A 10-foot ladder rests against a vertical wall. Let x be the distance from the bottom of the ladder to the wall and y be the distance from the floor to the top of the ladder. If the bottom of the ladder slides away from the wall, how fast does the top of the ladder fall down the wall with respect to x

Answers

Answer 1

Answer:

The rate of change of the top of the ladder with respect to x is -x/y

Step-by-step explanation:

The given parameters are;

The length of the ladder = 10 ft.

The horizontal distance of the bottom of the ladder from the wall = x

The distance of the top of the ladder from the floor = y

By Pythagoras's theorem, we have;

10 = y² + x²

Therefore, we have;

x² = 10 - y²

d(x²)/dx = 2·x =  d(10 - y²)/dx = -2·y·dy/dx

∴ 2·x = -2·y·dy/dx

dy/dx = 2·x/(-2·y) = -x/y

Therefore, the rate of change of the top of the ladder with respect to x, dy/dx = -x/y.


Related Questions

Tìm m để hàm số sau là hàm số bậc nhất:
(2m-1)x+2018

Answers

Answer:

2mx-x+2018

Step-by-step explanation:

multiply each term in the parentheses by x

if measure of three angles of a quadrilateral are 65 degree 95 degree and 45 degree then find the measure of the fourth​ angle?

Answers

Answer:

155 degrees

Step-by-step explanation:

Hi there!

The sum of the interior angles of a quadrilateral is always 360 degrees. To find the measure of the fourth angle, subtract 65, 95 and 45 from 360:

360-65-95-45

= 155

Therefore, the measure of the fourth angle is 155 degrees.

I hope this helps!

Answer:

155 degrees

Step-by-step explanation:

A quadrilateral has a total internal angle sum of 360 so we can set up an equation where x is the fourth angle

360=65+95+45+x

360=205+x

x=155

which of the following are remote interior angles of 5 ?

Answers

Answer:

The answer is B and C.

Answer: B AND C

Step-by-step explanation:

Remote interior angles are angles that are opposite from the exterior angles (5 in this case).

due to Deepavali or TV is sold for rupees 14900 after allowing a discount of 23% what is the Marked price​

Answers

Answer:

Correct option is

C

Rs.8000

SP=xRs

CP=(0.8x+600)Rs

P%=14

7

2

%

SP=

100

CP(100+P%)

x=

100

(0.8x+600)(100+

7

100

)

x=

7×100

(0.8x+600)(800)

700x=640x+480,000

x=8,000

What is the volume of the sphere below PLEASE HELP FAST

Answers

Answer:

c. 256π/3 units^3

Step-by-step explanation:

Recall that the volume V of a sphere with radius r is given as

V = 4 /3πr3

Hence from the image given, the radius of the sphere which is the distance from the center to any point on the circumference is 4 units hence the volume

V = 4/3 * π * 4^3

= 4/3 * π * 64

= 4*64/3 * π

= 256π/3 units^3

Option c is right

I NEEEDDDD HELPPPP ITS URGENTTTTT!!!!!! I’ll mark you brainliest

Answers

Answer:

(x+2)^2 + (y-15)^-1 = 64

Step-by-step explanation:

plz mark brainlist

(x + 15)^2 + (y + 1)^2 = 4
if it’s urgent, trust me on this. desmos doesn’t lie ;))

If necessary, write in simplest radical form

Answers

Answer:

2*sqrt(5)

Step-by-step explanation:

By using Pythagoras theorem, we have

4^2+2^2=(the third side)^2

16+4=(the third side)^2

Third side=sqrt(20)=2*sqrt(5)

steps to describe an inscribed regular hexagon.

Answers

Answer:

many sides

unique shape

Tom is a builder and earns $38.50 an hour. Calculate his weekly wage if he works for 38 hours?

Answers

Answer:

$1,463

Step-by-step explanation:

38.50x38=1,463

You multiple both numbers together
38.50 x 38 = 1463

Predict what will happen to the graph of the line 2y=3x-6 if the slope was changed to 2

Answers

Answer:

y = 3/2x-3 vs. y = 2x-3

Step-by-step explanation:

2y=3x-6  ------ y = 3/2x-3

Two similar polygons have areas of 4 square inches and 64 square inches.

The ratio of a pair of corresponding sides is .
The ratio of a pair of corresponding sides is .
The ratio of a pair of corresponding sides is .
The ratio of a pair of corresponding sides is .

Answers

Answer:

4

Step-by-step explanation:

The ratio of the area of similar figures is the ratio between corresponding sides squared. This means that 64/4 or 16 is the square of the ratio of corresponding sides. By taking the square root of 16, we get that ratio is 4.

