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:
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.
Related Questions
A single bus fare costs $2.35. A monthly pass costs $45.75. Celine estimates that she will ride the bus 25 times this month. Kamal estimates that he will ride the bus 18 times. should they both buy monthly passes? Explain.
Answers
Answer:
No they shouldn't.
Step-by-step explanation:
Monthly pass: Celine: $1,143 Kamal: $823
Single Pass: Celine: $58 Kamal: $42
A biker cycles 9 miles in 2 3 of an hour. b The distance here varies directly with time. What is the constant of variation? (It is the hikers’ rate .)
Answers
Answer:
27/2
Step-by-step explanation:
Hope this helps! Also dont add comments to get gems like bruh ;-;
Answer: 27/2
Step-by-step explanation:
[tex]9\cdot \:1=x\frac{2}{3}[/tex]
[tex]x\frac{2}{3}=9\cdot \:1[/tex]
[tex]x\frac{2}{3}=9[/tex]
[tex]3x\frac{2}{3}=9\cdot \:3[/tex]
2x= 27
x= 27/2
Add Me Brainliest!
Harry and Selma start driving from the same location. Harry drives 42 miles north and Selma drives 144 mies east. How far apart are Harry and Selma when they stop?
Answers
Answer:
150 miles
Step-by-step explanation:
use the pythagoerean theorem
42^2 + 144^2 = c^2
1764+20736=c^2
22500 = c^2
c= 150 miles
URGENT SOMEONE HELP PLEASE!!
Answers
a = 9b - 8 — (2) [given]
a = a
sub. in the eqns (1) and (2)
2b + 6 = 9b - 8
collect like terms :
6 + 8 = 9b - 2b
14 = 7b
b = 2
Write the equation of the line fully simplified slope-intercept form
Answers
Cause slope is -4/1
Y-intercept is -6
Answer:
y=-3x+6
Step-by-step explanation:
that might not be fully simplified, but that should be the equation
ANSWER PLSSS THANK YOUUUUU
Answers
Answer:
As a fraction: 81/100 (cannot be simplified) Decimal: 0.81 and a percent 81%
Step-by-step explanation:
Count the blocks and convert (you can also use an array.) Hope this helps you!
Answer:
Fraction: 81/100
Decimal: 0.81
Percent: 81%
Step-by-step explanation:
The box is a 10x10 so it has 100 squares inside.
There are 81 squares shaded so the fraction would be 81/100
To get the decimal just divide 81 by one hundred so the decimal is .81
As a percent is would be 81%
Hope this helps ya!!
ASAP answer it please.!!!!!!!!!!!!!!!!!!! thank uuu
Answers
Answer:
X=120 and y=10,z=120
Step-by-step explanation:
corresponding angles
thus 120=(13y-10)=x
Which number sentence is true?
A. –2.0 + (–0.5) = 2.5
B. –4.5 + 6.5 = –2.0
C. 3.0 + (–0.5) = –2.5
D. 5.5 + (–2.5) = 3.0
answer soon please!
Answers
Answer:
B. and D.
Step-by-step explanation:
Answer:
D
Step-by-step explanation:
Here are the correct sums:
A. –2.0 + (–0.5) = -2.5
B. –4.5 + 6.5 = 2.0
C. 3.0 + (–0.5) = 2.5
D. 5.5 + (–2.5) = 3.0
Only D is correct.
Answer: D
(BRAINLYEST TO RIGHT ANSWER) pls i need help!
Answers
Answer:
What is the question?
Step-by-step explanation:
Answer:
where is the question
Step-by-step explanation:
PLEASE HELP I WILL MARK AND 5 STARS SOLVE AND EXPLAIN THANKS
Answers
What is the square root of 40000 step by step
Thx for everything that answers
Answers
The answers 200 of u have an iPhone u can ask siri what the square root of whatever number is and it will tell u the correct answer
How do you find the slope of the table below
Answers
Pick any two sets and plug in.
(24-16)/(21-14) = 8/7
I will give brainliest answer to these questions
Answers
Answer:
THATS MADDDD CAPPPP U NEED 25 POINTS OF THE QUESTION FOR BRAINLIEST
Help me
Line ℓ is perpendicular to line m. Find the value of x and w.
Answers
w° = 180° - 138°
w = 42
19° + x° + w° = 90°
sub. in w=42,
19° + x° + 42° = 90°
x° = 90° - 19° - 42°
x° = 29°
x = 29
1. What value is equivalent to 3 x 12 - (4 + 2)?
Answers
Answer:
30
Step-by-step explanation:
(3x12)-(4+2)
36-6
30
Distribute the negative: 3 x 12-4-2
Use PEMDAS
Compare data set A and data set B.
Set A: mean = 79.6, standard deviation = 9.8
Set B: mean = 79.6, standard deviation = 2.3
Answers
Answer:
Set A: mean = 79.6, standard deviation = 9.8
Step-by-step explanation:
Set A has a larger spread of data.
If Set A: mean = 79.6, standard deviation = 9.8 and Set B: mean = 79.6, standard deviation = 2.3 then set A has larger spread of data compared to set A.
What is Statistics?Statistics is the study and manipulation of data, including ways to gather, review, analyze, and draw conclusions from data.
Given,
Set A:
mean = 79.6,
standard deviation = 9.8
Set B:
mean = 79.6,
standard deviation = 2.3
As we compare both set A and set B the mean of set A and set B are same whereas set A has more standard deviation than set B.
As Standard deviation is an important measure of spread or dispersion.
if the standard deviation is small, then this tells us that the results are close to the mean, whereas if the standard deviation is large, then the results are more spread out.
