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>
$125,060,000
one-hundred twenty-five million, and sixty thousand dollars
Also, 125.06 expressed as a fraction is 6253/50, if that representation is acceptable.
You can refer to it as 125.06 million dollars when using the figure from the prompt.
<span>15000 feet
The height of Mt. Whitney is listed as 14,505 feet. To round this figure to the closest thousand, we examine the hundreds digit, which is 5. According to the rounding rule, "5 or above, round up, 4 or below, round down". Given that the digit is 5, we round up to yield 15000 feet</span>
Response:
This is the C=intercept of the regression line
Step-by-step clarification:
The regression line's slope is logically interpreted as the average increase in collar size for each 1cm increment in height.
Let M represent the intersection point of the medians.
Assign the distance from D to M as x and from Q to M as y.
Based on the properties of triangle medians, we understand that

Furthermore,

Recognizing that the medians are perpendicular permits us to deduce that:

Thus, since