The straight line 2x + 3y = 7 meets the curve
xy + 10 = 0 at the points P and Q. Calculate the
gradient of the curve at P and at Q.​

Answers

Answer 1

Step-by-step explanation:

xy + 10 = 0. => y = -10/x.

2x + 3y = 7. => 3y = -2x + 7, y = -2/3 x + 7/3.

When -10/x = -2/3 x + 7/3,

-10 = -2/3 x² + 7/3 x, 2/3 x² - 7/3 x - 10 = 0.

=> 2x² - 7x - 30 = 0

=> (2x + 5)(x - 6) = 0

=> x = -2.5 or x = 6.

dy/dx = d/dx [-10/x] = 10/x².

When x = -2.5, dy/dx = 10 / (-2.5)² = 1.6.

When x = 6, dy/dx = 10 / (6)² = 5/18.

Hence the gradients at the points are 1.6 and 5/18.


Related Questions

A rectangle is 36 m long and 25m broad .Find the cost of carpeting the floor at the rate of R.s 650 \ square meter .

Answers

Answer:

585000Rs

Step-by-step explanation:

Area=l×b

Area =total cost/rate or rate ×area

please help will give brainliest if correct i know it's not C ​

Answers

Answer:

Table 1

Step-by-step explanation:

Table represents a function because the Input does not repeat.

Answer:

the answer would be the first one

Step-by-step explanation:

A 5.5-foot-tall woman walks at 8 ft/s toward a street light that is 22 ft above the ground. What is the rate of change of the length of her shadow when she is 20 ft from the street light? At what rate is the tip of her shadow moving?

Answers

Answer: [tex]\frac{8}{3}\ ft/s[/tex]

Step-by-step explanation:

Given

length of shadow =22 ft

height of woman =5.5 ft

speed of woman [tex]\frac{dy}{dt}=8\ ft/s[/tex]

from the figure, we can write

[tex]\frac{22}{x+y}=\frac{5.5}{x}[/tex]

at given instant

y=20 ft

so, using similar triangle properties

[tex]\frac{22}{x+20}=\frac{5.5}{x}\\22x=5.5x+110\\16.5x=110\\x=6.67\ ft[/tex]

Again we can write

[tex]\dfrac{22}{x+y}=\dfrac{5.5}{x}\\22x=5.5x+5.5y\\16.5x=5.5y\\3x=y\\\text{differentiate w.r.t time} \\3\frac{dx}{dt}=\frac{dy}{dt}\\\frac{dx}{dt}=\frac{1}{3}\times 8=\frac{8}{3}\ ft/s\ \text{away from the woman}[/tex]

Help Help Help meeeeeeeeeeeeeee pleasee with math thank you

Answers

Answer:

b

Step-by-step explanation:

i got it right oon plato

Answer:

it should be y= 5x + 5 or y= 15x + 5

Step-by-step explanation:

I had something similar like a week ago and I am 100% its one of those

Which expression simplifies 6(2 + x + x + y) using only 3 terms

Answers

Answer: 6(2+2x+1y)

Step-by-step explanation:

i think that is the anwser

CORRECT ANSWERS ONLY

Answers

Answer:

-5x^3+8

Hope this helps

How to I do this problem ?

Answers

Answer:Takeyour time

Step-by-step explanation:

the race is 20 minutes long. aritza gets a 5 meter head start after 2 minutes she is at 10 meters what is her equation

Answers

5+2+10 is what i thibnk the answer is

Solve for x.
3x-6
130
8x+4

Answers

Answer: x = 12

Step-by-step explanation:

(180 - 130) + (3x - 6) + (8x + 4) = 180

180 - 130 + 3x - 6 + 8x + 4 = 180

48 + 11x = 180

48 + 11x - 48 = 180 - 48

11x = 132

11x ÷ 11 = 132 ÷ 11

x = 12

The required value of variable "x" is 12 which is determined by the property of interior angles.

What is a Triangle?

Triangle is defined as a basic polygonal shape of a triangle that has three sides and three interior angles. It is one of the fundamental shapes in geometry and is represented by the symbol Δ.

We know that the linear pair of angles are adjacent angles the sum of their measures is 180°

Since the sum of all interior angles of the triangle = 180°

(180 - 130) + (3x - 6) + (8x + 4) = 180

180 - 130 + 3x - 6 + 8x + 4 = 180

Rearrange the terms of  variable "x" and combine them,

48 + 11x = 180

48 + 11x - 48 = 180 - 48

11x = 132

x = 132/11

x = 12

Therefore, the required value of variable "x" is 12.

Learn more about the triangles here:

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Please help I need to catch up on school.

Answers

Answer:

D: y=-2x+5

Step-by-step explanation:

Answer:

y=-2x+5

Step-by-step explanation:

The basic formula you go by for these problems is y=mx+b.

