Una escalera de 131313 metros está recargada contra una pared cuando su base empieza a resbalar. Cuando la base está a 121212 metros de la pared, se mueve a una razón de 5\text{ m/s}5 m/s5, start text, space, m, slash, s, end text. En ese momento, ¿a qué razón está cambiando el ángulo \thetaθtheta entre el piso y la escalera?

Answers

Answer 1

Answer:

El ángulo entre el piso y la escalera está cambiando a una razón de -1 radian por segundo.

Step-by-step explanation:

Sea [tex]x[/tex] la distancia horizontal entre la pared y la base de la escalera y [tex]l[/tex] la longitud de la escalera, medidas en metros. Además, tenemos que [tex]\theta[/tex] es el ángulo entre la escalera y el piso, medido en radianes.

Si la pared y el piso son ortogonales entre sí, entonces podemos utilizar la siguiente relación trigonométrica que relaciona las variables anteriores:

[tex]\cos \theta = \frac{x}{l}[/tex]  (1)

Por diferenciación implícita y la definición de razón de cambio tenemos que:

[tex]-\sin \theta \,\dot \theta = \frac{\dot x}{l}[/tex] (2)

Donde:

[tex]\dot x[/tex] - Razón de cambio de la distancia horizontal entre la pared y la base de la escalera, medida en metros por segundo.

[tex]\dot \theta[/tex] - Razón de cambio del ángulo entre el piso y la escalera, medida en radianes por segundo.

Pero tenemos que el seno del ángulo está definido por:

[tex]\sin \theta = \frac{\sqrt{l^{2}-x^{2}}}{l}[/tex] (3)

Si aplicamos (3) en (2), expandimos la ecuación como sigue:

[tex]-\frac{\sqrt{l^{2}-x^{2}}}{l}\,\dot \theta = \frac{\dot x}{l}[/tex]

[tex]\dot \theta = - \frac{\dot x}{\sqrt{l^{2}-x^{2}}}[/tex] (4)

Si tenemos que [tex]\dot x = 5\,\frac{m}{s}[/tex], [tex]l = 13\,m[/tex] y [tex]x = 12\,m[/tex], entonces la razón de cambio del ángulo es:

[tex]\dot \theta = -\frac{\left(5\,\frac{m}{s} \right)}{\sqrt{(13\,m)^{2}-(12\,m)^{2}}}[/tex]

[tex]\dot \theta \approx -1\,\frac{rad}{s}[/tex]

El ángulo entre el piso y la escalera está cambiando a una razón de -1 radian por segundo.

Una Escalera De 131313 Metros Est Recargada Contra Una Pared Cuando Su Base Empieza A Resbalar. Cuando

Related Questions

Expand and simplify 3(2x + 1) +2(x + 4)

Answers

Answer:

8+11

Step-by-step explanation:

Answer:

3(2x + 1) +2(x + 4)

6x + 3 + 2x + 8

8x + 11

Step-by-step explanation:

How many minutes of calling time do the plans cost the same amount ?

Answers

D 200 minutes

.15*200 = 30+45= Plan A= $75
.25*200= 50+25= Plan B= $75

Answer is D

You had $1.65. After a friend returned the money you had loaned her, you
had $3.50. How much did she give you? _____

Answers

Answer:

$1.85

Step-by-step explanation:

Simple Subtraction!

$3.50 - $1.65 = $1.85

$1.85

CORRECT ANSWER= BRAINLIEST
A right triangle has legs that measure 7 meters and 16 meters. What is the length of its hypotenuse to the nearest whole
number?
14 meters
16 meters
17 meters
18 meters

Answers

Answer:

17 meters

Step-by-step explanation:

I did 16^2 and 7^2 to get, 256 + 49 = 305. 305 squared is 17.4... Once you round it you should get the answer 17 meters.

Hope this helps :)

Answer:

The answer is 17 meter

Step-by-step explanation:

So the formula for this is a^2 + b^2 = c^

The two legs are a and b

So plug those into the equation

It should look something like this 7^2 + 16^2 = c^2

Then solve the exponents and you get 49 + 256 = c^2

After that just add the two integers and you have 305

Finally take the square root of 305 and you get 17

pls mark brainliest because i didnt waste your time Lol

50% of 320 is equal to 80% of what number?

Answers

Answer:

128

Step-by-step explanation:

plzzzzzz helpppppp plzzz

Answers

Answer:

D. 6

Step-by-step explanation:

Answer:

B, 6

I think! hope it helped

Last one , will mark brainliest !!!!

Answers

Answer:

Step-by-step explanation:

Part 1:y=426x+4298

        y=223x+6129

Part 2: x=9.020 (x is the number of months and y is the miles)

Part 3: y=8140.394, or 8,140 since it's rounding to the nearest mile

Answer:

See answers in explanation below

Step-by-step explanation:

1.   4298 + 426t = 6129 + 223t

2. Basically get into the graphing page and find "function" section then select "f(x) = mx + b", then graph f(x) = 426x + 4298 and f(x) = 223x + 6129

and find the answer at where these two lines intersect with each other, x=9.0197 (months)

3. sub x=9.0197 into any of the two equation and f(x) = 8140 (miles)

Kiera wants to increase her savings account to a balance of $1,350. Her current balance is $174 and she adds $84 a month to her savings.

