Answer:
B. 1/4
Step-by-step explanation:
Even though A is a fraction it is also an integer (4)
Answer:
Step-by-step explanation:
Step one:
Given data for Heather's company
Fixed cost = $5000
Additional cost = $250
in a week there are 168 hours
hence they will produce a total of 168/5= 33.6
=34 systems
the expression for the total cost can be modeled as
c=mn+f
where c=total cost
m= the Additional cost
n= number of systems produced per hour
h= the number of systems produced per hour
f= fixed cost
Step two:
c=mn+f
given that n=34, we can find the total cost as
c=250(34)+5000
c=8500+5000
c=13500
the total cost for each week is $13,500
Answer:
F(2)=2x+1=2*2+1=5
Step-by-step explanation:
The slope of the function is most positive either side of x=0 and x=2π.
On the interval [0, π/4], the average slope is
On the interval [7π/4, 9π/4], the average slope is
The average rate of change is highest on the intervals [0, π/4] and [7π/4, 9π/4].
Answer:
a) f(16) = 42
b) f(16) = 54
c) f(16) = 162
d) f(16) = 30
Step-by-step explanation:
a) y = mx + b ∧ m = (f(8) - f(4))/(8-4) ⇒ m = (18 - 6)/(8 - 4) = 3
b = y - mx = 6 - 3(4) = 6 - 12 = - 6
f(16) = 3(16) - 6 = 42
b) y = kxⁿ ∧ f(4) = 6 = k4ⁿ ∧ f(8) = 18 = k8ⁿ ⇒ 18/6 = (k8ⁿ)/(k4ⁿ) ⇒ 3 = 2ⁿ
n = ㏑(3) / ㏑(2) ⇒ k = y/xⁿ ⇒ k = 6/4ⁿ = 2/3
f(16) = 2/3 × 16ⁿ = 54
c) y = aeᵇˣ ∧ f(4) = 6 = aeᵇ⁴ ∧ f(8) = 18 = aeᵇ⁸ ⇒ 18/6 = (aeᵇ⁸)/(aeᵇ⁴) ⇒ 3 = e⁴ᵇ
b = ㏑(3/4) ∧ a = y / eᵇˣ ⇒ a = 6 / e⁴ᵇ = 2
f(16) = 2eᵇ¹⁶ = 162
d) y = a㏑(bx) ∧ f(4) = 6 = a㏑(b4) ∧ f(8) = 18 = a㏑(b8)
⇒ 18 - 6 = a㏑(b8) - a㏑(b4) ⇒ 12 = a㏑(8b/4b) ⇒ a = 12 / ㏑(2)
f(4) = 6 = a㏑(4b) ⇒ b = (√2)/4
f(16) = a㏑(b16) = 30
