Find dy/dx by Implicit Differentiation x³ +y³ = 36
a 6 -x
b 3x² +3y² c −x²/y²
d 0

Answers

Answer 1

To find dy/dx using implicit differentiation, we differentiate both sides of the equation x³ + y³ = 36 with respect to x:

d/dx(x³) + d/dx(y³) = d/dx(36)

Using the power rule of differentiation, we get:

3x² + 3y²(dy/dx) = 0

Simplifying and solving for dy/dx, we get:

dy/dx = -(3x²)/(3y²) = -x²/y²

Therefore, the answer is (c) -x²/y².

Differentiation is a mathematical operation that gives us the rate at which a function changes with respect to its input variable. In other words, it gives us the instantaneous rate of change of a function at a particular point.

More formally, the derivative of a function f(x) at a point x is defined as the limit of the ratio of the change in the function value to the change in the input variable as the change in the input variable approaches zero:

f'(x) = lim(h→0) [f(x+h) - f(x)] / h

Geometrically, the derivative of a function at a point represents the slope of the tangent line to the graph of the function at that point.

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Related Questions

The relationship between temperature in degrees Fahrenheit and1 degrees Celsius is shown in the graph. What is the meaning of the y- intercept?

The relationship between temperature in degrees Fahrenheit and1 degrees Celsius is shown in the graph.

Answers

The y-intercept is the initial condition, it represents the degrees Fahrenheit with 0 Celcius.

Hence, the third option is correct.

Is (5,7) a solution to this system of equations? y=3x–8 y=2x–3

Answers

Answer:

yes

Step-by-step explanation:

to determine if (5, 7 ) is a solution substitute the x- coordinate 7 into the right side of both equations.

if the corresponding value of y for both is equal to the y- coordinate 7 then it is a solution to the system.

y = 3(5) - 8 = 15 - 8 = 7 ← equals y- coordinate

y = 2(5) - 3 = 10 - 3 = 7 ← equals y- coordinate

since both equations are true then (5, 7 ) is a solution to the system

To determine if the point (5, 7) is a solution to the system of equations y = 3x - 8 and y = 2x - 3, we can substitute the values of x and y from the point into both equations and check if they are satisfied.

Let's substitute x = 5 and y = 7 into both equations:

For the equation y = 3x - 8:

7 = 3(5) - 8

7 = 15 - 8

7 = 7

The equation is satisfied.

For the equation y = 2x - 3:

7 = 2(5) - 3

7 = 10 - 3

7 = 7

The equation is also satisfied.

Since both equations are satisfied when we substitute x = 5 and y = 7, we can conclude that (5, 7) is indeed a solution to the system of equations y = 3x - 8 and y = 2x - 3.

what is the y-intercept​

what is the y-intercept

Answers

Answer:

(0,6)

Step-by-step explanation:

The y intercept is where the line crosses the y axis or the coordinate where x = 0.

Here, when x is equal to 0, y is equal to 6 meaning that the y intercept is at (0,6)

please help thank you

please help thank you

Answers

Answer:

goofy

Step-by-step explanation:

what is y-2=-3 (x-7) in standard form

A.y-2=--3x+21
B.y=-3x+23
C.3x+y-23=0
D.3x+y=23​

Answers

9514 1404 393

Answer:

  D.  3x +y = 23​

Step-by-step explanation:

If you know what "standard form" is, then you recognize that only one offered answer choice is actually in standard form. That is the correct choice.

  3x + y = 23​

_____

Standard form for a linear equation is ...

  ax +by = c

where a, b, c are mutually prime integers and a ≥ 0. If a = 0, then b > 0. (The leading coefficient is positive.)

in 2016 the better business bureau settled 80% of complaints they received in the united states. suppose you have been hired by the better business bureau to investigate the complaints they received this year involving new car dealers. you plan to select a sample of new car dealer complaints to estimate the proportion of complaints the better business bureau is able to settle. assume the population proportion of complaints settled for new car dealers is 0.80, the same as the overall proportion of complaints settled in 2016. (a) suppose you select a sample of 220 complaints involving new car dealers. show the sampling distribution of p.

Answers

The sampling distribution of p is approximately normal with a mean of 0.80 and a standard error of 0.00309.

The sampling distribution of p can be determined using the formula for standard error.