16 + 28 = ___ ´ (4 + 7).

Answers

Answer:

Solution given:

16+28=44

(4+7)=11

Answer:

The solution is 4

Step-by-step explanation:

Step 1:  Find the correct answer

I'm not really sure what you are asking but I will give it a shot.

16 + 28 = ___ (4 + 7)

44 = ___ (11)

44 / 11 = ___ (11) / 11

4 = ___

Answer:  The solution is 4

Vector u has its initial point at (-7, 2) and its terminal point at (11, -5). Vector v has a direction opposite that of vector u, and its magnitude is three times the magnitude of u. What is the component form of vector v?

A. v = <-54, 63>
B. v = <-162, -63>
C. v = <-54, 21>
D. v = <-162, 21>

Answers

Answer:

Answer is C) V= <-54,21>

Step-by-step explanation:

Compenent form of v is <-54,21>

I just really need to finish this math stuff so plz help

Answers

Answer:

wx/5

Step-by-step explanation:

Divide the denominator and the numerator by 7y.

Answer:

wx / 5

Step-by-step explanation:

here..

7wxy / 35y

7/35 is 1/5

and wxy /y is wx as we can cancel out y

thus..

7wxy/35y = wx/5

Find the value of x in each case

Answers

Answer: x=45

Step-by-step explanation:

To solve for x, we first need to understand the figure. We know TV and RS are parallel lines. If we extend TV to the left, we get a straight line parallel to RS. By Alternate Interior Angles, We know ∠R is equivalent to ∠T on the very left. Therefore, we can set it equal to 180° and solve.

x+2x+x=180          [combine like terms]

4x=180                  [divide both sides by 4]

x=45

Now, we know x=45.

It’s 11 but I need help

Answers

A,12/15=4/5

B,20/25=4/5

C,25/30=5/6

D,28/35=4/5

=> C

Question 4 of 40
If cose= -
5
in quadrant II, what is sine?

Answers

Step-by-step explanation:

cosx=adjacent/hypotenuse

adj=3, hyp=5

by pythagoras theorem,

opp^2+3^2=5^2

opposite=4

sine=opp/hyp

sinex=4/5 (second quadrant so sin is positive)

The solution is, The value of sin ∅ in quadrant 2 is 4/5.

What are trigonometric relations?

Trigonometry is the study of the relationships between the angles and the lengths of the sides of triangles

here, we have,

The six trigonometric functions are sin , cos , tan , cosec , sec and cot

Let the angle be θ , such that

sin θ = opposite / hypotenuse

cos θ = adjacent / hypotenuse

tan θ = opposite / adjacent

here, we have,

given that,

cos∅ = - 3/5, in quadrant II,

We have;

adjacent = -3

hypotenuse = 5

Let's find the opposite side, using Pythagorean theorem

5^2 = x^2 + (-3)^2

25 = x^2 + 9

collect like terms

x^2 = 25 - 9

x^2 = 16

x = √ 16

x = 4

We have that

sin ∅ = opposite/hypotenuse

sin ∅ = 4/5

It is important to note that the trigonometric identity 'sine' is positive in quadrant 2

sin ∅ = 4/5

Hence, the value of sin ∅ in quadrant 2 is 4/5

Learn more about trigonometric relations here:

brainly.com/question/863849

#SPJ7

HELP ASAP

The graph of f(x)= |x| is chosen below. Write the equation for the stretched graph, g(x).

Answers

Answer:

y = |3x|

Step-by-step explanation:

Y = 2x + 3

(2, 7)

(1, 3)

(-3, 6)

(0, 2)

Answers

Answer:

(2,7)

Step-by-step explanation:

The surface area of a cylinder is given by the formula

S = 30πr + 2πr2

How many times greater is this compared to a circle with A = πr2

Answers

Answer:

[tex] x = \frac {30}{r} + 2 [/tex]

Step-by-step explanation:

Given the following data;

S.A of cylinder = 30πr + 2πr²Area of circle = πr²

To find how many times greater is the S.A compared to the area, we would have to divide the surface area (S.A) of the cylinder by the area of circle.

Let the unknown variable be x.

[tex] x = \frac {30 \pi r + 2 \pi r^{2}}{\pi r^{2}} [/tex]

Factorizing the numerator, we have;

[tex] x = \frac {\pi r(30 + 2r)}{\pi r^{2}} [/tex]

Dividing both sides by πr, we have;

[tex] x = \frac {30 + 2r}{r} [/tex]

Simplifying further, we would have;

[tex] x = \frac {30}{r} + 2 [/tex]

You are in a hot air balloon that is 600 feet above the ground where you can see your friend. If the angle from your line of sight to your friend is 20°, how far is he from the point on the ground below the hot air balloon to the nearest foot?

