Answer:
The Multiplication Property of Equality states that if you multiply both sides of an equation by the same number, the sides remain equal.
Step-by-step explanation:
so for example if a=b then a x c=b x c
because your doing the same thing to both sides.
<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>
Answer:
8 floors
Step-by-step explanation:
The number of employees is directly proportional to the number of floors that each building has.
The first building has 32 floors and it occupies 189 employees. Therefore:
189 α 32
=> 189 = k * 32 = 32k
where k = constant of proportionality
=> k = 189/32
The new building has 50 employees, therefore:
50 = kN
where N = number of floors
=> 50 = 189/32 * N
N = (50 * 32) / 189 ≅ 8 floors
The new building should have 8 floors
The slope-intercept form: y = mx + b
