Answer:
Cross price elasticity using midpoint method = 0.56
Step-by-step explanation:
Using the mid-point method
Cross-price Elasticity of Demand = <u>% change in Quantity demanded of UPS</u>
% change of price of FedEx
%change in Quantity demanded of UPS
using Mid-point method = <u> Q2-Q1 </u> × 100
(Q1+Q2)÷ 2
= <u>1.3-1.2 </u> × 100
(1.2+1.3)÷2
= <u>0.1 </u> × 100
1.25
= 8%
% change in price of FedEx
using midpoint method =<u> P2-P1 </u>× 100
(P1+P2)÷ 2
=<u> 75-65 </u>× 100
(65+75)÷2
=<u> 10 </u> × 100
70
= 14.28%
Cross-price Elasticity of Demand = 8% ÷ 14.28%
using midpoint method = 0.56
The paraboloid meets the x-y plane when x²+y²=9. A circle of radius 3, centre origin.
<span>Use cylindrical coordinates (r,θ,z) so paraboloid becomes z = 9−r² and f = 5r²z. </span>
<span>If F is the mean of f over the region R then F ∫ (R)dV = ∫ (R)fdV </span>
<span>∫ (R)dV = ∫∫∫ [θ=0,2π, r=0,3, z=0,9−r²] rdrdθdz </span>
<span>= ∫∫ [θ=0,2π, r=0,3] r(9−r²)drdθ = ∫ [θ=0,2π] { (9/2)3² − (1/4)3⁴} dθ = 81π/2 </span>
<span>∫ (R)fdV = ∫∫∫ [θ=0,2π, r=0,3, z=0,9−r²] 5r²z.rdrdθdz </span>
<span>= 5∫∫ [θ=0,2π, r=0,3] ½r³{ (9−r²)² − 0 } drdθ </span>
<span>= (5/2)∫∫ [θ=0,2π, r=0,3] { 81r³ − 18r⁵ + r⁷} drdθ </span>
<span>= (5/2)∫ [θ=0,2π] { (81/4)3⁴− (3)3⁶+ (1/8)3⁸} dθ = 10935π/8 </span>
<span>∴ F = 10935π/8 ÷ 81π/2 = 135/4</span>
Answer:
<em>Scott will take 221 minutes to run 52 km</em>
Step-by-step explanation:
<u>Speed</u>
The speed of an object can be calculated with the formula:
Where d is the distance traveled and t is the time taken.
Scott can run d=20 km in 85 minutes. Thus, his speed is:
Now he wants to know how many minutes it will take him to run d=52 km. Solving the formula for t:
Since the speed has been already determined:
Multiplying by the reciprocal of the denominator:
t = 221 min
Scott will take 221 minutes to run 52 km