How many months will it take for her to reach her goal of $1,350?

18 months
16 months
12 months
14 months

Answers

Answer:

Her goal : 1350

What she has now: 174

she earns 84$ a month

answer is 14 months because 84* 14 is 1176 and if u add 174 $ to that it will give u 1350.

Step-by-step explanation:

I think 14 months bc if uu add 84 to 14 it will get you 1,350

Solve for x:
3x+c=12
Please show work

Answers

Answer:

x=3 c=3

Step-by-step explanation:

How to solve for x is 12 divided by 3 equals 4 so x would equal 3 and C would give you an answer of 3 also if i am correct. 3×3 + 3 = 12

PLS HELP I WILL GIVE BRAINLIEST

Answers

Answer:

6x-2

Step-by-step explanation:

the side lengths are x+2, x+2, 2x-3 and 2x-3

(the other two are the same as the ones shown because it's a rectangle)

when you combine like terms you get 2x+4 and 4x-6

combine like terms again and you get 6x-2

hope this helps :)

2x+2y=38
Y=x+3

Substitute to solve

Correct answer gets Brainliest

Answers

Answer:

x=8

y=11

Step-by-step explanation:

2(8) + 2(11) = 38

8 + 3 = 11

Use substitution to solve the following system of equations. What is the value of y?
6x + 2y = 4
3x - 5y = 44
A. y = 7
B. y = -7
C. y = -4.5
D. y = 4.5

Answers

B in my opinion if I’m wrong I’ll do my equation

Answer:

B

Step-by-step explanation:

selena paid $15.00 for 6 gallons of gasoline what was the price per gallon

Answers

Answer:

$2.50

Step-by-step explanation:

Is Selena paid $15 for 6 gallons and you want to find the price for one gallon, all you need to do is divide the price of 6 gallons ($15) by the number of gallons (6).

15/6 = 2.5. Your answer is $2.50. Hope this helps ^-^

The chart shows number of minutes students spent studying for a test and their grade on the test. Draw a scatter plot of the data.

Which equation is closest to the line of best fit?

A) y=-1/3x-52

B) y= 1/3x + 52

C) y=-52x + 1/3

D) y=52x-1/3

Answers

i believe the right answer is A

Answer:

the answer is A). y=1/3×-52

David's bowling score is 6 less than 3 times Aaron's score. The sum of their scores is 214. Find the score of each student. Use the variable a for Aaron's score.

plz help​

Answers

Step-by-step explanation:

Let aron's variable be = a

Let davids variable be( 6 less tan 3 times aron) = 3×a-6

Thier sum is =214

So,

3×a-6 + a = 214

3a -6 +a = 214

(transpose)

3a + a = 214 + 6

4a = 220

a = 220/4

a= 55

Thus,aron's score is = 55

And davids score is (3×a-6) = 3×55-6 = 159

Checking,

Aron score + david score = 214

55 + 159 = 214

SO, ITS CORRECT

HOPE IT HELPS :)

Orchestra Tonight is selling tickets for its local performance. Orchestra fans can buy tickets to sit in the balcony or on the floor of the concert hall. Tickets for floor seats are $83 each. Tickets for the balcony are 60% of the price of the floor tickets. Which inequality represents all possible combinations of f, the number of tickets for floor seats, and b, the number of tickets for balcony seats, that a person can buy and spend no more than $560?

Answers

Answer:

[tex]83f+49.8b \leq 560[/tex]

Step-by-step explanation:

Given that the cost of 1 floor ticket = $ 83.

Cost for f floor tickets = $ 83f

Ticket for 1 balcony ticket = 60% of floor ticket.

= 0.60 x 83 = $49.8

Cost for b balcony tickets = $ 49.8b.

Total cost for f floor tickets and b balcony tickets, C= 83f+49.8b.

As the person can spend a maximum of $560,

So, [tex]C\leq 560[/tex]

[tex]\Rightarrow 83f+49.8b \leq 560[/tex].

Hence, the required inequality is [tex]83f+49.8b \leq 560[/tex].

help please #16 already found x can’t figure out y

Answers

Answer:

x=26 y=137

Step-by-step explanation:

5x-17+3x-11=180

8x=208

x=26

2y+5+3x-11=180

2y+5+(3*26)-11=180

2y=274

y=137

Sonia and Layla are both running for class president. The senior class has 220 students. After 60% of
the students have voted, Sonia has received 25% of the casted votes, and Layla has received 75%. How
many more votes does Sonia need to receive 50% of the total votes?

Answers

Answer: 33 votes

Step-by-step explanation:

First, we have to calculate 60% of 220 to Kno.the number of people who voted. This will be:

= 60% × 220

= 0.6 × 220

= 132 students

Sonia has received 25% of the casted votes. The number of votes Sonia got will be:

= 25% × 132

= 0.25 × 132

= 33 votes

Layla has received 75%. Her votes will be:

= 75% × 132

= 0.75 × 132

= 99 votes.