Answers

Answer:

218.38 feet

Step-by-step explanation:

tan(20) = x/600

tan(20) = 0.3639

600 x 0.3639 = 218.38 feet

hope this helps


often contains information about the author's experiences with the subject matter of
9. The author's introduction to a book, also called a/an
the book.
A. glossary
B. Index
C. table of contents
D. preface


Im quite sure it’s d wanna make sure

Answers

you’re correct, it’s d
The answer is D - preface.

indices-find The value of 6*7^3​

Answers

Answer:

[tex]6 * 7^3 = 2058[/tex]

Step-by-step explanation:

Given

[tex]6 * 7^3[/tex]

Required

Solve

App;y law of indices:

[tex]6 * 7^3 = 6 * 7*7*7[/tex]

Multiply

[tex]6 * 7^3 = 2058[/tex]

Write this rate as a unit rate 1/7inch 1/14 minute

Answers

Answer:

2 inches per minute

Step-by-step explanation:

Work out the value of 10^2 - 4^3
Give your answer as a power of 6.

Answers

Answer:

6^2 = 36

Step-by-step explanation:

10^2 = 10 * 10 = 100

4^3 = 4 * 4 * 4 = 64

10^2 - 4^3= 100 - 64 = 36 = 6^2

Hi there!  

»»————- ★ ————-««

I believe your answer is:  

[tex]6^2[/tex]

»»————- ★ ————-««  

Here’s why:  

⸻⸻⸻⸻

[tex]\boxed{\text{Calculating the answer...}}\\\\10^2 - 4^3\\---------------\\\rightarrow 10^2 = 100\\\\\rightarrow 4^3 = 64\\\\\rightarrow 100 - 64 = \boxed{36}\\\\\text{Since we know that '36' is a perfect square, we can rewrite our answer as: } \boxed{6^2}[/tex]

⸻⸻⸻⸻

»»————- ★ ————-««  

Hope this helps you. I apologize if it’s incorrect.  

Find the measurement of ∠ABE. Show all your work that leads to the final answer.

Answers

Answer:

m∠ABE = 129 degrees

Step-by-step explanation:

360 degrees = max/total degrees in a circle

Given angles = 65 degrees & 37 degrees

Unknown/congruent angles = m∠ABE & m∠DBC

••••••••••••••••••••••••••••••••••••••••••

That was just information for the shape!

Now let’s get into the question.

Question: Find the measurement of m∠ABE

65 + 37 + m∠ABE + m∠DBC = 360 degrees

Add 65 and 37

102 + m∠ABE + m∠DBC = 360 degrees

Subtract 102 from 360 degrees

m∠ABE + m∠DBC = 258 degrees

Divide 258 in half

m∠ABE & m∠DBC = 129 degrees
—————————————————

Therefore m∠ABE = 129 degrees

What is the area of the shape below?


A.
886 cm2
B.
781.5 cm2
C.
1,019 cm2
D.
990.5 cm2

Answers

Answer:

Area = 886cm^2

Step-by-step explanation:

34 • 16 = 544

19 • 11 = 209

25 - 11 = 14

14 • 19 = 266/2

266/2 = 133

544 + 209 + 133 = 886cm^2

PLEASER HELP WILL GIVE BRAINLIEST!

Answers

Answer:

$250

Step-by-step explanation:

the class width (just choose one of the rows, it could be the same) =>for example:the first row = $(749-500+1) = $250

HELP ASAP PLEASEREEEEE

Answers

Answer:

uh

Step-by-step explanation:

my guy, I DK.

Tìm giá trị lớn nhất giá trị nhỏ nhất
Cos(x+π/3)+ cos(x-π/3)

Answers

Answer:

GTLN : 1  GTNN: -1

Step-by-step explanation:

Ta có:

[tex]y=cos(x+\frac{\pi }{3} ) + cos(x-\frac{\pi }{3} ) \\ = 2.cosx.cos\frac{\pi }{3} \\ = cosx[/tex]

mà [tex]-1\leq cosx \leq 1[/tex]

Nên Max [tex]y=1[/tex]  , [tex]x[/tex] ∈ [tex]R[/tex]

       Min [tex]y = -1[/tex], [tex]x[/tex] ∈ [tex]R[/tex]

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