Step 1: Calculate the standard deviation (σ) using the population proportion (p) and the sample size (n).
σ = √(p * (1-p) / n)
  = √(0.80 * (1-0.80) / 220)
  = √(0.16 / 220)
  ≈ 0.0457

Step 2: Calculate the standard error (SE) by dividing the standard deviation by the square root of the sample size.
SE = σ / √n
  = 0.0457 / √220
  ≈ 0.00309

Step 3: The sampling distribution of p is approximately normal, centered around the population proportion (0.80) with a standard error of 0.00309.

The sampling distribution of p is a theoretical distribution that represents the possible values of the sample proportion. In this case, we are interested in estimating the proportion of complaints settled for new car dealers. The population proportion of settled complaints is assumed to be the same as the overall proportion of settled complaints in 2016, which is 0.80.

To construct the sampling distribution, we calculate the standard deviation (σ) using the population proportion and the sample size. Then, we divide the standard deviation by the square root of the sample size to obtain the standard error (SE).

The sampling distribution is approximately normal, centered around the population proportion of 0.80. The standard error reflects the variability of the sample proportions that we would expect to see in repeated sampling.

The sampling distribution of p for the selected sample of new car dealer complaints has a mean of 0.80 and a standard error of 0.00309. This information can be used to estimate the proportion of complaints the Better Business Bureau is able to settle for new car dealers.

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which expression is equivalent
HELP ME PLEASE

which expression is equivalentHELP ME PLEASE

Answers

Answer:

the 4th option is correct

Step-by-step explanation:

\(xy^{2/9}\)   Original expression

\(x(y^{2})^{1/9}\)   Split up the exponent

\(x(\sqrt[9]{y^{2} } )\)   The 1/9 of an expression is the same thing is the 9th root of the expression.

5. How many combinations are possible to select a student president, vice president, and treasurer among 23 students? Assume a student cannot hold more than one office. 12,167 10,626 9297

Answers

we have

3P23=23*22*21=10,626

answer is option

10,626i use permutation, because the order is important

what is the decrease of 3/2

Answers

Answer:

3/2

Step-by-step explanation:

3/2 is in the simplest form; it can't be decreased any more.

PLEASE HELP
A bookshelf holds 6 different biographies and 4 different mystery novels. How many ways can one book of each type be selected?
11
30
24
20

Answers

Answer:

There are 24 ways to select one book of each type.

Step-by-step explanation:

In mathematics, the procedure to select k items from n distinct items, without replacement, is known as combinations.

The formula to compute the combinations of k items from n is given by the formula:

\({n\choose k}=\frac{n!}{k!(n-k)!}\)

It is provided that there are 6 different biographies and 4 different mystery novels on a bookshelf.

Compute the number of ways to select a biography as follows:

Number of ways to select a biography =

\(={6\choose 1}\\\\=\frac{6!}{1!(6-1)!}\\\\=\frac{6\times 5!}{1\times 5!}\\\\=6\)

There are 6 ways to select a biography.

Compute the number of ways to select a mystery novel as follows:

Number of ways to select a mystery novel =

\(={4\choose 1}\\\\=\frac{4!}{1!(4-1)!}\\\\=\frac{4\times 3!}{1\times 3!}\\\\=4\)

There are 4 ways to select a mystery novel.

Then the total number of way to select one book of each type is:

\({6\choose 1}\times {4\choose 1}=6\times 4=24\)

Thus, there are 24 ways to select one book of each type.

-
19. higher order thinking to find
357 - 216, tom added 4 to each number
and then subtracted. saul added 3 to each
number and then subtracted. will both
ways work to find the correct answer?
explain.

Answers

Both Tom's and Saul's methods will work to find the correct answer for the subtraction problem of 357 - 216. Adding a constant value to each number before subtracting does not change the relative difference between the numbers, ensuring the same result.

In the given problem, Tom adds 4 to each number (357 + 4 = 361, 216 + 4 = 220) and then subtracts the adjusted numbers (361 - 220 = 141). Similarly, Saul adds 3 to each number (357 + 3 = 360, 216 + 3 = 219) and then subtracts the adjusted numbers (360 - 219 = 141).
Both methods yield the same result of 141. This is because adding a constant value to each number before subtracting does not affect the relative difference between the numbers. The difference between the original numbers (357 - 216) remains the same when the same constant is added to both numbers.
Therefore, both Tom's and Saul's methods will work to find the correct answer. Adding a constant to each number before subtracting does not alter the result as long as the same constant is added to both numbers consistently.

