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]

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Related Questions

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!

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.

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 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

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

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"

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

Answers

Answer:

it'sssssss 2.51

Step-by-step explanation:

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!!!!!:!:!:!:!:!!:!’dmemdmsmsms

Answers

DI AKO KRINUSHBAK SANA KAYO DIN

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!

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 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!

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]

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

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).

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.

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

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

Please help i am confused

Answers

Answer: 12.16

Step-by-step explanation:

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 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:

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

:)

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

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

Answers

Answer:

angle 1=angle 4 ( vertical opposite angle)

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.

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.

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

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:

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:

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