Fine The Gradient of the curve xy=6, at point 1 & 6.
[tex] \\ \\ \\ \\ \\ \\ \\ [/tex]
Thnx ~~​

Answers

Answer 1

Answer:

[tex]\fbox{Gradient of curve = -6}[/tex]

Step by step explanation:

Given:

Equation of curve ↦ xy = 6

Point ↦(1,6)

To find:

The gradient of curve = ?

Solution:

[tex]Using \: the \: equation, \\ xy = 6 \\ [/tex]

Taking log both the side,

[tex]log(xy) = log(6) \\ log(x) + log(y) = log(6) \\ Taking \: derivative \: both \: the \: side \\ \frac{1}{x} + \frac{1}{y} \cdot\frac{dy}{dx} = \: 0 \\ (Derivative \: of \: any \: constant =0) \\ \frac{1}{y} \cdot\frac{dy}{dx} = - \frac{1}{x} \\ \frac{dy}{dx} = - \frac{y}{x} \\ To \: find \: gradient \: at \: point (1,6) \\ \frac{dy}{dx} \mid_{(1,6)} = \frac{ - 6}{1} \\ \frac{dy}{dx} \mid_{(1,6)} = - 6 \\ \fbox{Gradient of curve = -6}[/tex]

Thanks for joining brainly community!


Related Questions

Which of the following statements is FALSE?

AO = 7.8 cm
c1 = 40°
BO = 7.8 cm
a2 = 40°

Answers

Parallelogram is a quadrilateral with equal diagonals. The statement BO = 7.8 cm is the only false statement

Properties of a parallelogram

From the given diagram, the opposite sides and angle of the figure are the same but the diagonals are not equal. This shows that:

m<B = m<D

m<A = m<C

Since the diagonals are not equal that is BD is not equal to AC, hence:

OB ≠ OC

Hence the statement BO = 7.8 cm is the only false statement

Learn more on parallelogram here: https://brainly.com/question/970600

Answer:BO = 7.8 cm

Step-by-step explanation: just did the quiz

Please help i am confused

Answers

Answer: 12.16

Step-by-step explanation:

What is the area of this figure?
Use 3.14 for TT.

Please help

Answers

Answer:

406.08

Step-by-step explanation:

First FInd the area of the rectangle : which is short side * long side

-> 15*12=180m

Then find the area of the half circle, the formula of the area of a circle is [tex]\pi r^2[/tex]

here it's half a circle so it's [tex]\frac{\pi r^2}{2}[/tex] where r is 12

-> [tex]3.14\cdot \frac{\left(12\right)^2}{2}=226.08 m[/tex]

Finally just add the area of the rectangle with the area of the half circle

-> [tex]180+226.08=406.08 m[/tex]


!!!!!:!:!:!:!:!!:!’dmemdmsmsms

Answers

DI AKO KRINUSHBAK SANA KAYO DIN

Terrence measured an Italian restaurant and made a scale drawing. The scale of the drawing was 7 centimeters = 2 meters. What scale factor does the drawing use?
Simplify your answer and write it as a fraction.

Answers

Answer:

200/7

Step-by-step explanation:

(2 meters)/(7 centimeters) or (2m/7cm)

1 meter = 100 cm

(2m/7cm)*(100cm/1m) = 200/7 (or   28.57) scale factor.

what is AxBxD and A=130 B=300 and D=? and when do the multiplication do the answer x 900 and than we are done :)

Answers

The answer is 35,100,000

f(x) = 4x -8;{-2, -1,0,1,2}
What is the range? Choose the correct answer below.
A. {-16,- 11,-8, -3,0)
B. {-16, -12,-8, -4,0}
C. {-17, -12,- 8, -4,1}
D. {-16, -11, -9,-3,0)

Answers

Answer:

B

Step-by-step explanation:

4(-2)-8 = -16, so not C
4(-1)-8 = -12, so not A or D
4(0)-8 = -8, so not D
4(1)-8 = -4, so not A or D
4(2)-8 = 0, so not D

Hello people ~
factorise ↷
x^2 + 6x + 8​

Answers

[tex]\qquad\qquad\huge\underline{\boxed{\sf Answer}}[/tex]

Let's solve ~ ☂

⧠ Here, I'm using middle term split method :

[tex] \qquad\rightarrowtail \sf {x}^{2} + 6x + 8[/tex]

[tex] \qquad\rightarrowtail \sf {x}^{2} + 4x + 2x+ 8[/tex]

[tex] \qquad\rightarrowtail \sf {x(x}^{} + 4) + 2(x+ 4)[/tex]

[tex] \qquad\rightarrowtail \sf (x + 2)(x+ 4)[/tex]

[tex]\\ \rm\rightarrowtail x^2+6x+8[/tex]

[tex]\\ \rm\rightarrowtail x^2+4x+2x+8[/tex]

[tex]\\ \rm\rightarrowtail x(x+4)+2(x+4)[/tex]

[tex]\\ \rm\rightarrowtail (x+2)(x+4)[/tex]

Done!

