The amount of fertilizer required to cover 1 square foot of ground is 0.72
What is Proportion?
The proportion formula is used to depict if two ratios or fractions are equal. The proportion formula can be given as a: b::c : d = a/b = c/d where a and d are the extreme terms and b and c are the mean terms.
Given data ,
Amount of fertilizer required to cover 25 square foot ground = 18 pound
Amount of fertilizer required to cover 1 square foot ground = Amount of fertilizer required / total square foot ground
Amount of fertilizer required to cover 1 square foot ground = 18 / 25
Therefore , Amount of fertilizer = 0.72 pound
Hence , the amount of fertilizer required to cover 1 square foot of ground is 0.72
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Simplify
12 - 6(2x + 7)
Answers
Answer:
-12x - 30
Step-by-step explanation:
12 - 6(2x + 7)
=> 12 - 12x - 42
=> -12x - 30
Answer:
6 (-5-2x)
Step-by-step explanation:
12-6(2x+7)
6(2-(2x+7)) factor the expression
6(2-2x-7) remove parentheses
6(5-2x) answer!
2x + 5y = 10
5y
x +
2.
+
= 4
Answers
An athlete runs at a speed of 9 miles per hour. If one lap is 349 yards, how many laps does he run in 22 minutes
Answers
An athlete run in 22 minutes is 19.232 laps
Given,
An athlete runs at a speed of 9 miles per hour.
and, If one lap is 349 yards.
To find the how many laps does he run in 22 minutes?
Now, According to the question:
Firstly, Convert the mph into yard per minute,
Remember that:
I mile = 1,760 yard
1hour = 60 minute
Convert the speed in miles/hour to yards/minute
9 \(\frac{miles}{hour}\) = 9\(\frac{1760}{60}\) = 264 yard/ min
We know that
The speed is equal to divide the distance by the time
Let
s → the speed
d → the distance in yards
t → the time in minutes
Using the formula :
Speed = distance/ time
Solve the distance:
d = speed x time
Speed = 264 yard/ minute
Time = 22 minute
Therefore,
Distance = 264 x 22
Distance = 5,808 yards
Divide the distance by 302 yards to find out the number of laps
= 5,808/ 302 = 19.232 laps
Hence, An athlete run in 22 minutes is 19.232 laps
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Your parents are purchasing a mobile home for $89,000. The sales tax is 4.2%, they make a $3,000 down payment, and they have an average credit score. How much is the PRINCIPAL BALANCE after applying their first month’s payment of $925.67?
Secured Unsecured
Credit APR (%) APR (%)
Excellent 4.75 5.50
Good 5.00 5.90
Average 5.85 6.75
Fair 6.40 7.25
Poor 7.50 8.40
A. $89,249.80
B. $88,245.05
C. $88,912.03
D. $89,021.98
Answers
The initial loan amount is the purchase price of the mobile home minus the down payment and the sales tax.
Initial loan amount = $89,000 - $3,000 - (4.2% * $89,000) = $81,738
Next, we need to determine the interest rate based on your parents' credit score. Since the problem states that they have an "average" credit score, we will use the average interest rates for secured and unsecured credit with an APR of 5.85% and 6.75%, respectively. Since this is a mobile home purchase, we will assume that the loan is secured and use an interest rate of 5.85%.
Using these values, we can calculate the principal balance after the first month's payment using the formula for the present value of an annuity:
PV = C * [(1 - (1 + r)^(-n)) / r]
where PV is the present value, C is the monthly payment, r is the monthly interest rate (5.85% / 12 = 0.4875%), and n is the number of months (30 years or 360 months).
Substituting the given values, we get:
PV = $925.67 * [(1 - (1 + 0.004875)^(-360)) / 0.004875]
PV = $81,276.05
Therefore, the principal balance after applying the first month's payment is $81,276.05.