For this example, b is 5 and m is -2.

This would make the problem y=-2x+5

PLS HELP ASAP I DONT HAVE TIME. IT ALSO DETECTS IF ITS RIGHT OR WRONG. SHOW PROOF.

Answers

Answer:

1,200 miles

Step-by-step explanation:

1/4 in = 100 miles

         |

There is 4/4 which makes 400 miles in 1 in.

        |

So 400*3=1,200

Somebody help plz i need some I’m dying inside help?

Answers

Answer:

1/3

Step-by-step explanation:

slope is just change in y over change in x

on a graph this can be found by counting the change in units

look at the point at (-3,0)

find the change in y by starting at that point and counting up or down until you reach another point.

the next point (-4,-3) is three units down (change of -3)

now go back to the first point and count left or right until you reach the other point to get change of x

the other point is one unit left (change of -1)

change of y over change of x = -1/-3=1/3

Answer:

slope = 3

Step-by-step explanation:

Calculate the slope m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (- 4, - 3) and (x₂, y₂ ) = (- 3, 0) ← 2 points on the line

m = [tex]\frac{0-(-3)}{-3-(-4)}[/tex] = [tex]\frac{0+3}{-3+4}[/tex] = [tex]\frac{3}{1}[/tex] = 3

which one should choose for my career cluster finances or business ​

Answers

you should choose business

Hannah deposited the same amount of money into her savings account each month after 5 months she had $2,550 into the savings account after 8 months she had $3,300 and the savings account create an equation that models the amount a and the savings account after x months not included interest show your work ever explain how you determine your equation

Answers

Answer:

a = 250x + 1300

Step-by-step explanation:

We have pairs (5, 2550) and (8, 3300)

Find the rate of change:

(3300 - 2550)/(8 - 5) = 750/3 =250

$250 is the amount added to savings account every month

Initial amount was:

2550 - 5*250 = 2550 - 1250 =1300

Since the change is linear and we have y-intercept and slope, we can show the amount after x months as:

a = 250x + 1300

Can someone please help me?

Answers

Answer:

yes

Step-by-step explanation:

Which equation in point slope form describes the line that passes through (3,-5) and has a slope of 2?

Answers

Answer:

y + 5 = 2(x - 3)

General Formulas and Concepts:

Algebra I

Point-Slope Form: y - y₁ = m(x - x₁)  

x₁ - x coordinate y₁ - y coordinate m - slope

Step-by-step explanation:

Step 1: Define

Point (3, -5)

Slope m = 2

Step 2: Write equation

Substitute in variables into the general form.

y + 5 = 2(x - 3)

The measure of each interior angle of a regular polygon is 120°. Find the number of sides.

Answers

Answer:

6

Step-by-step explanation:

You can memorize these for the smaller shapes

for equilateral polygons:

triangle: 60

square: 90

pentagon: 108

hexagon: 120

Otherwise, I believe the formula is the total degrees in a polygon (s-2)*180 where s is the number of sides.

So the measure of each angle on average would be (s-2)*180/s.

There (s-2)*180/s = 120

180(s-2) = 120s

180s-360 = 120s

60s = 360

s = 6

During the month of January George worked a total of 21 days, 8 hours each day. He did not work any overtime hours during October. Henry earns $29 per hour. What was his earned wages for the month of January ?

A) $232.00
B) $4,872.00
C) $4,640.00
D) $609.00

Answers

Answer:

B

Step-by-step explanation:

21*8=168

29*168=$4,872.00

Please answer correctly !!!!!!!!!!!!!!! Will mark Brianliest !!!!!!!!!!!!!!!!!!!!

Answers

Answer:

MQ = 16 units

Step-by-step explanation:

[tex]\frac{x}{14}[/tex] = [tex]\frac{9}{63}[/tex]

x = [tex]\frac{14*9}{63}[/tex] = 2

MQ = 14 + 2 = 16 units

Please help fast!

the following students bought different lunch items from the menu below. use the clues to match each student with the total price they paid for their lunches, each students total was different

Answers

Answer:

I filled it in for you. Hope it helps xx

Which ordered pair is the solution to this system of equations?
y = r +4
x + y = 2

A. (1,5)
B. (0,2)
C. (-1,3)
D. (-4,0)

Answers

The answers is B!!!!!

