Answer:
361
Step-by-step explanation:
discriminant = b² - 4ac
= (21)² - 4(1)(20)
= 441 - 80
= 361
Using Lagrange multipliers, we have the Lagrangian
with partial derivatives (set equal to 0)
Substituting the first three equations into the fourth allows us to solve for
:
For each possible value of
, we get two corresponding critical points at
.
At these points, respectively, we get a maximum value of
and a minimum value of
.
Answer:20=x i played around with the angles a bit untill it all fit in 360 (the angles all together equal up to 360 in a polygon)
Step-by-step explanation:
Answer:
The linear speed of the windmill is 32.682 ft/s.
Step-by-step explanation:
Given;
radius of the windmill, r = 26 ft
number of revolutions per minute, θ = 12 rpm
The angular speed of the windmill is given as;
The linear speed of the windmill is given as;
v = ωr
v = 1.257 rad/s x 26 ft
v = 32.682 ft/s
Therefore, the linear speed of the windmill is 32.682 ft/s.
Answer:
D) 13.9 in
Step-by-step explanation:
The diagonal of a rectangle is longer than the longest side. It will never be more than 42% of the shortest side longer than the longest side.
Here, the longest side is 11 inches. 42% of the shortest side is about 3.6 inches, so the diagonal length will be between 11 and 14.6 inches. Only one answer choice is in that range: 13.9 in.
Of course, the length of the diagonal can be figured to any desired accuracy using the Pythagorean theorem.
... √(8.5² +11²) = √193.25 ≈ 13.9014 . . . . inches
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<em>Comment on the solution</em>
For this multiple-choice problem, it is sufficient to estimate the length of the diagonal. The estimate we suggested was to add 0.42 times the short side to the long side.
An even closer estimate can be had by multiplying that value (.42×short side) by the ratio of the short to long sides prior to adding it to the long side. This will get you within 1.5% of the correct value without the need for a square root.