Answer:
$13,954.90
Step-by-step explanation:
We assume James wants to fence the four sides of a rectangle with the given dimensions. The perimeter length of a rectangle is ...
P = 2(L +W) = 2(124.6 ft + 138.7 ft) = 526.6 ft
The material cost is the product of the number of feet and the price per foot:
cost = $26.50/ft × 526.6 ft = $13,954.90
Answer:
a. C(1,000) = 420,491.11
b. c(1,000) = 420.49
c. dC/dx(1,000) = 429.72
d. x = 900
e. c(900) = 420
Step-by-step explanation:
We have a cost function for x units written as:
a. The total cost for x=1000 units is:
b. The average cost c(x) can be calculated dividing the total cost by the amount of units:
c. The marginal cost can be calculated as the first derivative of the cost function:
d. This value for x, that minimizes the average cost, happens when the first derivative of the average cost is equal to 0.
e. The minimum average cost is:
A. 6.4/2
$3.20 per pound
3.2/16
$0.20 per ounce
b. 0.90/6
$0.15 per ounce
So b would e the best buy
Answer:
a solution is 1/2 *tan⁻¹ (2*y) = - tan⁻¹ (x²) + π/4
Step-by-step explanation:
for the equation
(1 + x⁴) dy + x*(1 + 4y²) dx = 0
(1 + x⁴) dy = - x*(1 + 4y²) dx
[1/(1 + 4y²)] dy = [-x/(1 + x⁴)] dx
∫[1/(1 + 4y²)] dy = ∫[-x/(1 + x⁴)] dx
now to solve each integral
I₁= ∫[1/(1 + 4y²)] dy = 1/2 *tan⁻¹ (2*y) + C₁
I₂= ∫[-x/(1 + x⁴)] dx
for u= x² → du=x*dx
I₂= ∫[-x/(1 + x⁴)] dx = -∫[1/(1 + u² )] du = - tan⁻¹ (u) +C₂ = - tan⁻¹ (x²) +C₂
then
1/2 *tan⁻¹ (2*y) = - tan⁻¹ (x²) +C
for y(x=1) = 0
1/2 *tan⁻¹ (2*0) = - tan⁻¹ (1²) +C
since tan⁻¹ (1²) for π/4+ π*N and tan⁻¹ (0) for π*N , we will choose for simplicity N=0 . hen an explicit solution would be
1/2 * 0 = - π/4 + C
C= π/4
therefore
1/2 *tan⁻¹ (2*y) = - tan⁻¹ (x²) + π/4
Answer:
x > 10
Step-by-step explanation:
Given
x + 3 > 13 ( subtract 3 from both sides )
x > 10
