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:
X=120 and y=10,z=120
Step-by-step explanation:
corresponding angles
thus 120=(13y-10)=x
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Answer:
150 miles
Step-by-step explanation:
use the pythagoerean theorem
42^2 + 144^2 = c^2
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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)
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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
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Step 2: Rewrite systems
x = 7y + 7
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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
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a = 9b - 8 — (2) [given]
a = a
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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]
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Answers
Cause slope is -4/1
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Answer:
y=-3x+6
Step-by-step explanation:
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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):
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s^2 - 10s + 24 = 0
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therefore s = 6 or s = 4
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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!)
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Ed wants to buy a basketball for $5, but
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Answer:
x=-3
Step-by-step explanation:
-5(x+1)=10
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Line ℓ is perpendicular to line m. Find the value of x and w.
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w° = 180° - 138°
w = 42
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X+y=4
{
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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]
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solving
[tex]-2y=-2[/tex]
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[tex]\frac{-2y}{-2}=\frac{-2}{-2}[/tex]
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[tex]\mathrm{For\:}x+y=4\mathrm{\:plug\:in\:}y=1[/tex]
[tex]x+1=4[/tex]
[tex]x=3[/tex]
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[tex]x=3,\:y=1[/tex]
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Answers
Answer:
-17/9
Step-by-step explanation:
You need to add 7 to both sides.
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Answers
Answer:
30
Step-by-step explanation:
(3x12)-(4+2)
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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
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Step-by-step explanation:
120 x 0.2 go get 24 and other will get 48
I will give brainliest answer to these questions
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THATS MADDDD CAPPPP U NEED 25 POINTS OF THE QUESTION FOR BRAINLIEST
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.
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Answer:
No they shouldn't.
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Answers
Answer:
Set A: mean = 79.6, standard deviation = 9.8
Step-by-step explanation:
Set A has a larger spread of data.
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Set B:
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Step-by-step explanation:
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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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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.
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My math class is real soon. Pls, answer them. Thanks!!
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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,
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8.5 x 10^12
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Answer:
IT'S A. HEHEHEHEHEHEHE
What is the square root of 40000 step by step
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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
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
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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
As a percent is would be 81%
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Answer:
B.
Step-by-step explanation: