The equation given is –2x – 4 + 5x = 8, and the task is to find the value of x. To start, combine like terms and reorganize the equation:
-2x + 5x = 8 + 4
Next, simplify both sides:
3x = 12
Divide both sides by 3 to isolate x:
x = 4.
Therefore, the solution for x is 4.
The tension does not approach infinity.
<span>Let's analyze free body diagrams (FBDs) for each mass, considering the direction of motion of m₁ as positive.
For m₁: m₁*g - T = m₁*a
For m₂: T - m₂*g = m₂*a
Assuming a massless cord and pulley without friction, the accelerations are the same.
From the second equation: a = (T - m₂*g) / m₂
Substitute into the first:
m₁*g - T = m₁ * [(T - m₂*g) / m₂]
Rearranging:
m₁*g - T = (m₁*T)/m₂ - m₁*g
2*m₁*g = T * (1 + m₁/m₂)
2*m₁*m₂*g = T * (m₂ + m₁)
T = (2*m₁*m₂*g) / (m₂ + m₁)
Taking the limit as m₁ approaches infinity:
T = 2*m₂*g
This aligns with intuition since the greatest acceleration m₁ can have is -g. The cord then accelerates m₂ upward at g while gravity acts downward, leading to a maximum upward acceleration of 2*g for m₁.</span>
The expression at hand is:
(-4a ^ -2 b ^ 4) / (8a ^ -6b ^ -3)
Using the laws of exponents, we can transform this expression.
This leads to:
(-4/8) * ((a ^ (- 2 - (- 6))) (b ^ (4 - (- 3))))
Rearranging gives us:
(-2/4) * ((a ^ (- 2 + 6)) (b ^ (4 + 3)))
(-1/2) * ((a ^ 4) (b ^ 7))
-1 / 2a ^ 4b ^ 7
Final Answer:
The exponent for b in Marina's simplification must be 7
Result:
6.1°; 425.86 m.
Step-by-step breakdown:
The information provided states that the airplane is at an altitude of 5.7 miles above ground level, while the "radius of Earth is about 4000 miles." Thus,
θ = 2 × cos^-1 (a/ (a + b)), where a = 4000 miles, and b = 5.7 miles.
θ = 2 × cos^-1 (4000/ (4000 + 5.7)) = 6.1°.
To calculate the distance in meters:
Change in distance = 6.1° /360° × 2π × 4000 miles = 425.86 meters.
Consequently, BD⌢ measures at 6.1° and the distance corresponding to this section of Earth is 425.86 meters.
