Let her sisters age be x.
=>sister .....x
Sarah.
twice x=2x. then less than 5
=> (2x-5 )
if Sarah = 15 years
by substation, 2x-5=15
Figure 4 is the image of the square LMNP after the translation.
<u>Step-by-step explanation:</u>
Let us see the coordinates of the pre image LMNP as,
L (-3,1)
M(-1,1)
N(-1,-1)
P(-3,-1)
after translation of (x,y) → (x+5, y -3) the coordinates of the image obtained as,
L'(2,-2)
M'(4,-2)
N'(4,-4)
P'(2,-4) which matches the image 4.
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.
Let
The curl is
where 
denotes the partial derivative operator with respect to 
. Recall that
and that for any two vectors 
and 
, 
, and 
.
The cross product reduces to
When you compute the partial derivatives, you'll find that all the components reduce to 0 and
which means 
is indeed conservative and we can find 
.
Integrate both sides of
with respect to 
and
Differentiate both sides with respect to 
and
Now
and differentiating with respect to 
gives
for some constant 
. So
Answer:
lolololololololoolololo
Step-by-step explanation:
