(a) The skater covers a distance of S=50 m in a time of t=12.1 s, so its average speed is the ratio between the distance covered and the time taken:

(b) The initial speed of the skater is

while the final speed is

and the time taken to accelerate to this velocity is t=2 s, so the acceleration of the skater is given by

(c) The initial speed of the skater is

while the final speed is

since she comes to a stop. The distance covered is S=8 m, so we can use the following relationship to find the acceleration of the skater:

from which we find

where the negative sign means it is a deceleration.
Answer:

First option
Explanation:
<u>Operations with functions
</u>
Given two functions f, g, we can perform a number of operations with them including addition, subtraction, product, division, composition, and many others
.
We have


We are required to find

We simply divide f by g as follows

We know rational functions may have problems if the denominator can be zero for some values of x. We must find out if there are such values and exclude them from the domain of the new-found function. We must ensure

or equivalently

Thus the first option is correct
Note: Since
is always a positive number (for x real), our function does not really have any restriction in its domain
Answer:
700 mL or 0.0007 m³
Explanation:
P₁ = Initial pressure = 2 atm
V₁ = Initial volume = 350 mL
P₂ = Final pressure = 1 atm
V₂ = Final volume
Here the temperature remains constant. So, Boyle's law can be applied here.
P₁V₁ = P₂V₂

So, volume of this sample of gas at standard atmospheric pressure would be 700 mL or 0.0007 m³
Complete question:
A solenoid of length 2.40 m and radius 1.70 cm carries a current of 0.190 A. Determine the magnitude of the magnetic field inside if the solenoid consists of 2100 turns of wire.
Answer:
The magnitude of the magnetic field inside the solenoid is 2.089 x 10⁻⁴ T.
Explanation:
Given;
length of solenoid, L = 2.4 m
radius of solenoid, R = 1.7 cm = 0.017 m
current in the solenoid, I = 0.19 A
number of turns of the solenoid, N = 2100 turns
The magnitude of the magnetic field inside the solenoid is given by;
B = μnI
Where;
μ is permeability of free space = 4π x 10⁻⁷ m/A
n is number of turns per length = N/L
I is current in the solenoid
B = μnI = μ(N/L)I
B = 4π x 10⁻⁷(2100 / 2.4)0.19
B = 4π x 10⁻⁷ (875) 0.19
B = 2.089 x 10⁻⁴ T
Therefore, the magnitude of the magnetic field inside the solenoid is 2.089 x 10⁻⁴ T.