50% of the total votes will be:

= 50% × 132

= 0.5 × 132

= 66 votes

The number of votes needed by Sonia to receive 50% of the total votes will be:

= 66 - 33

= 33 votes

2/3 of a number is 20 less than the original number. Find the original number

Answers

Answer:

60

Step-by-step explanation:

Let the original number be x.

According to the question we can write as (2/3)x+20x

On rearranging x−(2/3)x=20

Now taking the L.C.M od 1 and 3 is 3

(3x−2x)/3=20

x/3=20

Again by transposing x=60

So the original number is 60

Answer:

60

Step-by-step explanation:

Let the number be x

2/3 x = x -20

20 =x -2/3x

1/3 x =20

60 = x.

PLEASE HELP!! I’LL GIVE BRAINLIEST AND 10 POINTS !! FOR THE CORRECT ANSWER

Answers

Answer: -9

Step-by-step explanation:

You count down the distance from T to K

Answer:

-9

Step-by-step explanation:

you are counting from t to k but its going to the left of the number line to its negative.

Which graph shows a linear function?

Answers

That one is an absolute I can’t see the other ones

Logan weighed two buckets of sand for a geology project. The first bucket weighed 5.19 pounds. The other bucket weighed 9.01 pounds. How much do the two buckets of sand weigh all together?

Answers

Answer:

14.2

Step-by-step explanation:

you just have to add both of the numbers shown in the question

Terry increased the size of his rectangular garden this summer. He increased to length by 50% and the width by 20% by what percentage has his garden changed with these changes?

Answers

Given :

Terry increased the size of his rectangular garden this summer. He increased to length by 50% and the width by 20%.

To Find :

By what percentage has his garden changed with these changes.

Solution :

Let, initial length and breadth is x and y.

So, initial area = xy .

Size after increasing them :

y' = y + 0.50y

y' = 1.5y

x' = x + 0.2x

x' = 1.2x

Final area = (1.5y)(1.2x) = 1.8xy

So, percentage increase is :

[tex]= \dfrac{new-original}{original }\times 100\%\\\\= \dfrac{1.8xy -xy}{xy }\times 100\\\\=80 \%[/tex]

Therefore, percentage increase in are is 80%.

Hence, this is the required solution.

Translate the number equation into a written equation: 2p + 4 = 20

Answers

Answer:

p is 8

Step-by-step explanation:

4 - 20

then 2 divided by 16

then you get 8

Answer:11. g. 10. 3g. 12. 2p. 4q. 20 g plus 10 is the same as. Twice p plus 4 times q is 20. 3 times g. 13. 4(a b). 9a. 14. 8.

Step-by-step explanation:

i think thats the answer

Classify the following triangle based on its shape.

Answers

Answer: a right triangle

Step-by-step explanation:

Doreen Schmidt is a chemist. She needs to prepare 28 ounces of a 8% hydrochloric acid solution. Find the amount of 14% solution and the amount of 7% solution she should mix to get this solution

Answers

Let, amount of 14% solution required is x ounces.

So, amount of 8% solution will be ( 28 - x ) ounces.

Now, mathematical equation is :

[tex]\dfrac{14x}{100}+\dfrac{7(28-x)}{100}= \dfrac{8\times 28}{100}\\\\14x + 196 - 7x = 224\\\\7x = 28\\\\x = 4\ ounces[/tex]

Therefore, amount of 14% solution and 8% solution required is 4 ounces and 24 ounces respectively.

Hence, this is the required solution.

.A carpenter bought some wood for #900. He used the wood to make a shelf which he sold for #3000. What percentage profit was this?. Single choice.



42.86%

233.33%

2100%

900%


Answers

Answer:

233.33%

Step-by-step explanation:

His profit is 233.33%.

What is percentage?

A percentage is a number or ratio that can be expressed as a fraction of 100.

Here, given that,

A carpenter bought some wood for #900.

He used the wood to make a shelf which he sold for #3000

Profit= #(3000-900)

        =#2100

So, percentage of profit = 233.33%

To learn more on percentage click:

brainly.com/question/13450942

#SPJ2

what is 2350 million in standard from

Answers

Answer:

2350000000

Step-by-step explanation:

What is the equation of the line through the origin and (3, 4)?​

Answers

Answer:

y = 4/3x

Step-by-step explanation:

Hope that helps you

Given AXYZ = ARST.mZR=(6n+1). m _Y=108°, and m _Z=(91-4)', what is the value of n?

Answers

Answer:

A

Step-by-step explanation:

Given that the triangles are congruent then corresponding angles are congruent, thus

∠ S = ∠ Y = 108°

∠ T = ∠ Z = 9n - 4

Given ∠ R = 6n + 1

The sum of the 3 angles in Δ RST = 180°

Sum the 3 angles and equate to 180, that is

6n + 1 + 108 + 9n - 4 = 180 , simplify

15n + 105 = 180 ( subtract 105 from both sides )

15n = 75 ( divide both sides by 15 )

n = 5 → A

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