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A particle of spin j=1 has an energy whose Hamiltonian is given as
the state of the system at time t=0 is given as
a) If at instant t = 0 the energy is measured, what valu

Answers

from the above calculation is that if at instant t=0 the energy is measured, then the possible energy values that can be measured are 2Aħ²/3, Aħ²/3 and 0.

Given a Hamiltonian representing the energy of a particle of spin j=1 and a state of the system at time t=0, the question is to find the possible energy values that can be measured at t=0

The energy of a particle of spin j=1 is given as H = E (j = 1) = A S²,

where A is the constant and S² is the square of the spin operator S.

The possible values of S² are (1) S² = 2ħ² (2) S² = ħ² (3) S² = 0.

The state of the system at time t=0 is given as | ψ (0) > = (1/√3) |1, 0 > + (1/√3) |-1, 0 > + (1/√3) |0, 1 >.

If the energy is measured at t=0, then the value of the energy E (j = 1) that can be measured will be the eigenvalue of the Hamiltonian operator H. The energy eigenstates of H are given as |ψ> = α |1, 0> + β |-1, 0> + γ |0, 1>. Here, α, β and γ are the coefficients that satisfy the normalization condition and the orthonormality condition. Thus, the value of E (j = 1) that can be measured at t=0 will be A times the eigenvalue of the operator S² that corresponds to the energy eigenstate.

Hence, the possible values of E (j = 1) are (1) E (j = 1)

= 2Aħ²/3 (2) E (j = 1)

= Aħ²/3 (3) E (j = 1) = 0.

The conclusion drawn from the above calculation is that if at instant t=0 the energy is measured, then the possible energy values that can be measured are 2Aħ²/3, Aħ²/3 and 0.

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A recipe calls for 4 cups of flour to 6 tablespoons of shortening. How many tablespoons of shortening are needed for 6 cups of flour?

Answers

Answer:

2 cups sorry if i am mistaken

Step-by-step explanation:

What is 3 percent of 98

Answers

Answer:

2.94

Step-by-step explanation:

I just found 1%

Which is 0.98

then times that by 3 which is 2.94

hope that helps!

Keith and Toby want to get a pizza that costs $18.95. Keith has $11.18, and Toby has $5.87. How much more money do they need to buy the pizza?

Answers

Answer: $1.90

Step-by-step explanation:

Solve 7x-c=k for x
...........

Answers

Answer:

The value of x in given question will be \(x=\frac{k+c}{7}\)

Step-by-step explanation:

Given data:

7x-c=k

Now,

7x-c=K

7x=K+c

\(x=\frac{k+c}{7}\)

Therefore,

The value of x in given question will be : k+c/7

How many insects were consumed throughout the month by the pitcher plants?

Answers

Answer:

I think 15 I am sure

Step-by-step explanation:

The number of insects consumed by pitcher plants is essential for their survival and growth, and it is fascinating to observe this unique aspect of their carnivorous nature.

Pitcher plants are carnivorous plants that trap and digest insects to obtain nutrients. The exact number of insects consumed by pitcher plants in a month can vary depending on factors such as the species of pitcher plant, its size, and the local environment. However, studies have estimated that a single pitcher plant can consume anywhere from a few dozen to hundreds of insects per month.

The mechanism of the pitcher plant is quite interesting. Insects are lured into the plant by its color and sweet-smelling nectar. Once inside, the insect becomes trapped and is unable to escape due to the slippery inner walls of the pitcher. The plant then secretes digestive enzymes that break down the insect's tissues, allowing the plant to absorb the nutrients.

Interestingly, not all insects are consumed by pitcher plants. They tend to prefer smaller insects such as ants and flies, but larger insects such as bees and wasps may occasionally become trapped as well.

