Use logarithmic differentiation to find dy/dx. - y = x2 – 36 x2 + 36 x> 6 dy dx = Need Help? Read It Watch It

Step-by-step explanation:

Standard form of a quadratic is f(x) = ax² + bx + c.

To convert to vertex form, the simplest method is to find the x-coordinate of the vertex using h = -b/(2a).

Then, plug back into the equation to find the y-coordinate of the vertex.  k = f(h).

Finally, the leading coefficient is the same as the standard form, a.

f(x) = a(x − h)² + k

Another method is to complete the square.

The standard equation of the sphere with the given characteristics, center (-1, -6, 3), and radius 5 is

\((x+1)^{2} +(y+6)^{2}+ (z-3)^{2} =25\).

The standard equation of a sphere is \((x-h)^{2} +(y-k)^{2}+ (z-l)^{2} =r^{2}\), where (h, k, l) is the center of the sphere and r is the radius.
Using this formula and the given information, we can write the standard equation of the sphere:
\((x-(-1))^{2}+ (y-(-6))^{2} +(z-3)^{2}= 5^{2}\)
Simplifying, we get:
\((x+1)^{2} +(y+6)^{2}+ (z-3)^{2} =25\).
Therefore, the standard equation of the sphere with center (-1, -6, 3) and radius 5 is \((x+1)^{2} +(y+6)^{2}+ (z-3)^{2} =25\).

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Answer:

\(8-6i\)

Step-by-step explanation:

Multiply out \((3-i)^2\) in order to find out which expression it is equivalent to.

1) Since the whole quantity is squared, write it out as \((3-i)(3-i)\).

\((3-i)^2\\(3-i)(3-i)\)

2) Multiply binomials by using the FOIL method. Multiply the terms that are listed first in each binomial, then the ones that are listed outermost when looking at both binomials, then innermost, and finally the last terms listed in each binomial. Simplify and combine like terms.

\((3-i)(3-i)\\9 - 3i - 3i + i^2\)

\(9 - 6i + i^2\)

3)  \(i = \sqrt{-1}\), so \(i ^2\) must be \((\sqrt{-1} )(\sqrt{-1})\). Thus, \(i^2\) is equivalent to -1. Knowing this, simplify and combine like terms.

\(9 - 6i + ((-\sqrt{1} )(\sqrt{-1} ))\)

\(9 - 6i -1\\8 - 6i\)

Thus, it is equivalent to  \(8 - 6i\) .

The  temperature in parts of Minnesota fell at an average rate of 1.17°F per hour during this 24-hour period.

To find the average temperature change per hour, we need to divide the total change in temperature by the time period over which the change occurred.

The change in temperature is:

41°F - 13°F = 28°F

The time period over which the change occurred is 24 hours.

Therefore, the average temperature change per hour is:

28°F / 24 hours = 1.17°F/hour (rounded to two decimal places)

So the temperature in parts of Minnesota fell at an average rate of 1.17°F per hour during this 24-hour period.

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Step-by-step explanation:

\(standard \: form \: \rightarrow \: slope - intercept \: form.\)

Slope-intercept form:

\(y = mx + b\)

Key:

m = slope.

m = slope.b = y-intercept.

How to solve?

Simplify the standard form equation algebraically.

Our equation:

\(y - 5 = 3(x - 1)\)

Use the Distributive Property:

\(y - 5 = 3x - 3\)

Add 5 to both sides of the equation:

\(y = 3x + 2\)

Therefore,

\(y = 3x + 2 \: is \: your \: slope - intercept \: form \: equation.\)

Answer:

7 a.m is 5.5

Step-by-step explanation:

(6=4)+1.5=(_+1.5)

make a T chart

thats how it should work for you

Answer:

D

Step-by-step explanation:

This comes out to 4. The other ones are absolute value, meaning there are no negatives. You can think of subtracting as adding a negative. When you role a dice however, you are never really moving backward.

Answer:

A

Step-by-step explanation:

Mark Branliest Please!

Five less than the sum of two times a number and five is equal to ten times the quotient of the of the number and four.

\((2x + 5) - 5 = 10 \times (x \div 4)\)

Goodluck!

The following parts can be answered by the concept of Probability.

