Mathematics College

Please help: Determine the points at which the graph of the function has a horizontal tangent line.

Answers

Answer 1

[tex]\\ \tt\hookrightarrow f(x)=\dfrac{x^2}{x-6}[/tex]

Find inverse

[tex]\\ \tt\hookrightarrow y=\dfrac{x^2}{x-6}[/tex]

[tex]\\ \tt\hookrightarrow x=\dfrac{x^2+6y}{y}[/tex]

[tex]\\ \tt\hookrightarrow f'(x)=\dfrac{x^2+6x}{x}=x+6[/tex]

Now

[tex]\\ \tt\hookrightarrow x+6=0\implies x=-6[/tex]

Find Horizontal tangency

[tex]\\ \tt\hookrightarrow f(6)=\dfrac{(-6)^2}{-6-6}[/tex]

[tex]\\ \tt\hookrightarrow f(6)=\dfrac{36}{-12}=-3[/tex]

(x,y) =(-6,-3)

Related Questions

Evaluate the following

2/3 + 11/3 – 1/3

Answers

Answer:

12/3 which is =4

Step-by-step explanation:

for adding fractions you keep the denominator the same and just add or subtract the numerators

2+11-1=12

Danny and Delilah were playing a game where they drew digits and placed them on a game board. Danny built the number 247. Delilah built the number 724. How much greater is the value of the digit 2 in Danny's number than the value of the digit 2 in Delilah's number?

Answers

Answer:

• This student received Met because the student stated that the 2 in Danny’s number is ten times greater than the 2 in Delilah’s number. The student stated that the 4 in Delilah’s number is one tenth the value of the 4 in Danny’s number. The student stated that the 7 in Delilah’s number is 100 times the 7 in Danny’s number.

This student received Progressing because the student correctly stated that Danny’s number was ten times bigger. The student also stated that the 4 in Delilah’s number is ten times smaller. The student stated the value of the digit 7 without referring to how the values compared.

Step-by-step explanation:

hope this helps :) (:

2(x - 10) = 59
What are the steps to come to the correct answer?

Answers

Answer:

39.5

Step-by-step explanation:

Open the bracket by multiplying the numbers in the bracket by 2

2x-20=59

collect like terms(-20 crossing over the equal sign will become +20

2x=59+20

2x=79

Divide both sides by 2

[tex]\frac{2x}{2} =\frac{79}{2}[/tex]

x=39.5

[tex] \sf \large↪2(x - 10) = 59[/tex]

[tex] \: \: [/tex]

[tex] \sf \large \: ↪2x - 20 = 59[/tex]

[tex] \: \: [/tex]

[tex]\sf \large \: ↪2x = 59 + 20[/tex]

[tex] \: \: [/tex]

[tex]\sf \large \: ↪2x = 79[/tex]

[tex] \: \: \: [/tex]

[tex] \sf \large \: ↪x = \cancel \frac{79}{2} [/tex]

[tex] \: \: [/tex]

[tex]\sf \large \color{purple} ↪39.5[/tex]

[tex] \: \: \: [/tex]

What is the bar model for 20-x=6

Answers

Answer:

Step-by-step explanation:

20-x=6

20-14=6

hope this will help you

2(x+5) = [ ]x + [ ] what is the answer

Answers

Answer:

2x + 10

Step-by-step explanation:

2(x+5)

(2)(x) + (2)(5)

2x + 10

Answer:

2x + 10

Step-by-step explanation:

2 × X= 2x

2×5=10

so it is 2x + 10

Express the area of the entire rectangle.
Your answer should be a polynomial in standard form.
x+2
x+4

Answers

Answer:

A=x²+6x+8

Step-by-step explanation:

Answer: A=x²+6x+8

Step-by-step explanation: Since we are looking to find the area of the entire rectangle, we would use the formula. is the length and is width. You would approach this problem like any other area of the rectangle problem, except you are dealing with polynomials instead.

PLEASE HELP WILL GIVE BRAINLIEST

Answers

So considering she’s using the Pythagorean Theorem, it implies that it’s a right triangle. In this case, a^2+b^2=c^2 is used to solve for any length. While “a” and “b” are interchangeable, c is always the hypotenuse. And as you may know, the hypotenuse is the longer side of the right triangle.

So now solve for it to be sure if it is in fact a right triangle.

8^2+15^2=17^2

64+225= 289

289=289

Which means B is the error made.

