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.
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Answer:
Y=6
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Step-by-step explanation:
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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
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2r-s=10
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Answers
Answer:
s = 6, r = 8 or s = 4, r = 7
Step-by-step explanation:
2r - s = 10
2r = 10 + s
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rs - s^2 = 12 --(2)
sub (1) into (2):
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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
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Line ℓ is perpendicular to line m. Find the value of x and w.
Answers
w° = 180° - 138°
w = 42
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sub. in w=42,
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Answer:
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Step-by-step explanation:
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Answer:
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Step-by-step explanation:
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Answer:
x=-3
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Answer:
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9461000000000
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Answer:
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Step-by-step explanation:
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Compare data set A and data set B.
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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:
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Set B:
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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.
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Answer:
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Answer:
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Step-by-step explanation:
Answer:
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Answers
Answer:
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Step-by-step explanation:
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Step-by-step explanation:
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[tex]3x\frac{2}{3}=9\cdot \:3[/tex]
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B. –4.5 + 6.5 = –2.0
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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
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{
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Answers
Answer:
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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
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[tex]x-y=2[/tex]
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Answer:
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Step-by-step explanation:
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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
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Answers
Answer:
X=120 and y=10,z=120
Step-by-step explanation:
corresponding angles
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ILL GIVE YOU BRAINLEST!!
Answers
Answer:
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Step-by-step explanation:
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Answers
Answer:
No they shouldn't.
Step-by-step explanation:
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Single Pass: Celine: $58 Kamal: $42
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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
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Answers
Answer:
30
Step-by-step explanation:
(3x12)-(4+2)
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30
Distribute the negative: 3 x 12-4-2
Use PEMDAS
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