<span>a) Differentiate both sides of lnq − 3lnp + 0.003p=7 with respect to p, keeping in mind that q is a function of p and so using the Chain Rule to differentiate any functions of q:
(1/q)(dq/dp) − 3/p + 0.003 = 0
dq/dp = (3/p − 0.003)q.
So E(p) = dq/dp (p/q) = (3/p − 0.003)(q)(p/q) = (3/p − 0.003)p = 3 − 0.003p.
b) The revenue is pq.
Note that (d/dp) of pq = q + p dq/dp = q[1 + dq/dp (p/q)] = q(1 + E(p)), which is zero when E(p) = −1. Therefore, to maximize revenue, set E(p) = −1:
3 − 0.003p = −1
0.003p = 4
p = 4/0.003 = 4000/3 = 1333.33</span>
Vertical stretch means the graph stretches upward, rising more rapidly than the original, the graph is steeper than the original.
It would be 50? your adding/increaseing 44.2 centimeters to 16 centimeters because
Hey there! :)
Answer:
m∠A = 72°.
m<B = 108°.
Step-by-step explanation:
In a parallelogram, the opposite angles are congruent.
Therefore, we can set the two expressions equal to each other:
5y - 3 = 3y + 27
Add 3 to both sides:
5y = 3y + 30
Subtract 3y from both sides:
2y = 30
Divide both sides by 2:
y = 15
Substitute this value of y into an expression to solve for the measure of ∠A:
5(15) - 3 = 72°. m∠A = 72°.
In parallelograms, the neighboring angles are supplementary. Therefore:
m∠A + m∠B = 180°
72° + m∠B = 180°
m<B = 108°.