Answer: B. $88,245.05 is not correct, the correct answer is $81,276.05
A pattern contains 3, 11, 5, 13, 7, and 15 dots. What are the next two terms of the sequence?
O9, 17
O 7, 13
O9, 15
O 7,11
Answers
The heights of the girls in Leila’s class to the nearest 1/2 inch are: 56 1/2,57,56 1/2,58,58,57 1/2,57 1/2,57,58 1/2, and57.Leila makes a dot plot of data. How many different heights will be included on the number line
Answers
If Leila makes a dot plot of the heights of the girls in her class to the nearest ¹/₂ inch, the number of different heights that will include on the number line is 5.
What is a dot plot?A dot plot is a data visualization tool that consists of data points plotted as dots on a graph with an x- and y-axis.
The number of dots plotted on each number line shows the frequency of the data group.
Height Frequency Cumulative Frequency
56¹/₂ 2 2
57 2 4
57¹/₂ 2 6
58 2 8
58¹/₂ 1 9
Thus, arranging the heights according to groups, the different heights on the number line can be classified into 5.
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The average age of doctors in a certain hospital is 42.0 years old with a standard deviation of 10.0 years. If 16 doctors are chosen at random for a committee, find the probability that the mean age of those doctors is less than 43.50 years. Assume that the variable is normally distributed. Group of answer choices
Answers
There is a 65.54% probability that the average age of those doctors is under 48.8 years.
What is probability?Science uses a figure called the probability of occurrence to quantify how likely an event is to occur.
It is written as a number between 0 and 1, or between 0% and 100% when represented as a percentage.
The possibility of an event occurring increases as it gets higher.
True mean = mean (or average)+/- Z*SD/sqrt (sample population)
Then,
Mean (average) = 48.0 years
The true mean must be less than 48.8 years.
SD = 6.0 years, and
Sample size (n) = 9 doctors
Using Z as the formula's subject:
Z= (True mean - mean)/(SD/sqrt (n))
Inserting values:
Z=(48.8-48.0)/(6.0/sqrt (9)) = 0.4
From the table of normal distribution probabilities:
At Z= 0.4, P(x<0.4) = 0.6554 0r 65.54%
Therefore, there is a 65.54% probability that the average age of those doctors is under 48.8 years.
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Complete question:
The average age of doctors in a certain hospital is 48.0 years old. suppose the distribution of ages is normal and has a standard deviation of 6.0 years. if 9 doctors are chosen at random for a committee, find the probability that the average age of those doctors is less than 48.8 years. assume that the variable is normally distributed.
Let i be the imaginary number √-1. Determine whether the expression a+bi, where a and b are real numbers, represents a real number or a non-real complex number for each case below. Select Real Number or Non-Real Complex number for each case.
Answers
Case 1: a = 0; b = 0 --> Real Number
Case 2: a = 0; b ≠ 0 --> Non-Real Complex Number
Case 3: a ≠ 0; b = 0 --> Real Number
Case 4: a ≠ 0; b ≠ 0 --> Non-Real Complex Number
Understanding Complex NumberFor each case, we can determine whether the expression a + bi represents a real number or a non-real complex number based on the values of a and b.
Case 1: a = 0; b = 0
In this case, both a and b are zero. The expression a + bi simplifies to 0 + 0i, which is equal to 0. Therefore, the expression represents a real number.
Case 2: a = 0; b ≠ 0
Here, a is zero, but b is nonzero. The expression a + bi becomes 0 + bi, where b is a nonzero real number multiplied by the imaginary unit i. Since the expression contains a nonzero imaginary part, it represents a non-real complex number.
Case 3: a ≠ 0; b = 0
In this case, a is nonzero, but b is zero. The expression a + bi simplifies to a + 0i, which is equal to a. As there is no imaginary part in the expression, it represents a real number.
Case 4: a ≠ 0; b ≠ 0
Here, both a and b are nonzero. The expression a + bi contains both a real part (a) and an imaginary part (bi). Thus, it represents a non-real complex number.
