The heat produced by current I is
H = I²R
where
R = resistance.
According to the formula, heat produced is proportional to the square of the current.

When a current of I = 2 amps is applied, the heat produced is
H = 10x³ + 80.
This heat includes heat due to a fixed current of 2 amps, and heat due to a variable current of x amps.

Because the heat produced is proportional to the square of the current, write the expressions as
H = (10x)*(x²) + 20*(2²)

The second term on the right is heat due to the fixed current of 2 amps, written as
20*(2²).
Therefore the fixed resistance is R = 20 ohms, and the square of the fixed current is 2².

The first term represents heat due to variable resistance, written as
(10x)*(x²).
Therefore the variable resistance is 10x, and the square of the variable current is x².

Answer:
The variable current is 10x.

6 0

3 years ago

A triangle has a 60° angle, and the two adjacent sides are 12 and "12 times the square root of 3". Find the radius of a circle w

shusha [124]

The radius of a circle with the same vertex as a center is 12 units

<h3>Application of Pythagoras theorem;</h3>

To get the radius of the circle, we need to determine the diameter of the circle first:

According to SOH CAH TOA:

$sin\theta = \frac{opp}{hyp} \\sin60 = \frac{12\sqrt{3}}{hyp} \\hyp =\frac{12\sqrt{3}}{sin60} \\hyp =\frac{2\times12\sqrt{3}}{\sqrt3}} \\hyp = 24 = diameter$