A football is punted from a height of 2.5 feet above the ground with an initial vertical velocity of 45 feet per second.

Write an equation to model the height h, in feet, of the ball t seconds after it has been punted.
The football is caught at 5.5 feet above the ground. How long was the football in the air?

Answers

Answer:

1.451 seconds.  Hurry.

Step-by-step explanation:

The position(height, h) of the foot ball will be given by the equation:

h = -32.2t^2 + 45t + 2.5

The term -32.2t^2 consists of the acceleration caused by gravity at Earth's surface ( -32 ft/sec^2) and the term +45t accounts for the initial velocity.  The + is assigned since the ball is moving vertically from ground.  The negative sign in -32t^2 is due to the acceleration being towards ground.  The term 2.5 accounts for the fact that the initial height of the ball is 2.5 feet above ground.

We can either calculate or graph with this function to find the time the ball spends in the air:

Calculate:

h = -32.2t^2 + 45t + 2.5

We need a value of t that would cause h to be 5.5 feet, the level it was caught:

5.5 = -32.2t^2 + 45t + 2.5

-32.2t^2 + 45t + 2.5 = 5.5

-32.2t^2 + 45t -3.0  = 0

Solve for t using the quadratic formula.  I get a value of 1.33 seconds.

Graph:

See the attached graph.  It confirms the 1.33 second value

50
The graph shows a proportional relationship between the
number of kilometers traveled by a bicycle (y) and the number of
minutes (x).
45
40
35
30
Distance traveled (km)
What is the unit rate, expressed in kilometers per minute?
25
20
O 0.30 km/min
15
(40, 12)
O 0.33 km/min
03.10 km/min
->
5 10 15 20 25 30 35 40 45 50
Time (min)
3.33 km/min
1
2
3
4
5
6
7
8
Next
9
10

Answers

Given a graph with a line running through coordinates (0,0) and coordinates (40,12), the unit rate of the relationship between the number of kilometers traveled by a bicycle (y) and the number of minutes (x) is given by the slope of the line.

use the terms 8 , 3x , 3/2 and 4x to complete the expression below so that’s is equivalent to 9x - 12

Answers

Answer:

A quadratic inequality is an equation of second degree that uses an inequality sign instead of an equal sign. The solutions to quadratic inequality always give the two roots. The nature of the roots may differ and can be determined by discriminant (b2 – 4ac).

Y= x + 6
y= -x+2

solve each system of equations by substitution

Answers

Answer:

x= -2
y=4

Step-by-step explanation:


Since we have an equation set equal to y, we can plug it in for either value of y.

I will be using y= x+6 in this case.

Plug in x+6 for the other equation, so instead of y=-x+2 it will now be that x+6 = -x+2

Now add x to both sides, and that will remove the x on the left side leaving us with 2x+6 = 2

Now, subtract 6 from both sides to get 2x isolated, and you will get 2x= -4

Divide both sides by 2 to get x= -2

Not plug x= -2 in back for the top (or bottom) equation and get that y=4

Hope this helps and isn't too complicated!

Please help, I’ll mark your answer as brainliest.

Answers

Answer:

it'sssssss 2.51

Step-by-step explanation:

========≈==================

What will be the sales price of the car if it has a regular price of $16 000 and is on sale for 20% off? Determine the cost of the car including 13% tax.

Answers

Answer:

14,464

Step-by-step explanation:

16,000 - 20% = 12,800

12,800 + 13% = 14,464

I hoope this is correct. Have a wonderful day and dream a good dream of good people. :)

Factor completely.
x2 - 10x + 24

Answers

Answer:

[tex]\boxed{\sf{(x-4)(x-6)}}[/tex]

Step-by-step explanation:

In order to solve this problem, all you have to do is multiply their expressions by their factors.

To begin, you must group these expressions.

[tex]\sf{x^2-10x+24=\left(x^2-4x\right)+\left(-6x+24\right)}[/tex]

After that, you factor.

Solve.