(a) The probability that all 5 people selected at random are right-handed is very low, as only about 9% of the population is left-handed.

(b) The probability that all 5 people selected at random are left-handed is even lower, as only about 9% of the population is left-handed.

(c) The probability that not all of the people selected at random are right-handed is relatively high, given that the majority of the population is right-handed.

(a) To calculate the probability that all 5 people selected at random are right-handed, we can use the probability of an individual being right-handed, which is approximately 91% (100% - 9% left-handed). Since the selection of each person is independent, we can multiply the probabilities together:

P(all are right-handed) = P(right-handed)⁵ = 0.91⁵

(b) Similarly, to calculate the probability that all 5 people selected at random are left-handed, we can use the probability of an individual being left-handed, which is approximately 9%. Again, since the selection of each person is independent, we can multiply the probabilities together:

P(all are left-handed) = P(left-handed)⁵ = 0.09⁵

(c) The probability that not all of the people selected at random are right-handed can be calculated by subtracting the probability that all 5 people are right-handed from 1, since the only other possibility is that at least one of them is left-handed:

P(not all are right-handed) = 1 - P(all are right-handed) = 1 - 0.91⁵

Therefore, the answers are:

(a) The probability that all 5 people selected at random are right-handed is 0.91⁵.

(b) The probability that all 5 people selected at random are left-handed is 0.09⁵.

(c) The probability that not all of the people selected at random are right-handed is 1 - 0.91⁵.

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Answer:

Well 10 to the 6th power right?

Step-by-step explanation:

well u multiply 10x10x10x10x10x10

1000000

im sorry if this is not correct im sorry if its not 10 to the 6th power ;ccc

Answer:

C.1/6

Step-by-step explanation:

yan po ung tamang sagut thank you

9514 1404 393

Answer:

  4.0 seconds

Step-by-step explanation:

The equation for ballistic motion is ...

  y = -4.9t^2 +22.1t

We want to find the larger value of t that makes y = 10.

  10 = -4.9t^2 +22.1t

  4.9t^2 -22.1t +10 = 0

Using the quadratic formula, we have ...

  t = (22.1 + √(22.1² -4(4.9)(10)))/(2·4.9) = (22.1 +√292.41)/9.8 = 39.2/9.8

  t = 4

The ball was in the air 4 seconds before it got stuck.

Answer:

\(1 \times { 10}^{ - 9} m\)

Step-by-step explanation:

It can be written in scientific notation as \(1 \times { 10}^{ - 9} m\),

Answer:

a) 1 nm = 0. 000 000 001 m

b) 1 nm = 1×10⁻⁹ m

Answer:8.908 × 10 to the 8th

Step-by-step explanation:trust me

Answer:

54 degrees

Step-by-step explanation:

Complementary angles total 90 degrees.

So, to find B, we subtract 36 from 90.

90-36= 54

Answer:

Sample Response: Complementary angles have a sum of 90°, so the sum of the measures of angles A and B is 90°. Subtract 36° from 90° and angle B has a measure of 54°.

Step-by-step explanation:

The distance between the two planes after 4 hours is approximately 150 km.

to find out how far apart the planes are after 4 hours, we can use the concept of vectors.

Let's start by finding the positions of the two planes after 4 hours.

The first plane flies at a speed of 110 km/h in a direction of 280°. To find its position after 4 hours, we can use the formula: distance = speed × time. So, the distance traveled by the first plane is 110 km/h × 4 hours = 440 km.

To determine the position of the first plane, we need to convert the direction (280°) into components. The x-component is given by: cos(280°) × distance = cos(280°) × 440 km. The y-component is given by: sin(280°) × distance = sin(280°) × 440 km.

Similarly, for the second plane, which flies at a speed of 250 km/h in a direction of 200°, the distance traveled after 4 hours is 250 km/h × 4 hours = 1000 km. To determine its position, we need to convert the direction (200°) into components. The x-component is given by: cos(200°) × distance = cos(200°) × 1000 km. The y-component is given by: sin(200°) × distance = sin(200°) × 1000 km.