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help me please andwer this

help me please andwer this

Answers

Answer:

B

Step-by-step explanation:

i am smart

There's still more, there's 3 parts I just can't see them until I have my answer

There's still more, there's 3 parts I just can't see them until I have my answer
There's still more, there's 3 parts I just can't see them until I have my answer
There's still more, there's 3 parts I just can't see them until I have my answer

Answers

The cost of endless chicken wings at Restaurant X is $5. So cost equation for n chicken wings at Restaurant X is,

\(c=5\)

The cost of chicken wings at Restaurant Z is 20 cents and $1.40 for sauce. So cost equation for Restaurant Z is,

\(\begin{gathered} c=\frac{20}{100}\cdot n+1.40 \\ =0.20n+1.40 \end{gathered}\)

So answer is,

Restaurant X: c = 5

Restaurant Z: 0.20n + 1.40

(b)

Plot the system of equation on the graph.

(c)

The lines of two restaurant X and restaurant Z intersect each other at point (18,5). This means that restaurant X and restaurant Z has same cost 5 at n = 18. So both restanurant has same cost for 18 chicken wings.

Answer: 18

There's still more, there's 3 parts I just can't see them until I have my answer

Annie is making three gift boxes, each in the shape of a cube, and wants to store them one inside the other. Her design calls for the first box to have a
2.5 inch edge with each larger box
edge increasing by ‡ inch. When she makes her largest box, what will its
surface area be?

Answers

The Surface area of the largest gift box will be 45.375 square inches.

The surface area of the largest gift box, we need to determine the edge length of the largest box and then calculate its surface area.

Given:

The first box has an edge length of 2.5 inches.

Each larger box has an edge length increasing by ⅛ inch.

To determine the edge length of the largest box, we need to know how many times the edge length increases by ⅛ inch. Since we are making three boxes in total, the edge length increases twice.

Edge length of the largest box = 2.5 inches + 2 * (⅛ inch)

                               = 2.5 inches + 2 * 0.125 inches

                               = 2.5 inches + 0.25 inches

                               = 2.75 inches

Now that we know the edge length of the largest box is 2.75 inches, we can calculate its surface area.

Surface area of a cube = 6 * (edge length)^2

Substituting the edge length:

Surface area of the largest box = 6 * (2.75 inches)^2

                             = 6 * (2.75 inches * 2.75 inches)

                             = 6 * (7.5625 square inches)

                             = 45.375 square inches

Therefore, the surface area of the largest gift box will be 45.375 square inches.

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Colin loves to eat tuna salad for lunch. His mom is always looking for a bargain on 12-ounce cans of tuna. Today, his local grocery store is offering 4 cans of Sea Star tuna for $3.28 and 2 cans of Ocean's Best tuna for $1.88.

Answers

Sea Star Tuna is a better bargain for 82 cents a can. Ocean’s Best Tuna is 94 cents a can.

calculate a correlation matrix for the following data. data correlations fructosamine group visits.xlsxdownload data correlations fructosamine group visits.xlsx fructosamine number of group visits attended infant birthweight in grams 152 6 3175 173 5 3225 174 4 3350 175 4 3400 176 3 3530 183 2 3540 188 3 3525 192 3 3650 202 2 3600 205 2 3550 210 1 3950 215 2 3325 220 2 4500 258 1 4800 how would you interpret the correlation between the number of group visits attended and fructosamine level? group of answer choices strong moderate weak weak to moderate

Answers

A moderately negative correlation between both of them variables is shown by the resultant correlation coefficient of -0.55.

We can construct a correlation matrix to determine the relationship between the number the group visits received and the fructosamine level. This indicates that the fructosamine level typically decreases as the amount of group visits increases.

This could imply that patients can keep better control of glucose, as seen by lower fructosamine levels, by participating in group visits and getting support or education about managing diabetes.

It's crucial to remember that a connection does not necessarily indicate a cause.

Further study is required to show a causal link between the fructosamine level and the number the group visits that participants attended. Overall, the moderately negative correlation points to some potential benefits of group visits for treating diabetes.