[tex]\sf{x^2-4=x(x-4)}[/tex]

-6x+24=-6(x-4)

Then rewrite the problem down.

x(x-4)-6(x-4)

Factor by the common term.

(x-4)(x-6)

Therefore, the final answer is (x-4)(x-6).

I hope this helps you! Let me know if my answer is wrong or not.

Find the median and mean of the data set below:

Answers

Median = middle number = 30
Mean = sum of all numbers / how many numbers = 135 / 5 = 27

Answer:

27=mean. 30=Median

Step-by-step explanation:

trust me I know what I'm doing

OMG I NEED HELP LIKE RIGHT NOW

Answers

Answer:

x coordinate is +3 and y coordinate is +1

Step-by-step explanation:

just count three squares right and one square down from D

What is the length of a diagonal of rectangle EFGH?

Answers

Answer:

[tex]\sqrt{53}[/tex]

Step-by-step explanation:

First, we find out the length of EH, which is 7. And then, we find the length of GH, which is 3. If we square both the numbers and add them, we get 53. And then we square root that to get [tex]\sqrt{53}[/tex]

Hope this helps <:)

Don't forget to put brainliest!

If the cost of a dozen pencil is ₹ 159.48, what will be the cost of 24 such pencil?​

Answers

Answer:

₹ 318.96.

Step-by-step explanation:

24/12 = 2 , so twice as much;

159.48 * 2 = 318.96

please help me with this question , we are now just learning it .

Answers

Answer:

angle 1=angle 4 ( vertical opposite angle)

A box of 15 cookies costs $9dollar sign, 9. What is the cost for 1 cookie?

Answers

Answer:

$1.66 or $1.70 if you round up

Step-by-step explanation:

Ben and Cam are scuba diving. Ben is 15.8 meters below the surface of the water. Cam is 4.2 meters below
Ben. Andrew is a further 16 meters.


Part 1 Write an expression That'll allow you to find Andrew's depth.

Part 2: What's Andrew's depth?

Answers

Answer:

27.6

Step-by-step explanation:

1) Say bens depth is x

Cam's depth is x + 4.2

Andrew's depth is x + 4.2 + 16 or x + 11.8

1) andrew's depth = x + 11.8, where x is 15.8.

Therefore, his depth is 27.6 meters.

Benjamin has 3 dimes and 4 nickels. What percent of a dollar does he have?

Answers

Answer:

50%

Step-by-step explanation:

Hope this helped

Maybe mark brainiest

Dime = 10 cents

Nickel = 5 cents

Total value of coins = 3(10) + 4(5) = 30 + 20 = 50

To find the percent, first create a fraction. The fraction will be the amount of money that Benjamin has over the total (one dollar).

50 / 100 = 5 / 10 = 0.5

0.5 x 100 = 50

50%

Answer: 50% of a dollar

Hope this helps!

Help will give brainleiest

Answers

Answer:

40" by 50"

Step-by-step explanation:

From inspection of the diagram,

height of 2 squares of the quilt ≈ height of doll plus a little bit

⇒ height of 2 squares of the quilt ≈ 18 + 2 = 20 in

⇒ height of 1 square of the quilt ≈ 20 ÷ 2 = 10 in

As the height of a square = width of a square

⇒ width of 1 square of the quilt ≈ 10 in

Dimensions of the quilt

width = 4 squares = 4 × 10 = 40 in

height = 5 squares = 5 × 10 = 50 in

Ratios

We can also work out the width and height by using ratios.

The ratio of width to height of the quilt = 4 squares : 5 squares

If we multiply by 10, the ratio becomes 40 : 50

Final Solution

40" by 50"

7. Find the volume of a rectangular prism if the height is 14 inches and the area of the base is 30 square inches. Type your answer without units.

Answers

Answer:

420

Step-by-step explanation:

V = whl is the volume of a rectangular prism. w*h is the area, so V is area times height.

This gives us: V = 30 * 14 = 420.

Select the values that would satisfy the following inequality:
K ≤ 12.75

|12.75|

|-12.75|

13

|-15|

0

Answers

Answer:

If it is a conjunction that uses the word and, the solution must work in both inequalities and the solution is in the overlap region of the graph. If it is a disjunction that uses the word or, the solution must work in either one of the equations.

Step-by-step explanation:

The question is in the image. I really need help, please.

Answers

Answer:

  (b)  65/27

Step-by-step explanation:

Here, we notice the index for the summation runs from 0 to 3, so there are a total of 4 terms.

The sum represented by the summation symbol is ...