Hope this helps!

Given two sides of a triangle, find a range of possible lengths for the third side.

4 cm, 17 cm

Answers

The third side will be 13

Really confused as to what I need to do. I tried to solve for Y and got 69 but that didn't work. Am I supposed to use a^2 + b^2= c^2? How do I do that when there are multiply letters? I really feel like there's just something I'm not seeing. Help is really appreciated, and please explain your answer.

Answers

Answer:

t = [tex]\sqrt{63} \\[/tex] or 7.94

Step-by-step explanation:

Yes, you have to use the Pythagorean theorem

A^2+B^2=C^2

So, A=9, B=t, C=12

9^2+t^2=12^2

81+t^2=144

-81 -81

t^2 = 63

t = [tex]\sqrt{63} \\[/tex]

in decimal 7.94

Hope this helps :)

pls give brainliest

Simplify the expression 6h +(-7.7d) – 16 + 5d - 2.6h.

Answers

Answer:

3.4h-2.7d-16

Step-by-step explanation:

Before we even start, we can already simplify some things

For example, in this equation it says +(-7.7d)

We can simplify this to 6h-7.7d-16+5d-2.6h

Now we have to get all of the common variables together

So the d’s and h’s have to be combined together in this equation

This makes a new equation of 3.4h-2.7d-16

That is our answer!

A half-ton pickup truck has a curb weight (weight empty but ready-to-drive) of 5/2 ton. If curb weight is evenly divided among four truck tires, how much weight is each tire bearing?

NO LINKS!!!

Answers

Answer:

0.625 tons or 5/8 tons

Step-by-step explanation:

(5/2)/4

0.625 tons or 5/8

Answer:

5/8 ton

Step-by-step explanation:

1/4 of 5/2 ton is on each tire, so the weight it is bearing is ...

(1/4)(5/2 ton) = 5/8 ton

Each tire is bearing 5/8 ton.

_____

Additional comment

If that is a US short ton (2000 lb), then the weight on each tire is 1250 pounds. If the tires are inflated to 50 pounds per square inch, then the area of rubber on the road at each tire is 1250 lb/(50 lb/in^2) = 25 in^2. That's the size of a 5-inch square.

(-4x-9)+(-2x-7) in simplest term

Answers

Answer:

-6x-16

Step-by-step explanation:
Combine like terms, (-4x-2x) + (-9-7) = -6x - 16

Step-by-step explanation:

We'll be combining like-terms.

Remove the addition sign, as it has no effect to the expression:

[tex] - 4x - 9 - 2x - 7[/tex]

Combine Like-Terms:

[tex] - 6x - 16[/tex]

-6x - 16 is your simplified expression.

Find the x - and y -intercepts of the graph of the linear equation -4x+8y=-16 .
The x -intercept is
.

The y -intercept is
.

Answers

Answer:

x -intercept is 4

y -intercept is -2

Step-by-step explanation:

SOLUTION:

(x -intercept)

-4x+8y= -16

-4x+8×0= -16

-4x+0= -16

-4x/-4 = -16/-4 (divide both sides by -4)

x=4

______________________

(y -intercept)

-4x+8y= -16

-4×0+8y= -16

0+8y= -16

8y/8 = -16/8 (divide both sides by 8)

y= -2

•| HOPE IT HELPS |•

Which expression is equivalent to 3m + 2m + m?

Answers

Answer:

Step-by-step explanation:

Combining like terms, we have

3m + 2m + m = (3 + 2 + 1)m = 6m.

Dividends for common stock must be in cash

Answers

Answer:

Legally, corporations must have a credit balance in Retained Earnings in order to declare a dividend. Practically, a corporation must also have a cash balance large enough to pay the dividend and still meet upcoming needs, such as asset growth and payments on existing liabilities.

The most likely sum that can occur when the two dice are rolled is
:: 4
:: 7
:: 10
:: 12

Answers

Answer:

Step-by-step explanation:

7 is the most common roll with two six-sided dice.

WILL GIVE BRAINLIEST AND 15 POINTS!

Answers

Answer:

Rational

Step-by-step explanation:

[tex]\sqrt[3]{125}[/tex] is also equivalent to 5

The definition of a rational number is any whole number, fraction, or decimal that ends or repeats, while an irrational number is any number that cannot be turned into a fraction.

5 is a whole number, and therefore, is a rational number.

