A=10x(15x)-p(4x)^2
A=150x^2-16px^2
A=(150-16p)x^2
From the table, y varies directly as x. Therefore, the constant of variation is k = 2 and y = 2x.
<h3>How to find a direct variation?</h3>
For direct variation,
y ∝ x
Therefore,
y = kx
where
- k = constant of proportionality
Hence,
(-2, -4)
-4 = -2k
k = -4 / -2
k = 2
(-4, -8)
y = -4(2) = -8
Therefore,
k = 2 and y = 2x
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Answer:
All of the above
Step-by-step explanation:
dy/dt = y/3 (18 − y)
0 = y/3 (18 − y)
y = 0 or 18
d²y/dt² = y/3 (-dy/dt) + (1/3 dy/dt) (18 − y)
d²y/dt² = dy/dt (-y/3 + 6 − y/3)
d²y/dt² = dy/dt (6 − 2y/3)
d²y/dt² = y/3 (18 − y) (6 − 2y/3)
0 = y/3 (18 − y) (6 − 2y/3)
y = 0, 9, 18
y" = 0 at y = 9 and changes signs from + to -, so y' is a maximum at y = 9.
y' and y" = 0 at y = 0 and y = 18, so those are both asymptotes / limiting values.
The marked angles are opposite angles, and as such they have the same measure. So, we have
Subtract 2a and 11 from both sides to get
Divide both sides by 4 to get
Now that we know the value of a, we can compute the measure of the angles. We can also verify that the solution we found is correct by verifying that both expressions actually give the same result:
