I hope this picture helps, but next time try to chose a number to cancel out the fraction. Example, y=1/3x+4 chose 3,6,9 and other multiples of 3.
Its the third pair of inequalities
b 26 < n < 30
so n = 28
the 3 numbers are 28, 30 and 32
Answer:
r = 9/sin Ф or r = 9 csc Ф
Step-by-step explanation:
The polar form is represented as:
x = r cos Ф and
y = r sin Ф
We are given:
y = 9
Putting value in y = r sin Ф
9 = r sin Ф
=> r = 9/sin Ф
1/sin Ф = csc Ф
or, r = 9 csc Ф
Y = log3 27
27 = 3^x
3^3 = 27
so x = 3
Answer:
Rolling case achieves greater height than sliding case
Step-by-step explanation:
For sliding ball:
- When balls slides up the ramp the kinetic energy is converted to gravitational potential energy.
- We have frictionless ramp, hence no loss due to friction.So the entire kinetic energy is converted into potential energy.
- The ball slides it only has translational kinetic energy as follows:
ΔK.E = ΔP.E
0.5*m*v^2 = m*g*h
h = 0.5v^2 / g
For rolling ball:
- Its the same as the previous case but only difference is that there are two forms of kinetic energy translational and rotational. Thus the energy balance is:
ΔK.E = ΔP.E
0.5*m*v^2 + 0.5*I*w^2 = m*g*h
- Where I: moment of inertia of spherical ball = 2/5 *m*r^2
w: Angular speed = v / r
0.5*m*v^2 + 0.2*m*v^2 = m*g*h
0.7v^2 = g*h
h = 0.7v^2 / g
- From both results we see that 0.7v^2/g for rolling case is greater than 0.5v^2/g sliding case.
