Here, we are required to determine after how many minutes will the two substances be at the same temperature.
The equation of when the two substances will be at the same temperature and the solution are as follows;
(a) The equation is 96.2 + 1.5(x) = 98.5 + 0.8(x).
(b) The solution is, x = 3.285minutes.
For substance A which is currently at 96.2° and rising at 1.5° each minute; It's temperature after x minutes is given as;
For substance B which is currently at 98.5° and rising at 0.8° each minute; It's temperature after x minutes is given as;
(a) For the two substances to be at the same temperature; T(a) must be equal to T(b).
The equation is therefore;.
96.2 + 1.5(x) = 98.5 + 0.8(x)
(b) To determine the solution;
1.5x - 0.8x = 98.5 - 96.2
0.7x = 2.3
x = 2.3/0.7
x = 3.285minutes.
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The perimeter of the square is calculated through the equation,
4x = P
where P is the perimeter and x is the measure of the sides.
When P is 32 units then,
32 units = 4(x)
x = 8 inches
This 8 inches is the diameter of the cylinder formed by the rotation.
The circumference of the base is calculated through,
C = 2πr = πD
Substituting the known values,
C = π(8 units) = <em>8π units
</em><em></em>When π is equal to 3.14, we solve for the numerical value of the cylinder as follows,
<em> C = 8(3.14) = 25.12 units
</em><em></em>Thus, the figure formed is a cylinder with base circumference equal to 25 units. The answer is the third choice. <em>
</em>
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