Teams must win at least 25 games. So far, the volleyball team has won 21. Describe the graph of an inequality showing how many m
2 answers:
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Answer:
Decrease in temperature = 4.6714°C
Step-by-step explanation:
We know that the formula fro deflection is:
δ = PL/AE + LαΔT
As deflection is equal to zero in this case, the formula becomes
ΔT = -P/αAE -------------- equation (1)
Now,
we see that only vertical force acting is weight
W = mg = 100*9.81
W = 981N = ∑ where 1N = 1kgm/s²
Now,
for horizontal forces
As we know that, Sum of all horizontal forces = 0
P - μN = 0
P - μW = 0
P = μW
P = 0.6 * 981
P = 588.8N or 589N
Now we need to calculate the area
area = width * thickness = 20 * 3
area = 60 mm²
Now by substituting all these values in equation 1, wee get
ΔT = -P/αAE = - 588.6/(20*10⁻⁶*60*10⁻⁶*105*10⁹)
ΔT = - 4.6714°C (negative sign indicates decrease)
Notice that
so the constraint is a set of two lines,
and only the first line passes through the first quadrant.
The distance between any point in the plane is
, but we know that
and
share the same critical points, so we need only worry about minimizing
. The Lagrangian for this problem is then
with partial derivatives (set equal to 0)
We have
which tells us that
so that is a critical point. The Hessian for the target function
is
which is positive definite for all , so the critical point is the site of a minimum. The minimum distance itself (which we don't seem to care about for this problem, but we might as well state it) is
.