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anyone know the answer to this question

anyone know the answer to this question

Answers

Answer:

A) There is a vertical shift

Step-by-step explanation:

There is clearly a vertical shift because since +6 is outside of the parentheses, you go up 6.

solve the following inequality-4<10+2x<=18

Answers

To solve the inequality we can subtract 10 as:

\(\begin{gathered} -4<10+2x\leq18 \\ -4-10<10+2x-10\leq18-10 \\ -14<2x\leq8 \end{gathered}\)

Then, dividing by 2, we get:

\(\begin{gathered} -\frac{14}{2}<\frac{2x}{2}\leq\frac{8}{2} \\ -7Therefore, the solution is:

-7 < x ≤ 4

Answer: -7 < x ≤ 4

Factor Completely
6p² +90p + 300

Answers

Answer:

6(p + 5)(p + 10)

Step-by-step explanation:

6p² + 90p + 300 ← factor out 6 from each term

= 6(p² + 15p + 50) ← factor the quadratic

consider the factors of the constant term (+ 50) which sum to give the coefficient of the p- term (+ 15)

the factors are + 5 and + 10 , then

p² + 15p + 50 = (p + 5)(p + 10)

and

6p² + 90p + 300

= 6(p + 5)(p + 10)

Can someone plz help !!!

Can someone plz help !!!

Answers

Answer:

3

Step-by-step explanation:

5 + 4 = 9

12 - 9 = 3

In order to find the missing length you will need to add up the given lengths then subtract that from the total perimeter.

A dart has a circumference of 26\pi(pi symbol)calculate the total area on which the dart may land

Answers

The total area on which the dart may land is 530.93 square units

How to find the area of the dart

The dart is a circle and hence the calculations will be accomplished using formula pertaining to a circle.

The circumference of a circle (dart) is given by the formula below

C = 2 * π * r

where

C is the circumference

π = pi is a constant term and

r is the radius.

26π = 2πr

Dividing both sides by 2π, we get:

r = 13

Area of the dart (circle)

A = πr²

A = π * (13)²

A = 169π (in terms of pi)

A = 530.93 square units (to 2 decimal place)

Therefore, the total area on which the dart may land is 169π square units.

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The maximum safe load of a bridge is 1500 kg to the nearest 10 kg.
An average soldier is 75 kg to the nearest kilogram.
Work out an estimate for the maximum number of soldiers that can safely cross the bridge at the same time.

Answers

If the maximum safe load of a bridge is 1500 kg to the nearest 10 kg. The estimate for the maximum number of soldiers that can safely cross the bridge at the same time. is: 19.

How to determine the maximum number of soldier?

First step is to find the lower bound and upper bound of 1500

Lower bound of 1500

1495

Upper bound of 1500

1505

Second step is to find the lower bound and upper bound of 75

Lower bound of 75

74.5

Upper bound of 75

75.5

Now let find the maximum number

Maximum number = Lower bound / Upper bound

Maximum number = 1495 / 75.5

Maximum number = 19.801

Maximum number = 19

Therefore the maximum number is 19 soldier.

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find an equation for the tangent plane to the surface z 1 = x y 3 cos ( z ) z 1=xy3cos(z) at the point ( 1 , 1 , 0 ) (1,1,0) .

Answers

Equation for the tangent plane to the surface z 1 = x y 3 cos ( z ) z 1=xy3cos(z) at the point ( 1 , 1 , 0 ) (1,1,0) is :

z = x + 3y - 4

To find the equation for the tangent plane to the surface z1 = xy^3cos(z) at the point (1, 1, 0), follow these steps:

1. First, find the partial derivatives of the given function with respect to x and y. The given function is z1 = xy^3cos(z).

2. Find ∂z1/∂x by differentiating with respect to x:
∂z1/∂x = y^3cos(z)

3. Find ∂z1/∂y by differentiating with respect to y:
∂z1/∂y = 3xy^2cos(z)

4. Now, evaluate the partial derivatives at the given point (1, 1, 0):
∂z1/∂x(1, 1, 0) = 1^3cos(0) = 1
∂z1/∂y(1, 1, 0) = 3*1^1*1^2*cos(0) = 3

5. Finally, write the equation for the tangent plane using the obtained values and the given point (1, 1, 0). The general equation for a tangent plane is:
z - z0 = ∂z1/∂x(x - x0) + ∂z1/∂y(y - y0)

Substitute the values to get the equation for the tangent plane:
z - 0 = 1*(x - 1) + 3*(y - 1)

Your answer: z = x + 3y - 4

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A mountain climber is scaling 500-foot cliff. The graph shows the elevation of the climb over time. What is the slope?

Answers

Where’s the graph you didn’t put it
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