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In a certain skyscraper, the elevators whisk you to a restaurant in the skyscraper at a speed of 900 feet in 120 seconds. If the restaurant is 600 foet up, how long will it take you to reach the restaurant by elevator?
It will take ___ seconds to reach the restaurant using the elevator
(Type a whole number or a decimal)
Answers
9514 1404 393
Answer:
80 seconds
Step-by-step explanation:
For a constant rate, the time is proportional to the distance.
time/distance = t/(600 ft) = (120 s)/(900 ft)
t = (600/900)(120 s) = 80 s . . . . . . multiply by 600 ft, cancel units of ft
The time required to reach the restaurant will be 80 seconds.
Answer:
The time required to reach the restaurant will be 80 seconds.
Step-by-step explanation:
help me please
and thanks
Answers
Almost anything to the 0 power is 1.
7^0 = 1
(-8)^0 = 1
123478714979^0 = 1
The only exception is 0^0, which is indeterminant.
PLEASE HELP ME 10 POINTS PLEASE HELP ME
The aquarium is draining a large fish tank. The pump they are using can drain 40 gallons per hour. After 2 hours,there are 95 gallons left in the tank. Let x represent the number of hours and y represent the water left in the aquarium.
Write the equation
[ Select ] y=40x-175 or y= 40+15 or y= -40+175 0r y= 175 + 40
How many gallons were originally in the tank?
[ Select ] -40, 95 or 175
How long does it take to drain the tank?
[ Select ] 2,5 or 4.375 or -4.375
How many gallons of water are in the tank after it drained for 4 hours?
[ Select ] -15 or 15 or the tank is empty
I NEED 4 ANSWERS
Answers
Answer:
Gallons originally in tank:175
How long to drain te tank:4.375
How many gallons of water in tank after drained for 4 hours:15
Davis spent at least 65% of the money he earned babysitting this month. If Davis spent $39, how much money did Davis earn.
babysitting this month?
Answers
Answer:
60
Step-by-step explanation:
Formula = Number x 100
Percent = 39 x 100
65 = 60
Following shows the steps on how to derive this formula and find out 65% of what number is 39.
Step 1: If 65% of a number is 39, then what is 100% of that number? Setup the equation.
39
65% = Y
100%
Step 2: Solve for Y
Using cross multiplication of two fractions, we get
65Y = 39 x 100
65Y = 3900
Y = 3900
100 = 60
hope this helps
PLEASE HELP ME ANSWER THIS QUESTION ASAP!!
Answers
Answer:
7z + 17
Step-by-step explanation:
Like terms
All the numbers without letters are like terms
All the numbers with letters are like terms
Since we have 2 numbers without letters, we'll combine those.
15 + 2 = 17
Since there's only one number with letters, we can keep it the same since there's no others to combine it with
7z + 17
Consider the following equation
3x + 9y = 8y - 2
Step 2 of 2: Find the equation of the line which passes through the point (13,5) and is perpendicular to the given line. Express your answer in
slope-intercept form. Simplify your answer.
Answers
Answer:
The perpendicular line is:
y = 1/3 x + 2/3
Step-by-step explanation:
The given equation can be reduced to its slope-intercept form as shown below:
3x + 9y = 8y - 2
subtract 8 y from both sides
3 x + y = -2
subtract 3 x from both sides
y = - 3 x -2
therefore we know that the slope of this line is -3, and then, a perpendicular line to it must have slope given by the "opposite of the reciprocal" of this slope. That is, the slope of any perpendicular line to this one must be: 1/3
We use this slope to find the equation of the line passing through the point (13. 5)
y = 1/3 x + b
passing through (13, 5) means:
5 = 1/3 (13) + b
therefore, we can find b from the above equation
b = 5 - 13/3 = 15/3 - 13/3 = 2/3
Then the equation of this perpendicular line is:
y = 1/3 x + 2/3