We are to show that the given parametric curve is a circle.
The trajectory of a circle with a radius r will satisfy the following relationship:
(with (x_c,y_c) being the center point)
We are given the x and y in a parametric form which can be further rewritten (using properties of sin/cos):
Squaring and adding both gives:
The last expression shows that the given parametric curve is a circle with the center (0,0) and radius A.
The density of gold is 2.8 N / 15 = 0.18 units
The density of mercury is 0.13/1 = 0.13 units
Since the density of gold is more than density of mercury, it will sink.
Since the gold will sink, it will displace mercury, but less than its own volume
-- First, we have to decide how to handle the two resistors.
The effective resistance of resistors in series is the sum
of their individual resistances. That is, they act like a single
resistor, whose resistance is the sum of all of them.
So in this question, the 4.0 ohms and the 7.5 ohms act like a
single resistor of 11.5 ohms.
-- The current in the circuit is
(the supply voltage) / (the total resistance)
= (9.0 volts) / (11.5 ohms)
= 0.783... Ampere (rounded)
