the curve with the equation y=8x^2 + 2/x has one turning point.
Find the coordinates of this turning point.

Answers

Answer 1

Answer:

(1/2, 6).

Step-by-step explanation:

Turning points in a graph may exist whenever the derivative equals 0. Hence, let’s differentiate and then solve our function.

We have:

[tex]\displaystyle y=8x^2+\frac{2}{x}[/tex]

Take the derivative of both sides with respect to x:

[tex]\displaystyle y^\prime=16x-\frac{2}{x^2}[/tex]

Simplify:

[tex]\displaystyle y^\prime=\frac{16x^3-2}{x^2}[/tex]

We will now set this equal to 0 and solve for x. Hence:

[tex]\displaystyle \begin{aligned} 0&=\frac{16x^3-2}{x^2} \\ 0&=16x^3-2 \\ 2&=16x^3 \\ \frac{1}{8}&=x^3 \\ \frac{1}{2}&=x \end{aligned}[/tex]

Hence, the graph turns at x=1/2. This is the x-coordinate.

Then it follows that the y-coordinate will be:

[tex]\displaystyle{\begin{aligned} y&=8(\frac{1}{2})^2+\frac{2}{\frac{1}{2}} \\ y&=8(1/4)+2(2) \\ y&=2+4 \\ y&=6\end{aligned}[/tex]

Hence, our coordinate Is (1/2, 6).


Related Questions

Hey everybody I have a quick math question but idk what the answer is! It would mean a lot if someone helped me. PS the pic is there!

Answers

Answer:

it would be 2.33 I divided it I hope I'm right :)

help please! pretty easy i just dont remember how to do it

Answers

Answer:

Step-by-step explanation:

the disc. is the part under the root in the general formula

which is equal b^2 - 4 x a x c

in this equation a = 1 " coefficient of x^2"

b = 0 "coefficient of x which isn't found here "

c = 12 " the absolute "

[tex]0^{2} - 4[/tex]×[tex]1[/tex]×[tex]12[/tex] = -4×12 = something i don't have a calculator

but it will be negative so the roots will be complex and unreal

:)

Ariana borrows $200 on a 6-year loan.She is charged 5% simple interest per year.How much interest is she charged for 6 years?What is the total amount she has to pay back? PLS HELP

Answers

Answer:

Results are below.

Step-by-step explanation:

Giving the following information:

Principal (P)= $200

Interst rate (r)= 0.05

Time (t)= 6

First, we need to calculate the total interest using the following formula:

I= P*r*t

I= 200*0.05*6

I= $60

Now, the total debt:

Total debt= P +I

Total debt= 200 + 60

Total debt= $260

What is the definition of a rhombus?

Answers

Answer:

not really sure what you are doing buta rhombus is just a sideways diamond

Step-by-step explanation:

Answer:

A rhombus is a parallelogram where all sides are equal in length.

Step-by-step explanation:

Properties of a rhombus are:

- Opposite angles are equal

- Diagonals are perpendicular and bisect each other and the angles they pass through.

- Opposite sides are parallel and are equal

- All sides are equal in length

Hope this helps :)

Use the given values to find the missing lengths in the figure. If necessary, express your answer as a
radical.


C = 7 cm and a = 4 cm
b= _____ cm

Answers

Answer:

√33 cm

Step-by-step explanation:

We know that this is a right triangle, which means that we can apply the Pythagorean Theorem, which states that for a right triangle with legs a and b and hypotenuse c:

a² + b² = c²

Here, a = 4 and c = 7, so plug thes in to find b:

a² + b² = c²

4² + b² = 7²

b² = 49 - 16 = 33

b = √33

The answer is thus √33 cm.

Which best describes the accuracy of Jill’s solution? Jill’s solution is accurate. Jill omitted a factor pair, which affected the GCF and factored expression. Jill made an error when determining the GCF from her list of factors. Jill made an error when writing the factored expression.

Answers

Answer:

Jill made an error when writing the factored expression.

Answer:

(B): Jill omitted a factor pair, which affected the GCF and factored expression.

Step-by-step explanation:

Hope this helps!! :D

I Need Help!!

Find the values of x and y that maximize the objective function P=2x+5y for the graph. What is the maximum value?

Answers

There is no local extremas but here is the objective function graphed

The Extreme Rock Climbing Club planned a climbing expedition. The total cost was $4600, which was to be divided equally among the members going. Prior to the trip,
10 members decided not to go. If the cost per person increased by $230, how many people went on the expedition?

Answers

If you divide the previous cost with the price per person, you would get the number of people who was previously planned to be going, which is 20. That said, with 10 people not going, there would be 10 people left with the price of 2300 to continue the expedition

Let x = number of people that were supposed to go to the trip, where x is greater than or equal to 0.

Let y = price per person initially with x people going on the trip.

xy = 4600

Solve for y.

y = 4600/x

(x - 10)(y + 230) = 4600

Replace y with the fraction 4600/x.

