<span>3.2 grams
The first thing to do is calculate how many half lives have expired. So take the time of 72 seconds and divide by the length of a half life which is 38 seconds. So
72 / 38 = 1.894736842
So we're over 1 half life, but not quite 2 half lives. So you'll have something less than 12/2 = 6 grams, but more than 12/4 = 3 grams.
The exact answer is done by dividing 12 by 2 raised to the power of 1.8947. So let's calculate 2^1.8947 power
= 12 g / (e ^ ln(2)*1.8947)
= 12 g / (e ^ 0.693147181 * 1.8947)
= 12 g / (e ^ 1.313305964)
= 12 g / 3.718446464
= 3.227154167 g
So rounded to 2 significant figures gives 3.2 grams.</span>
Answer:
(C) greater than zero but less than 45° above the horizontal
Explanation:
The range of a projectile is given by R = v²sin2θ/g.
For maximum range, sin2θ = 1 ⇒ 2θ = sin⁻¹(1) = 90°
2θ = 90°
θ = 90°/2 = 45°
So the maximum horizontal distance R is in the range 0 < θ < 45°, if θ is the angle above the horizontal.
Answer:

Explanation:
This is a uniformly accelerated motion, so we can determine the deceleration of the car by using a suvat equation:

where
v is the final velocity
u is the initial velocity
a is the acceleration
s is the distance covered
For the car in this problem,
u = 27.8 m/s
v = 0
s = 17 m
Solving for a, we find the acceleration:

Answer:
Given: V = 220V, Pmin = 360W, Pmax = 840W
For minimum heating case:
We know that
Pmin = VI
360 = 220 X I
I = 1.63 amp
R = V/I
R = 220/1.63
R = 134.96ohms
For maximum heating case:
We know that
Pmax = VI
840 = 220 X I
I = 3.81 amp
R = V/I
R = 220/3.81
R = 57.74 ohms