You have a styrofoam container with 751 g of tomato juice (specific heat of 3,980 J/(kg · °C)) at 39.0° and you add a 62 g chunk of ice at 0°C. Assume the liquid and water mix uniformly as the ice melts and determine the final temperature of the mixture (in °C).

The temperature of the mixture in degrees centigrade is 36.5°C.

The heat lost by the melting ice is equal to the heat gained by the tomato juice and water.

Where;

Heat lost by ice = mL = 0.062 Kg × 33600 J/Kg = 2083.2 J

Heat gained by tomato juice = 0.751 Kg × 3,980 J/kg · °C ( T - 39°C)

Heat gained by water = 0.062 Kg × 4200 J/kg · °C ( T - 0°C)

Hence;

2083.2  = [2988.98T - 116570] + [260.4T - 0]

2083.2 = 2988.98T + 260.4T -  116570

2083.2 =3249.38 T - 116570

2083.2 + 116570 = 3249.38 T

T = 36.5°C

Learn more: link

Because of the interstellar dust and interior location of the solar system.

Explanation:

We will probably not be able to detect the neutral hydrogen that gives rise to the 21-cm radio signal if we point a large optical telescope to the region because, the interstellar dust obscures the location of the spiral arm of the Milky way galaxy and this makes neutral hydrogen that gives rise to the 21-cm radio signal difficult to detect.

Also, the interior location of the solar system also makes the neutral hydrogen that gives rise to the 21-cm radio signal difficult to detect.

So, the interstellar dust and the interior location of the solar system makes it difficult to detect the neutral hydrogen that gives rise to the 21-cm radio signal with a large optical telescope.