Answer:

rational

hope it helps you

Today is saturday what day will it 21 day later

Answers

It will be Saturday because 21 days later is three weeks. Every week, or seven days, it will be that day again.

Answer:

thise day is

Tuesday

February 17 2022

Saturday

How do I find the product of (10−11i) and its conjugate?

Answers

Step-by-step explanation:

Given - 10 - 11i

1st requirement - conjugate

Z = X + Yi

Change the sign between x & yi to find the conjugate of a complex

number.

Z = 10 + 11i

Now multiply the conjugate & the 1st complex number

=10-11i × 10+11i

= (10 × 10)+ (10× 11i)+ (-11i × 10) + (-11i × 11i)

Recall that i = √-1

= 100 + 110i - 110i + (-(-(11 × 11))...since √-1 × √-1 = -1.

= 100 + 121

= 221.

If 600 people submitted the survey above, how many were in the 21-30 year old group? A) 112 B) 122 C) 132 D) 142

Answers

The survey is an illustration of expected value

132 people in the survey were in the 21 - 30 year old group

How to determine the number of people in the group

From the complete question, 22% of people are in the 21 - 30 year old group

Given that 600 people were surveyed.

The number of people in the 21 - 30 year old group would be:

n = 22% * 600

This gives

n = 132

Hence, 132 people in the survey were in the 21 - 30 year old group

Answers

Answer:

x=70°

Step-by-step explanation:

y=350° (angle inside triangle equal to 35°)

x=180-y-(180-105)

x=70°

Hope it helps!

Solution:

We can see that two lines are parallel, intersecting a line. We can also see a triangle formed with the lines.

=> x + (180 - 105) + 35 = 180 [The '35' came from Alternate inner angles]=> x + 75 + 35 = 180=> x + 110 = 180=> x = 180 - 110=> x = 70

The measure of x is 70°.

Find the area and the circumference of a circle with radius 3 cm.
Write your answers in terms of it, and be sure to include the correct units in your answers.

Answers

1. Observe problem

Solve for the area and Circumference of a circle who's radius is 3 cm

Area for circle formula:

pi*r^2=

9pi

I simplicity is needed, 9 pi is around

28.2743338823cm^2

Circumference for circle formula: 2*pi*r

which is

6pi

if simplicity is again needed, its around

18.8495559215cm

Male mosquitos have pretty short lifespans. Males of a certain species have lifespans that are strongly skewed to the right with a mean of 888 days and a standard deviation of 666 days. A biologist collects a random sample of 505050 of these male mosquitos and observes them to calculate the sample mean lifespan. We can assume that the mosquitos in each sample are independent.

What will be the shape of the sampling distribution of the sample mean lifespan?

Answers

Answer:

Approximately Normal

Step-by-step explanation:

The sample size is large (n50≥30n), so the sampling distribution of the sample mean will be approximately normal even though the population is skewed.

make h the subject of formula
[tex]a = \frac{1}{2} bh[/tex]

Answers

Answer:

[tex]a = \frac{1}{2} bh \\ \\ h = a \div ( \frac{1}{2}b ) \\ \\ h = a \times \frac{2}{b} \\ \\ h = \frac{2a}{b} [/tex]

cassidy had 8 7/10 inches of string. she used 5 3/8 inches of string

Answers

Answer:

Cassidy has 4 in of string left.

Step-by-step explanation:

I hope it helps! Have a great day!

Lilac~

Answer:

Step-by-step explanation:

4 inches

Brainliest if correct

Answers

9y-18 9y-18 9y-18

PLZZZZZZZZZZZ HELP!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

Answers

Answer:

Step-by-step explanation:

Your first step is to figure out which variable you want to cancel out.

Luckily, all these problems have x or y already set up to eliminate.

You can find these variables because they are opposite signs of each other, such as -x and x

Add the y's together and the #'s on the other side together, then solve to find the 2nd variable. Once you find one, you can plug that answer into the easier of the two equations and solve for the other variable.

why me lol? - whats 1+1

Answers

Answer:2

Step-by-step explanation:So the tides connection so therefore the magnetically magnetic magnitude yeah

if x varies direcly as y and x=9 when y=3 find x when y=12

Answers

Answer:

Step-by-step explanation:

x = 9 and y = 3

3 times 3 equal 9 so if y is 12 then 12 x 3 = 36

HELPPPPPPPPPPPPHHHHHHH

Answers

Answer:

26.3

Step-by-step explanation:

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