Now, let's calculate the x and y components for both planes:

For the first plane:
x-component = cos(280°) × 440 km
y-component = sin(280°) × 440 km

For the second plane:
x-component = cos(200°) × 1000 km
y-component = sin(200°) × 1000 km

the distance between the two planes, we can use the distance formula, which is given by: distance = √((x2 - x1)^2 + (y2 - y1)^2), where (x1, y1) and (x2, y2) are the positions of the first and second planes respectively.

Now, substitute the values we calculated into the distance formula:

distance = √((x2 - x1)^2 + (y2 - y1)^2)
distance = √((cos(200°) × 1000 km - cos(280°) × 440 km)^2 + (sin(200°) × 1000 km - sin(280°) × 440 km)^2)

After evaluating the above expression, the distance between the two planes after 4 hours is approximately 150 km.

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Answer:

Step-by-step explanation:

You keep the same slope since it's supposed to be parallel. But first you need to write it in slope intercept form. So the y can't have a number in front of it, so you must divided everything after the equal sign by the 3. So the equation becomes y=2/3x−1. Now you plug in the points to find a parallel equation using point slope form y−(4)=(23)(x−(−3)). Then you solve that and you get y=2/3x+6.

Hey! Your question was incomplete because I have double-checked my work, and even checked reliable sources to see if I missed something in my work, but I keep getting –238. I did play around with the question by switching the negative symbol around in the equation to see if I would get a balanced answer. I say this because when you solve the question you posted, the answer I got was w = –238, but when I went back to check my work by plugging that number in as the value of w, I got –238 ≠ 238 (or something like that. The number is the same, but the signs are not). If the signs and numbers don't both equal each other something is wrong with the problem. I believe I figured out where your question went wrong. Instead of the question being 34 = –w/7, I believe that the correct question should have been –34 = w/7. What I think happened was that when you typed your question, you swapped the negative on the 34 with the variable of w. If I am incorrect, and you typed your question correctly, I am sorry in advance because my work wasn’t matching what I got for w. But for now, I will solve what I think the question should have said. Again, sorry in advance. Solve for w in the following equation: –34 = w/7.

Write the equation:

–34 = w/7

Multiply both sides by 7:

7 × –34 = w/7 × 7

Multiply:

–238 = 1w

Divide:

–238/1 = 1w/1

–238 = w or w = –238

Check your work by plugging –238 back into the equation as w:

–34 = w/7

–34 = –238/7

Multiply both sides by 7:

–34 × 7 = –238/7 × 7

–238 = –238 ✔

Thus, w = –238

Hope that helps! Have an amazing rest of your day!! :)

The quotient and remainder are x³ -5x² + 10x - 17 and 55.

What is Synthetic division?

When the divisor is a linear factor, synthetic division is a technique used to carry out the division operation on polynomials.

Here, (x+2) is a linear factor which indicates that synthetic division can be applied.

So, we will divide the x^4 - 3x^3 - 7x + 1 by x+2.

(refer the attached solution)

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The equation that represents the relationship between the radius, r, and arc length, s is s = Θ * r

See attachment for the complete question

From the complete question, we have:

The angle is given in radians.

So, the arc length is calculated using

Arc length = Angle * Radius

Substitute known values

s = Θ * r

Hence, the equation that represents the relationship between the radius, r, and arc length, s is s = Θ * r

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Answer:

A

Step-by-step explanation:

On Edge

The answer to the given question is <0.01.

What is confidence level?

The confidence level is the percentage of times we expect to get near to the same approximate if we run our experiment again or resample the population in the same way. The confidence level is the probability that the null hypothesis is true.

What is p-value?

P-value is the probability of getting the results you did, given that the null hypothesis is true.

When we are conducting a hypothesis testing and we determine the confidence level needed is 99%; then in order to reject the null hypothesis, the p-value needs to be below 0.01 (<0.01).

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Answer:

you see he is 4 pens down you see is 3 pence for every one he gets right. after doing 20 sums he is 4 down so 20 dived by is 5 if there is an answer choice for 16 pick 16 if both pick 5 first trust me.

1. The cheese production for 2006 is 7.76 billion.

2. The cheese produced in 2014 is 9.84 billion.

It should be noted that a function is simply used to show the relationship between the variables that are given.

In this situation, there's a 3% growth per year and the function for the cheese production is modelled as:

y = 7.1(1.03)^x

y = cheese production

x = number of years after 2003.