  5(-2/3)^0 +5(-2/3)^1 +5(-2/3)^2 +5(-2/3)^3

  = 5(1 -2/3 +4/9 -8/27)

  = 5/27(27 -18 +12 -8)

  = 5(13/27) = 65/27

__

There is a formula for the sum of a geometric series:

  Sn = a1×(1 -r^n)/(1 -r)

Here, the first term is a1 = 5(-2/3)^0 = 5. The common ratio is the base of the exponential, r = -2/3. So, the sum of n=4 terms is ...

  S4 = 5×(1 -(-2/3)^4)/(1 -(-2/3)) = 5×(1 -16/81)/(5/3) = 65/27

Do problems #4-6. Your answer choices are in a table below. Type your answer numbers the blank to move on! No spaces, no commas. Put it all together. *

I need help with 5

Answers

Answer:

[tex]\frac{1}{2a}[/tex]

Step-by-step explanation:

Simplify or expand

[tex](2a)^{-1}[/tex]

Simplify using negative exponent rule [tex]a^{-n}=\frac{1}{a^n}[/tex]

[tex]\frac{1}{2a}[/tex]

I hope this helps you

:)

Simplify the following if x = 3 & y = 4:

1. 2x + y =

2. 3x + 2y =

3. 3y + 2x =

4. 10x + 4y + 2x =

5. 6y + 5x =

6. 7x + 4y =

Use your knowledge about parentheses and substitution to solve the following:

q = 1; r = 2; s = 3; t = 4; x = 5; y = 6

7. 2(x+4) + 10 =

8. 3(4x) + 4 =

9. 10(xy) =

10. 2(x + y) =

11. 3(rs) + 4(x)

12. 2(q) + 2(x + t) =

13. 6(3t + 4s) =

14. 10(10x) + 10y =

15. x(xy) =

16. r(s)(t) =

17. (r)(s)(t)(x)(y) =

18. 6(2x + 3Y) =

Answers

The top one is correct …..correct is correct

Answer: (All below)

Step-by-step explanation:

1. 2x + y = 10

2(3) + 4) = 10

6 + 4 = 10

2. 3x + 2y =

3(3) = 2(4) =

9 + 8 = 17

3. 3y + 2x = 18

3(4) + 2(3) = 18

12 + 6 = 18

4. 10x + 4y + 2x = 52

10(3) + 4(4) + 2(3) = 52

30 + 16 +6 = 52

46 + 6 = 52

5. 6y + 5x =39

6(4) + 5(3) = 39

24 + 15 = 39

6. 7x + 4y = 37

7(3) + 4(4) = 37

21 + 16 = 37

7. 2(x+4) + 10 = 28

2( 5 + 4) + 10 = 28

2(9) + 10 = 28

18 + 10 = 28

8. 3(4x) + 4 = 64

3(4(5)) + 4 = 64

3(20) + 4 = 64

60 + 4 = 64

9. 10(xy) = 300

10(5(6)) = 300

10(30) = 300

10. 2(x + y) = 22

2(5 + 6) = 22

2(11) = 22

11. 3(rs) + 4(x)

3(2(3)) + 4(5) =

3(6) + 20 =

18 + 20 = 38

12. 2(q) + 2(x + t) = 20

2(1) + 2(5 + 4) =  20

2 + 2(9) = 20

2 + 18 = 20

13. 6(3t + 4s) = 84

6(3(1) + 4(3)) = 84  

6(2 + 12) = 84

6(14) = 84

14. 10(10x) + 10y = 560

10(10(5)) + 10(6) = 560

10(50) + 60 = 560

500 + 60 = 560

15. x(xy) = 150

5(5(6)) = 150

5(30) = 150

16. r(s)(t) = 24

2(3(4)) = 24

2(12) = 24

17. (r)(s)(t)(x)(y) =720

(2)(3)(4)(5)(6)= 720

6(20)(6) = 720

120(6) = 720

18. 6(2x + 3Y) = 1080

6(2(5) + 3(6)) = 1080

6(10 + 18) = 1080

6(180) = 1080

On Monday, Payton rode 7 miles on a bike. On Tuesday, she rode 23
miles. On Wednesday, she rode 3 times as much as she did Monday
and Tuesday combined. What equation could you use to find how
many miles Payton rode on Wednesday, r?

Answers

Answer:

483

Step-by-step explanation:

I really really pray and hope this helpss.