(x - 10)[(4600/x) + 230)] = 4600

What you need to do:

1. Solve (x - 10)[(4600/x) + 230)] = 4600 for x.

2. When you find x, subtract 10 from the value of x to find the number of people that went on the expedition.

You finish.

Can someone do my khan academy? It would really help me out .

Answers

Answer:

sorry but Im really busy.Maybe when Im done I can help you

A baseball team has won 8 out of the first 20 games and has 40 games remaining. The team needs a winning percentage of 62.5% make the playoffs. How many more wins does the team need in order to get into the playoffs? If the team wins the number of games to get into the playoffs, what is the final win percentage if the team wins 2 and loses 3 games in the playoff?

Answers

Answer:

30 More Games for Playoffs | Win Percentage of 40% in Playoffs

Step-by-step explanation:

We find the total amount of games by adding first 20 and 40 remaining

This will leave us with 60 games

In order to calculate the playoff, we would have to calculate 62.50% in those 60 games.

62.50% is 5/8, we divide 60 by 8 and get 7.50

We multiply both sides by 7.50 and get 37.50/60

We subtract 8 from 37.50 and get 29.50

We round it to the nearest ones and get 30

In order to win the game they would need to win 30 more games

To calculate the final win percentage, we would add 2 and 3, which would give us 5.

After winning 2 and losing 3,

it would give us 2/5,

which in percentage is 40%

Help again! This is super important!!!

Answers

Answer:

2 and 4 are Not a function

1 and 3 are a function

Step-by-step explanation:

Answer:

2nd and 3rd are functions and 1st and last are not functions

Step-by-step explanation:

Evaluate: -30 ÷ 2

a. 10
b. 15
c. -15
d. -10

Answers

C......................
Answer:-15Step-by-step explanation:-30/2=1530/2=15

1000 digits of pi...

Answers

3.1415926535 8979323846 2643383279 5028841971 6939937510 5820974944 5923078164 0628620899 8628034825 3421170679 8214808651 3282306647 0938446095 5058223172 5359408128 4811174502 8410270193 8521105559 6446229489 5493038196 4428810975 6659334461 2847564823 3786783165 2712019091 4564856692 3460348610 4543266482 1339360726 0249141273 7245870066 0631558817 4881520920 9628292540 9171536436 7892590360 0113305305 4882046652 1384146951 9415116094 3305727036 5759591953 0921861173 8193261179 3105118548 0744623799 6274956735 1885752724 8912279381 8301194912 9833673362 4406566430 8602139494 6395224737 1907021798 6094370277 0539217176 2931767523 8467481846 7669405132 0005681271 4526356082 7785771342 7577896091 7363717872 1468440901 2249534301 4654958537 1050792279 6892589235 4201995611 2129021960 8640344181 5981362977 4771309960 5187072113 4999999837 2978049951 0597317328 1609631859 5024459455 3469083026 4252230825 3344685035 2619311881 7101000313 7838752886 5875332083 8142061717 7669147303 5982534904 2875546873 1159562863 8823537875 9375195778 1857780532 1712268066 1300192787 6611195909 2164201989

Answer:

3.1415926535 8979323846 2643383279 5028841971 6939937510 5820974944 5923078164 0628620899 8628034825 3421170679 8214808651 3282306647 0938446095 5058223172 5359408128 4811174502 8410270193 8521105559 6446229489 5493038196 4428810975 6659334461 2847564823 3786783165 2712019091 4564856692 3460348610 4543266482 1339360726 0249141273 7245870066 0631558817 4881520920 9628292540 9171536436 7892590360 0113305305 4882046652 1384146951 9415116094 3305727036 5759591953 0921861173 8193261179 3105118548 0744623799 6274956735 1885752724 8912279381 8301194912 9833673362 4406566430 8602139494 6395224737 1907021798 6094370277 0539217176 2931767523 8467481846 7669405132 0005681271 4526356082 7785771342 7577896091 7363717872 1468440901 2249534301 4654958537 1050792279 6892589235 4201995611 2129021960 8640344181 5981362977 4771309960 5187072113 4999999837 2978049951 0597317328 1609631859 5024459455 3469083026 4252230825 3344685035 2619311881 7101000313 7838752886 5875332083 8142061717 7669147303 5982534904 2875546873 1159562863 8823537875 9375195778 1857780532 1712268066 1300192787 6611195909 2164201989

Step-by-step explanation:

Write each percent as a decimal 21% 0.4%​

Answers

21% is 0.21
0.4% is 0.004

Answer:

21% would convert to 0.21 and 0.4% would convert to 0.004

10 = n +19
Inverse operation
Answer: 9=n

Answers

Answer:

n=-9

Step-by-step explanation:

subtract 19 to both sides

19-19=0

10-19=(-9)

n=-9

to verify add 19+(-9)=10

hope this helps :3

if it did pls mark brainliest

n = -9
10 = n + 19
n + 19 = 10
n + 19 - 19 = 10 - 19
n = -9

Describe the shape of the distribution.
A. It is skewed.
B. It is bimodal
C. It is uniform
D. It is symmetric
Please hurrry

Answers

Answer:

A

Step-by-step explanation:

the picture shown above is skewed

Answer:

It is skewed

Step-by-step explanation:

Just did test

Determine the number that can be used in place of the question mark to make the equation true.
49^? = 7
The solution is

Answers

49^x = 7
2x = 1, x = 1/2
The solution is 1/2

Who cursed Narcissus with forcing him to fall in love with his reflection?