The NYC DOE Laptop weighs around 48 oz (ounces). Note: 1 pound 16 ounces Find this weight in pounds What would be the weight in pounds for two NYC DOE Laptop's? (Explain your thinking)

Answers

Answer:

Step-by-step explanation:

ohh i seeee

у = -3х + 4
у = 3х - 2

Answers

Answer:

y =2

then u should put 2 in y = 3x -2 or y = -3x + 4

= y =3x - 2

= 2 = 3x - 2

= 2 + 2 = 3x

= 4 = 3x

=x = 4/3

Answer:Y=2


Explanation:

Can someone plz help me on number 4 plz

Answers

Answer: 6:5

Step-by-step explanation:

Let each little rectangle have the dimensions a by b (where a is the length and longer than b, the width). We find that l=3a because there are 3 lengths of a along l at the top of the crate and that l=4b because there are 4 lengths of b along l at the bottom of the crate. In addition, w=2b+a because there are 2 lengths of b and one length of a along w. Therefore, we can find b and a in terms of l and plug them into w=2b+a to find w in terms of l:

l=4b

b=l/4

l=3a

a=l/3

w=2b+a

w=2(l/4)+(l/3)

w=l/2+l/3

w=5l/6

If w=5l/6, l:w=l/(5l/6)=l(6/5l)=6/5

The correct answer is 6:5.

Helpppppppppppppppppppppppppp

Answers

Answer:

1.

[tex]x < - \frac{5}{13} [/tex]

2.

[tex]x \geqslant - \frac{1}{5} [/tex]

Step-by-step explanation:

[tex] - \frac{13}{16}x + \frac{3}{8} < \frac{11}{16} \\ \frac{ \: \: \: \: \: \: \: \: \: \: \: \: - \frac{3}{8 } < - \frac{3}{8} }{ \frac{ - \frac{13}{16}x }{ - \frac{13}{16} } < \: \: \: \frac{ \frac { 5}{16} }{ - \frac{ 13}{16} } } \\ \\ x < \frac{ - 5}{ \: 13} [/tex]

[tex] \frac{1}{3} \geqslant \frac{2}{9} - \frac{5}{9} x \\ \frac{ - \frac{ 2}{9} \geqslant - \frac{2}{9} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: }{ \frac{ \: \: \: \frac{1}{9}x }{ - \frac{ 5}{9} } \geqslant \frac{ - \frac{5}{9} }{ - \frac{5}{9} } } \\ \\ x \geqslant - \frac{1}{5} [/tex]

Find the equation of the line.



Answers

y=3/4x -2

3/4 is the slope, which means that the line goes up 3 and to the right 4.

-2 is the y intercept, which means that the line crosses the y axis at this point.

Select the graph for the solution of the open sentence lxl +3>3

No solution
Closed circle on 0 going to the right
Open circle going out left and right
Open circle only going to the right

Answers

Answer:

[tex]x>0\:or\:x<0[/tex]

As seen in graph, there is an open circle on 0, and it goes out left and right.

Option C is correct option.

Step-by-step explanation:

We need to draw the graph for the solution of the open sentence [tex]|x| +3>3[/tex]

First we will solve the inequality: [tex]|x| +3>3[/tex]

Adding -3 on both sides

[tex]|x| +3-3>3-3\\|x| >0[/tex]

We know that [tex]If\:|x|>0,\:then\:x>0\:or\:x<0[/tex]

So, we have

[tex]x>0\:or\:x<0[/tex]

Now, the graph is attached in the figure below

As seen in graph, there is an open circle on 0, and it goes out left and right.

Option C is correct option.

Maria Louisa looks at a sequence of shapes and records the number of vertices in each of the shapes in the sequence. The first shape has 7 vertices, the second shape has 13 vertices, and the third shape has 19 vertices. If Maria Louisa assumes that the number of vertices in the sequence of shapes follows the same pattern, how many vertices would she expect the 17 shape to have?

Answers

Answer:

103

Step-by-step explanation:

appears to be an arithmetic sequence question where sequence is 7, 13, 19 meaning the initial value is 7 and the common difference is 6 so we'll plug into this formula:

[tex]a_{17}[/tex] = 7 + (17 - 1) · 6

    = 7 + (16 · 6)

    = 7 + 96

'7' because that's the initial value

'6' because that the common difference

'17' because that's the position the question is asking

Find the missing side length, N. ​

Answers

Answer : 15

We know these triangles are congruent. To find the missing side, you first have to find out what the scale factor is. To do this you can just divide side QS by side AC, which would give you 2.5.
You would then multiply this scale factor by side BC, giving you side N, which is 15.

We know these triangles are congruent with the missing side, N would be equal to 15.

What is the congruent triangle?

Two triangles are said to be congruent if the length of the sides is equal, a measure of the angles are equal and they can be superimposed.

We know these triangles are congruent.

To find the missing side, N

ΔABC ≅ΔQRS

AC/QS = BC/RS

2/5 = 6/n

n = 6 x 5/2

n = 30/2

n = 15

Thus, the value of N is 15.

Learn more about triangles;

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Plz I need help with this!

Answers

Answer:

what do you mean?

Step-by-step explanation:

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