Find dy/dx by implicit differentiation and evaluate the derivative at the given point.
xy = 35 ...?
Answers
Since that, the first thing you should do is to differentiate with respect to x
(look at the pic. 1), as you can see this is simply 1, which means you have to simplify
Then we need to perform solving for for dy/dx as we are about to get the derivative of y with respect to x. pic.2
Get back to the oroginal function, now we can substitute this for y to get the func which will depend only on x pic.3
Then pic.4
Final answer:
To find dy/dx by implicit differentiation of the equation xy=35, differentiate both sides with respect to x. Use the product rule to obtain x * (dy/dx) + y = 0 and solve for dy/dx, giving dy/dx = -y / x. Evaluate this at a specific point by substituting the x and y values from that point into the derived formula.
Explanation:
To find dy/dx by implicit differentiation of the equation xy = 35, we differentiate both sides of the equation with respect to x. Since y is a function of x, when we differentiate y we must apply the chain rule, resulting in the derivative y with respect to x, or dy/dx.
Starting with the original equation:
xy = 35
We apply differentiation to both sides with respect to x:
Using the product rule for the left side: d/dx (xy) = d/dx (35)
This gives us x * (dy/dx) + y * (1) = 0 because the derivative of a constant, like 35, is 0.
We then solve for dy/dx: dy/dx = -y / x.
To evaluate the derivative at a given point, you substitute the x and y coordinates of that point into the derivative equation. For example, if we are given a point (5,7), we substitute into the dy/dx equation to find the derivative at that point:
dy/dx = -y / x = -(7) / (5)
Therefore, dy/dx at the point (5,7) is -7/5 or -1.4.
Related Questions
Which is an equation in point-slope form for the given point and slope?
Point: (7, 4); Slope: 6
y – 7 = 6(x + 4)
y – 4 = 6(x – 7)
y – 4 = 6(x + 7)
y + 4 = 6(x – 7)
Answers
y=6x-38
A rectangular box has a perimeter of 36 inches. Which of the following equations represents the area of the rectangular box in terms of its width, w?
a. A = 36w - w2 b. A = 18w - w2 c. A = 36 - w2 d. A = 18 - w2
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Which of the following sets represents the domain of the function shown?
{(2, 7}, (15, 13), (21, –4), (24, 18)}
A) {-4,2,7,13,15,18,21,24}
B) {7,2),(13, 15),(-4,21),(18,24)
C) {2,15,21,24}
D) {-4,7,13,18}
Answers
The function is { ( 2, 7 ) , ( 15, 13 ), ( 21, - 4 ), ( 24, 18 ) }
The domain is:
C ) { 2, 15, 21, 24 }
( the range is D ) )
What do you do when you must solve a system of equations by elimination but all of the coefficients on the variables are different? What is important to remember when doing this?
Answers
A hotel cost $198including tax. what is a room for 2 weeks
Answers
What is a math teachers favorite breakfast? Its an algebra math worksheet riddle
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The math teacher's favorite breakfast is Pi.
Pi (π)The number pi is a mathematical constant whose value is (3.141592653589793238...). its decimal representation is neither end (such as 1/4 = 0.25) nor becomes repetitive (such as 1/6 = 0.166666...). And it is generally denoted by the Greek letter p or π.
In geometry, the pi is generally defined as the ratio of the circumference of the circle to its diameter.
[tex]\rm{\pi=\dfrac{Circumference}{Diameter}[/tex]
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what are the base seven counting numbers just before and after 16 base seven ? ...?
Answers
Final answer:
In base seven, the number just before 16 is 15, and the number just after 16 is 20. These correspond to 5 and 14 in decimal notation, respectively.
Explanation:
The question asks for the base seven counting numbers just before and after 16 in base seven. In base seven, counting is similar to decimal but stops at 6 before moving to the next place value. The number 16 in base seven is written as 6 in base 10, since base seven does not have a digit for '7' or higher. Therefore, the counting sequence in base seven goes ...14, 15, 16, 20, 21... Thus, the number just before 16 in base seven is 15 (which is 5 in base 10), and the number just after 16 in base seven is 20 (which represents 14 in base 10).
a new website didicated to helping users research their ancestry had 200 visitors in the first week. the marketing director beleives that without an advertising compaign, the site will gain 50 new users each week. how many total visitors will they have after 12 weeks?
Answers
You can acquire this answer buy multiplying 50 by 12 to get the amount of new users after 12 weeks to get 600, and then add 200 to 600 for the current users.
In the equation below, what is the coefficient of the variable?
15 = 8x
A. =
B. 8
C. x
D. 15
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but i have to write more to let me post this so here it is
A blouse that cost $16.85 is on sale for 45% off. What is the amount of the discount?