Set A has a larger spread of data.
Hence Set A has larger spread of data compared to set A.
To learn more on Statistics click:
https://brainly.com/question/29342780
#SPJ2
solve for x: -5|x + 1| = 10
Answers
Answer:
x=-3
Step-by-step explanation:
-5(x+1)=10
-5x-5=10
-5x= 15
x=-3
pls help!! would be greatly appreciated<3
Answers
Answer:
x=7
Step-by-step explanation:
Ed wants to buy a basketball for $5, but
his bank account only contains $3. If Ed
purchasos tho baskotball, how much
money will his bank account show?
Answers
What is the slope of the line passing through the points (-6, 33) and (-2, 15)?
Please answer quick
Answers
Answer:
The slope is -9/2
Step-by-step explanation:
m=y²-y¹/x²-x¹
m=15-33/(-2)-(-6)
m=-18/4
m=-9/2
What is a first step to solving for x in the equation −=9 x minus 7 equals 10? How would you check your solution
Answers
Answer:
-17/9
Step-by-step explanation:
You need to add 7 to both sides.
-9x - 7 = 10
-9x -7 + (7) = 10 + 7
-9x = 17
Then both sides for (-9)
-9x/(-9) = 17/(-9)
x = -17/9
Solve the system of equations. If the system has no solution, say that it is inconsistent. Graph the lines of the system.
X+y=4
{
X-y=2
Answers
Answer:
The solution to the system of the equations will be:
[tex]x=3,\:y=1[/tex]
Step-by-step explanation:
Given the system of the equations
[tex]x+y=4[/tex]
[tex]x-y=2[/tex]
solving the system of the equations
[tex]\begin{bmatrix}x+y=4\\ x-y=2\end{bmatrix}[/tex]
[tex]x-y=2[/tex]
[tex]-[/tex]
[tex]\underline{x+y=4}[/tex]
[tex]-2y=-2[/tex]
solving
[tex]-2y=-2[/tex]
Divide both sides by -2
[tex]\frac{-2y}{-2}=\frac{-2}{-2}[/tex]
[tex]y=1[/tex]
[tex]\mathrm{For\:}x+y=4\mathrm{\:plug\:in\:}y=1[/tex]
[tex]x+1=4[/tex]
[tex]x=3[/tex]
Therefore, the solution to the system of the equations will be:
[tex]x=3,\:y=1[/tex]
ILL GIVE YOU BRAINLEST!!
Answers
Answer:
24 pennies
Step-by-step explanation:
120 x 0.2 go get 24 and other will get 48
13 pretty please
:)tyyyyyyy
Answers
Answer:
B.
Step-by-step explanation:
Please solve this simultaneous equation, i'm not that good at it.
2r-s=10
rs-s^2=12
Answers
Answer:
s = 6, r = 8 or s = 4, r = 7
Step-by-step explanation:
2r - s = 10
2r = 10 + s
r = 5 + s/2 --(1)
rs - s^2 = 12 --(2)
sub (1) into (2):
(5 + s/2)s - s^2 = 12
5s + 0.5s^2 - s^2 = 12
-0.5s^2 + 5s - 12 = 0
s^2 - 10s + 24 = 0
(s - 6)(s - 4) = 0
therefore s = 6 or s = 4
when s = 6, r = 8 and when s = 4, r = 7
if you would like to discover more about simultaneous equations, you can have a look at my Instagram page (learntionary). I'll be posting mathematics related stuff there and some of my notes (simultaneous enq notes are already posted!)
Solve the system of equations
-6y+11x=-36
-4y+7x=-24
x=
y=
Answers
Answer:
Y=6
X=0
Step-by-step explanation:
Hope this helps
help me pleaseeeeeeeee help nowww
Answers
Answer:
IT'S A. HEHEHEHEHEHEHE
there are 175 total balloons the ratio of gold to silver balloons is 3:2 how many balloons are gold out of the 175 balloons
Answers
I have 1 word problem and a math problem. (word prob)A light-year is the distance that light travels in a year and is equivalent to 9.461 * 10^12. Write this distance in standard form.
(math prob) Order the list of numbers from least to greatest.
8.5*10^12,3.6*10^8,5.85*10^-3, 2.5*10^-1,8.5*10^8. ( This ^ means there are square roots for the numbers).
My math class is real soon. Pls, answer them. Thanks!!
Answers
Answer:
1. 9461000000000
move the desimal in 9.461 12 places to the right to get:
9461000000000
2.
5.85 x 10^-3,
2.5 x 10^-1,
3.6 x 10^8,
8.5 x 10^8,
8.5 x 10^12
the smallest exponent is the smallest. Since 8.5 x 10^8 and 3.6 x 10^8 have the same exponent, go to the desimal
Solve by substitution x-7y=7 6x-7y=-28
Answers
Answer:
(-7, -2)
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDASEquality PropertiesAlgebra I
Solving systems of equations using substitution/eliminationStep-by-step explanation:
Step 1: Define systems
x - 7y = 7
6x - 7y = -28
Step 2: Rewrite systems
x = 7y + 7
6x - 7y = -28
Step 3: Solve for y
Substitute: 6(7y + 7) - 7y = -28Distribute 6: 42y + 42 - 7y = -28Combine like terms: 35y + 42 = -28Isolate y term: 35y = -70Isolate y: y = -2Step 4: Solve for x
Define original equation: x - 7y = 7Substitute in y: x - 7(-2) = 7Multiply: x + 14 = 7Isolate x: x = -7And we have our answer!