1. Therefore, since 2006 is 3 years after 2003, this will be

y = 7.1(1.03)^x

y = 7.1(1.03)³

y = 7.1 × 1.093

y = 7.76 billion

The production is 7.76 billion.

2. The production in 2014 will be;

y = 7.1(1.03)^x

y = 7.1(1.03)^11

y = 7.1 × 1.385

y = 9.84 billion

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Answer:

ob) 4

Step-by-step explanation:

th coefficient is the number that multiplies a variable

Answer:

Yes,the coefficient is 4

Step-by-step explanation:

You can suggest that managers should avoid the quick-fix mentality that makes management by best-seller so tempting by implementing the following strategies:

1. Understand the Unique Nature of Your Business: Managers should take the time to understand the unique nature of their business. They should realize that what worked for another company may not work for their own company.

2. Avoid Short-Term Solutions: Managers should avoid short-term solutions that provide quick results. They should focus on long-term solutions that will benefit the organization in the long run.

3. Develop a Comprehensive Strategy: Managers should develop a comprehensive strategy that includes long-term goals and objectives. They should also have a plan in place to achieve those goals.

4. Invest in Employee Development: Managers should invest in employee development by providing training and development opportunities. This will help to build a strong workforce that is capable of handling complex challenges.

5. Encourage Collaboration: Managers should encourage collaboration among team members. This will help to create a culture of teamwork and cooperation.

6. Monitor Progress: Managers should monitor progress and adjust strategies as necessary. This will help to ensure that the organization is on track to achieving its goals.

By following these strategies, managers can avoid the quick-fix mentality that makes management by best-seller so tempting. They can focus on long-term solutions that will benefit the organization in the long run.

Hope this helped you...

The required equation of the line using the given gradient and the points is given by y = (3/5)x - 7/5.

Points through which line passes are (x₁, y₁) = ( 4, 1 )

Gradient of the line = ( 3 / 5 )

Standard gradient-intercept form of a straight line is y = mx + c.

where 'm' is the gradient of the line

And 'c' is the y-intercept.

Point-slope form of a straight line is equal to,

y - y₁ = m(x - x₁)

Substitute the given values, we have,

⇒ y - 1 = ( 3/5 )( x - 4 )

Expanding the right-hand side we get,

⇒ y - 1 = (3/5)x - (3/5)4

⇒ y - 1 = (3/5)x - 12/5

Add 1 to both sides of the equation we get,

⇒ y = (3/5)x - 12/5 + 1

⇒ y = (3/5)x - 7/5

Therefore, the equation of the line that passes through the point (4,1) and has a gradient of 3/5 is y = (3/5)x - 7/5.

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To sketch the graph of a function that has a local maximum at 6 and is differentiable at 6, we can consider a function that approaches a maximum value at 6 and has a smooth, continuous curve around that point.

In the graph, we can depict a curve that gradually increases as we move towards x = 6 from the left side. At x = 6, the graph reaches a peak, representing the local maximum. From there, the curve starts to decrease as we move towards larger x-values.

The important aspect to note is that the function should be differentiable at x = 6, meaning the slope of the curve should exist at that point. This implies that there should be no sharp corners or vertical tangents at x = 6, indicating a smooth and continuous transition in the graph.

By incorporating these characteristics into the graph, we can represent a function with a local maximum at 6 and differentiability at that point.

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E) 10 minutes. At the local fast food joint, cars arrive randomly at a rate of 12 every 30 minutes, which is equivalent to a rate of 0.4 cars per minute (12 arrivals / 30 minutes). The service time for each car averages 2 minutes per arrival and follows an exponential distribution.

To find the average time in the queue for each arrival, we can use Little's Law. Little's Law states that the average number of customers in a system (L) is equal to the arrival rate (λ) multiplied by the average time a customer spends in the system (W). In other words, L = λW.

In this scenario, we are given the arrival rate (λ) and the service time (μ), but we want to find the average time a customer spends in the system (W). To do this, we can use the formula for the average time in an M/M/1 queue: W = 1 / (μ - λ).

Plugging in the values, we get W = 1 / (0.5 cars/minute - 0.4 cars/minute) = 1 / 0.1 cars/minute = 10 minutes. Thus, the average time in the queue for each arrival is 10 minutes.

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