Answers
Answer: the answer
Step-by-step explanation: is 7.58
The amount of the discount if A blouse that cost $16.85 is on sale for 45% off is $7.6.
What is percentage?The percentage is a relative figure used to denote hundredths of any quantity. Since one percent (symbolized as 1%) is equal to one-hundredth of something, 100 percent stands for everything, and 200 percent refers to twice the amount specified.
Given:
The cost of the blouse, c = $16.85
The discount of the sale, d = 45%,
Calculate the amount of discount as shown below,
The amount of discount = 45% of The cost of the blouse
The amount of discount = 45 / 100 × 16.85
The amount of discount = 0.45 × 16.85
The amount of discount = 7.5825
Thus, the amount of the discount is $7.6.
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an aeroplane moving horizontally with a speed of 180 km/hr drops a food packet while flying at a height of 490m . the horizontal range of the packet is?? ...?
Answers
s = ut + 1/2 at²; u is 0
480 = 4.9t²
t = 9.90 seconds
Horizontal distance = horizontal speed x time
The speed will be converted to m/s from km/h
= 180 km/hr x 1000m/km x 1hr/3600 seconds x 9.90 seconds
= 495 m
What is the simplest form of expression? 2a^2b^2/4a
Answers
Final answer:
To find the simplest form of the expression 2a^2b^2/4a, you divide both the numerator and the denominator by the common factor 2a. The resulting simplest form of the expression is ab^2/2.
Explanation:
The student has asked: What is the simplest form of the expression 2a^2b^2/4a? The simplest form is achieved by simplifying the expression through division since there are common factors in the numerator and the denominator. Here, we can divide both the numerator and the denominator by 2a, which is a common factor. This simplification process will give us the simplest form of the expression.
To simply the expression 2a2b2/4a, we can follow these steps:
Divide the numerator and denominator by the common factor 2a.This results in a2b2/2a becoming ab2/2 after reduction.Therefore, the simplest form of the expression is ab2/2.
WILL UPVOTE
Solve: 16x2 − 81 = 0.
x = 4, 9
x = −4, −9
x = 9 over 4, x = −9 over 4
x = 81 over 16, x = −81 over 16
Answers
I NEED HELP FAST!!!!!
Monique is factoring the expression 4x+16xy Her work is shown below.
Factors of 4x: 1, 2, 4, x
Factors of 16xy: 1, 2, 4, 8, 16, x, y
GCF: 4x
Factored expression: 4x(0+4y)
Which best describes the accuracy of Monique’s solution?
A. Monique’s solution is accurate.
B. Monique made an error when listing the factors, which affected the GCF and the factored expression.
C. Monique made an error when determining the GCF from her list of factors.
D. Monique made an error when writing the factored expression.
Answers
Answer with explanation:
Monique is factoring the expression 4x+16xy Her work is shown below.
Factors of 4 x→: 1, 2, 4, x
Factors of 16 x y:→ 1, 2, 4, 8, 16, x, y
G CF: 4 x
Factored expression: 4 x(0+4 y)→Incorrect
→4 x +16 x y= 4* x + 4 *4* x* y
= 4* x* (1+4 y)
while writing the factored expression, we have to break the terms into smaller terms that is into monomials and then we should take out the common factor between the two terms.
Option D: Monique made an error when writing the factored expression.
a baker makes 84loaves of bread but she burns 4 of them what fraction of the loaves does the baker burn? 1/88, 1/80,1/21,1/20 ...?
Answers
Given that the baker makes 84 loaves of bread, and out of the 84, she burns 4 of them. So in fraction it will be expressed in 4/84. So to know the final answer, we will simplify this fraction and we get 1/21. So the answer would be the third option. Hope this answer helps.
passes through (4,-5), slope = 3/4
Answers
y = 3/4x + b
Calculation for b.,
-5 = 3/4 * 4 + b
b = -5/3
So, your final answer is y = 3/4x - 5/3
Hope this helps!
A container holds 16 pints of lemonade. how much is this in gallons?
Answers
Answer: 2 gallons of lemonade.
Step-by-step explanation:
The container holds 16 pints of lemonade, and we know that a pint corresponds to 0.125 gallons.
So 16 pints are equal to 16 times 0.125 gallons:
16*0.125 gallons = 2 gallons
Then the container holds 2 gallons of lemonade.
Evaluate |3 - 5 + 7|.
-5
5
-15
15
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How do I set the proportions up
Answers
How to divide 219 by 3?
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Write each fraction as an expression with negative exponents.
v/w raised to the second power ...?