Answer:

X=3(7+23)

Step-by-step explanation:

Other Questions
I need help I failing Is the conflict an important part of the story. Why or why not correctly label the following components of the kidney. What is a theme of the play The Glass Menagerie?Select the two correct answers.Guilt can affect a person's perspective about life.Living in denial can prevent one from dealing with reality.Parents sometimes go to extremes to ensure their children have the chance to succeed.There is always a chance of failing when one takes a risk.To find happiness, one must follow one's true path. X 2.6.PS-14Question Help0Marcia drew a plan for a rectangular piece of material that she will use for a blanket. Three of thevertices are (-2.8, -1.7), (-2.8,3.7), and (2.8,3.7). What are the coordinates of the fourth vertex?The coordinates of the fourth vertex are 1(Type an ordered pair, using integers or decimals.)Enter your answer in the answer box and then click Check Answer.Clear AllAll parts showingCheck AnswerReview progressQuestion 5of 8BackNext Identify the key characteristics of the exponential function.y =2(1)" A rock is dropped from the top of a building and hits the ground at a velocity of 72ft/sec. If the acceleration due to gravity is 32ft/sec^2, what is the height of the building? Please answer number 33 correct!! The crunchy granola company is a diversified food company that specializes in all natural foods. the company has three operating divisions organized as investment centers. condensed data taken from the records of the three divisions for the year ended june 30, 20y7, are as follows: cerealdivisionsnack cakedivisionretailbakeries divisionsales$25,000,000 $8,000,000 $9,750,000 cost of goods sold16,670,000 5,575,000 6,795,000 operating expenses7,330,000 1,945,000 2,272,500 invested assets10,000,000 4,000,000 6,500,000 the management of the crunchy granola company is evaluating each division as a basis for planning a future expansion of operations.required:question content area1. prepare condensed divisional income statements for the three divisions, assuming that there were no support department allocations.2. using the dupont formula for return on investment, compute the profit margin, investment turnover, and return on investment for each division. if required, round your answers to one decimal place.3. when faced with limited funds for expansion, management should consider an expansion of the division first. 20) Which of these sentences might BEST serve as a topic sentence of a paragraph telling how to write a book report? A) Be sure that your book report gives clear details about the book. B) Writing a good book report takes preparation and planning. C) Book reports should be submitted in the correct format. D) You may need to refer back to the book while you write your reportPlease WILL GIVE BRAINLEST Which value of fff makes 3f+5=323f+5=323, f, plus, 5, equals, 32 a true statement?Choose 1 answer:Choose 1 answer:(Choice A)Af=6f=6f, equals, 6(Choice B)Bf=8f=8f, equals, 8(Choice C)Cf=9f=9f, equals, 9(Choice D)Df=12f=12 Why did the Anti-Federalists propose adding the Bill of Rights to the United States Constitution?A. to delay ratification of the Constitution for as long as possibleB. to place limits on the power of the new federal governmentC. to ensure a separation of powers between branches of governmentD. to provide a fair system of representation for smaller states Leyla is redecorating her living room. The room is in the shape of a right rectangular prism. The dimensions of the room are 15 feet in length by 10 feet in width by 8 feet in height.She plans to cover the floor with hardwood. The cost of the hardwood is $3 per square foot. She plans to cover the walls and the ceiling with paint. Each container of paint costs $30 and can cover 275 ft.What is the total cost of the hardwood flooring and paint needed for this room?Drag and drop the responses to correctly complete these sentences. Which sentence from the article would be MOST important to include in a summary of the article? (A) It's a terrific boredom-buster, can improve your memory, and is fun for the whole family. (B) Reading books that you enjoy and want to continue reading is a great way to maintain your habit and become a life-long reader. (C) If you travel a lot, read on the plane, bus or train instead of watching a movie or scrolling through social media. (D) Curling up with a soft blanket and squashy pillow can make reading a delightful way to rest and recharge. What are the two chemical components of chromosomes?. how were the peace plans that ended world war 2 different from the treaties of versilles (05.02)A line passes through (2, 8) and (4, 12). Which equation best represents the line?oy-x+6=2y = 2x + 7y = 2x + 4oy-*x+10= Mood swings __________ question 2 options: are a sign that something is wrong. do not lead to strong feelings. can always be controlled. are part of growing up. What phrase is a description of 2m + 7 For this assignment, you will develop a model to describe the cycling of matter and the flow of energyamong living and nonliving parts of an ecosystem. This project includes both an individual and a grouppart. On your own, you will research an organism that is assigned to you. In your group, you will combineyour organism with the organisms researched by other students to create a food web. Together, you willwrite two short paragraphs explaining how energy and matter move through the food web.