Hera
Aphrodite
Hestia
Persephone

Answers

It should be Aphrodite

MAKE SURE TO USE SURDS ANSWE ASAP

Answers

Answer:

22 +  2 √ 2

Step-by-step explanation:

hope this helps

What is the inverse of the function f(x)=-\dfrac{1}{2}(x+3)f(x)=−1/2

(x+3)f, left parenthesis, x, right parenthesis, equals, minus, start fraction, 1, divided by, 2, end fraction, left parenthesis, x, plus, 3, right parenthesis?

Answers

Answer:

-2x - 3

Step-by-step explanation:

I hope this helps!!

Answer:

-2x-3

Step-by-step explanation:

The value of a rare baseball card issued in 1989 is represented by the function , where x represents the number of years since the baseball card was issued. Use the Remainder Theorem to find the value of the card in 1999.

Answers

Answer: 5

Step-by-step explanation:

which property is used in the equation below?
3(2x + 6) = 6x + 18

Answers

Answer:

distributive property

Step-by-step explanation:

:)

How would you express the area of the rectangle using the Distributive Property?

A. 5(x + 3)
B. x(3 + 5)
C. 3(x + 5)
D. 3x + 5

Answers

C. but I'm not sure, but I do think that's it

Tell me the ordered pair for the y intercept

Answers

Answer:

(0, 3)

Step-by-step explanation:

The y-intercept is point on the y-axis that the line passes through.

You can see the line passes through 3 on the y-axis.

On the y-axis, every point has a 0 for the x-coordinate.

The ordered pair for the point that is 3 on the y-axis is (0, 3).

Anyone know how to do this??

Answers

Answer:

A

Step-by-step explanation:

11 is the soln for step 2 as you find that 16=16

The student ends up messing up in step 2

so that rules out b,c and d is also false,because when plugging in 11 to the original, you get a wrong answer.

40 percent of students in a class of 35 students are girls. how many girls are in this class?

Answers

Answer:

14 girls

Step-by-step explanation:

40% of 35 = [tex]\frac{40}{100}[/tex] × [tex]\frac{35}{1}[/tex]  [tex]\frac{40}{100}[/tex] × [tex]\frac{35}{1} = \frac{1400}{100}[/tex]  [tex]\frac{1400}{100} = \frac{14}{1} = 14[/tex]  

I hope this helps!

Answer:

14 girls in the class

Step-by-step explanation:

use percentage equation, p = nw or part of the question = the percentage times the total amount.

So in this case our p, or girls in the class (which is part of the total), is unknown. We have the percentage and we have the total. So all we need to do is multipy them. However how do you multiply percentage . . . well 40 percent also equalts to 0.40. So all you have to do is multiply .40 by 35 and you have your answer.

. A honeybee leaves the hive, traveling at a speed of 4 mph and returns 1 hour later. What was the distance traveled and the displacement of the honeybee in miles?

Answers

Answer:

4miles

Step-by-step explanation:

Step one:

given

speed, v= 4mph

time taken t=1 hour

The velocity is defined and the rate of change of displacement

Required:

Distance traveled

we know that the expression relating distance, velocity and time is

velocity= distance/time

distance= velocity* time

substitute we have

Distance=4*1

Distance= 4miles

The distance traveled and the displacement of the honeybee in miles  4miles

Angle ABC has a measure of 125° Angle ABC is rotated 75° about point B to create angle A'B'C'. What is the measure, in degrees, of angle A'B'C

Answers

Answer:

m∠A'B'C' is 125°

Step-by-step explanation:

The given parameters are;

The measure of ∠ABC = 125°

The form of transformation applied to ∠ABC = 75° rotation about the point B

Given that a rotation of a geometric figure is a form of rigid transformation, the distance between the coordinates of the points in the preimage are equal to the distance between the coordinates of the points on the image;

Therefore, the angle formed by the ray AB and CB and the angle formed by the ray A'B' and C'B' are equal

From which we have;

m∠ABC = m∠A'B'C' = 125°

Help I appreciate it thank you

Answers

Answer:

Yes.

Step-by-step explanation:

As long as there is exactly one y value for each x value, it is a function.

Simplify
[tex]-3\sqrt{5}+3\sqrt{6}-2\sqrt{54}[/tex]

Answers

Answer:

-3/5 -3/6

Step-by-step explanation:

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