Last one because it has an odd number of negative signs
I think it’s proportional!
Assuming metric units, metre, kilogram and seconds
Best approach: draw a free body diagram and identify forces acting on the child, which are:
gravity, which can be decomposed into normal and parallel (to slide) components
N=mg(cos(theta)) [pressing on slide surface]
F=mg(sin(theta)) [pushing child downwards, also cause for acceleration]
m=mass of child (in kg)
g=acceleration due to gravity = 9.81 m/s^2
theta=angle with horizontal = 42 degrees
Similarly, kinetic friction is slowing down the child, pushing against F, and equal to
Fr=mu*N=mu*mg(cos(theta))
mu=coefficient of kinetic friction = 0.2
The net force pushing child downwards along slide is therefore
Fnet=F-Fr
=mg(sin(theta))-mu*mg(cos(theta))
=mg(sin(theta)-mu*cos(theta)) [ assuming sin(theta)> mu*cos(theta) ]
From Newton's second law,
F=ma, or
a=F/m
=mg(sin(theta)-mu*cos(theta)) / m
= g(sin(theta)-mu*cos(theta)) [ m/s^2]
In case imperial units are used, g is approximately 32.2 feet/s^2.
and the answer will be in the same units [ft/s^2] since sin, cos and mu are pure numbers.
Answer:
+1 and -1
Step-by-step explanation:
The function in this problem is:
First of all, we have to define the domain of the function, which is the set of values of x for which the function is defined.
In order to find the domain, we have to require that the denominator is different from zero, so
which means:
So the domain is all values of x, except from 4 and -7.
Now we can solve the problem and find the zeros of the function. The zeros can be found by requiring that the numerator is equal to zero, so:
This is verified if either one of the two factors is equal to zero, therefore:
and
We see that both values are part of the domain, so they are acceptable values: so the zeros of the function are +1 and -1.