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v/w raised to the second power is (v/w)²
(v/w)² = v²/w²
Since xᵃ = 1/x⁻ᵃ, then v²/w² = 1/v⁻²w²
Since 1/xᵃ = x⁻ᵃ, then 1/v⁻²w² = w⁻²/v⁻²
HELP
What is the equation of a line that is parallel to 2x+3y=3 and passes through the point (3,−4)?
Answers
the slope for ax+by=c is -a/b
that means that a line paralell to 2x+3y=3 will have 2x+3y=something
find that something
given
(3,-4)
x=3 and y=-4 is a soltuion
2x+3y=something
2(3)+3(-4)=something
6-12=something
-6=something
2x+3y=-6
What is 22.5% written as a mixed number
Answers
So, your final answer is 22 1/2
Hope this helps!
Which function is NOT continuous?
a. your altitude as a function of time while flying from reno to dallas?
b. time to travel from miami to pensacola as a function of driving speed?
c. number of tennis balls that can fit completely inside a particular box as a function of the radius of the tennis balls?
d. area of a circle as a function of radius.
Answers
The reason for this is because the number of these balls is discreet, not continuous (meaning that there cannot be 6.5 balls).
Answer:
C. number of tennis balls that can fit completely inside a particular box as a function of the radius of the tennis balls.
Step-by-step explanation:
"1.Provide the reasons for the proof.
Given: m angle1 = m angle2
Prove:
Answer:
StatementsReasons
a. m angle 1 = m angle 2a. Given
b. angle 1 is supplementary to angle 2.b. Definition of supplementary angles.
c. m angle 1 + m angle 2 = 180 c.
d. m angle1 + m angle1 = 180
2(m angle1) = 180d.
e. m angle1 = 90e.
f. angle 1 is a right angle.f. GIVEN OR PROVE IF PROVE PUT REASON....EXAMPLE: SUPPLEMENTARY......"
Answers
Switch the reasons for b) and c)
b) the angles form a linear pair , from the picture, so this is linear pair postulate
C) Then the measures add to 180, because they are supplementary. Defn of supplementary.
E) you have divided both sides of the equation by 2; or multiplied by 1/2; multiplication property of equality
F) definition of right angle
G) definition of perpendicular
I hope my answer has come to your help. Have a nice day ahead and may God bless you always!
What is the greatest factor of: 6x^2y^3 + 18x^3y^3 + 36x^3y^2
Answers
The greatest factor of the given expression is 6x^2y^2, found by identifying the common variables with the lowest exponents and the greatest common divisor of the coefficients.
Explanation:The student is asking to find the greatest common factor (GCF) of the algebraic expression 6x^2y^3 + 18x^3y^3 + 36x^3y^2. To find the GCF, we look for the highest exponents of the variables that are common in each term, and the largest coefficient that can evenly divide all the coefficients of the terms.
Firstly, we notice that each coefficient (6, 18, 36) is divisible by 6, so 6 is part of our GCF. Next, we see that the smallest exponent of x is 2 and the smallest exponent of y is 2 as well. So, x^2 and y^2 are also part of our GCF. The greatest factor is then 6x^2y^2.
Therefore, when we factor out the GCF from the expression, it would be written as:
6x^2y^2 (y + 3x + 6xy)
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A line segment has an endpoint at (5, 2) and has a negative slope. Which of the following points could be the other endpoint?
A. (6, 3)
B. (5, 1)
C. (4, 3)
D. (4, 1)
Answers
If you eat two slices of a medium pizza with eight slices, what is the simplest fraction for the number of slices of pizza leftover?
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you eat 2/8=1/4 of pizza
1 - 1/4 = 3/4 leftover
jasmine has taken an online boating safety course and is now completing her end of course exam.As she answers each question, the progress bar at the bottom of the screen shows what portion of the test she has finished. She has just completed question 16, and the progress bar shows she is 20% complete. How many total questions are on the test.
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Ronnie is scheduling a chess tournament in which each player plays every other player once. He created a table and found that each new player adds more games to the tournament in an arithmetic sequence. Answer this set of project questions regarding the chess games.
table:
# of players | # of games
1 | 0
2 | 1
3 | 3
4 | 6
5 | 10
Which of the following is a recursive rule for the original sequence?
A) an = an-1 + n + 1
B) an = an-1 + n - 1
C) an = an-1 + n
D) an = n2+ n
How many games must be played when 7 players are in the tournament?
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2) And what about the recursive rule for the original sequence, the approrpiate one is an = an-1 + n - 1, so the answer is lying in the second option from the scale.
According to the fact that the number of games is actually the sum of integers from 1 to n-1 we expect to have n number of players.
I am sure it's clear now!