A hot air balloon rising vertically is tracked by an observer located 2 miles from the lift-off point. At a certain moment, the angle between the observer's line-of-sight and the horizontal is , and it is changing at a rate of 0.1 rad/min. How fast is the balloon rising at this moment

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Answer 1

We have that for the Question, it can be said that

the balloon rising at [tex]0.266miles/min[/tex]

From the question we are told

An observer located 2 miles from the lift-off point. At a certain moment, the angle between the observer's line-of-sight and the horizontal is , and it is changing at a rate of 0.1 rad/min.

From,

[tex]tan\theta = \frac{h}{2}[/tex]

differentiate with respect to h

[tex]sec^2\theta * \frac{do}{dz} = \frac{1}{2} * \frac{dh}{dz}\\\\\frac{dh}{dz} = 2 sec^\theta * \frac{d\theta}{dz}\\\\\theta = \frac{\pi}{6} and \frac{d\theta}{dz} = 0.1rad/min\\\\\frac{dh}{dz} = 2sec^2 (\frac{\pi}{6}) * (0.1)\\\\= 0.266miles/min[/tex]

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IF YOU GIVE ME THE CORRECT ANSWER I WILL GIVE YOU THE CROWN!!
Miranda found four different bottles filled with unknown pure liquids. She measured the mass, volume, and boiling point of these liquids, and calculated the density which are displayed in Table 1.

What conclusion can you make on whether any of the liquids are the same. Explain based on the information in the table.

Answers

Answer:

Samples 2 and 4 are the same liquid

Explanation:

Samples 2 and 4 should be the same liquid because they have the same density as well as the same boiling point. The mass and volumes given do not matter in this case, however they could be used to calculate the density which was already given.

The liquid present in sample 2 and 4 is same as according to forces of attraction they have same density and boiling points.

What are forces of attraction?

Forces of attraction is a force by which atoms in a molecule combine. it is basically an attractive force in nature. It can act between an ion and an atom as well.It varies for different states of matter that is solids, liquids and gases.

The forces of attraction are maximum in solids as the molecules present in solid are tightly held while it is minimum in gases as the molecules are far apart . The forces of attraction in liquids is intermediate of solids and gases.

The physical properties such as melting point, boiling point, density are all dependent on forces of attraction which exists in the substances.

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