Which set of ordered pairs represents a function? A {(22, 5), (23, 10), (22, 7), (23, 5)} B {(22, 5), (26, 10), (23, 7), (23, 5)
balu736 [363]
Answer:
C
Step-by-step explanation:
A function is a special kind of relation in which each valid input gives exactly one output.
C {(22, 10), (23, 10), (24, 7), (25, 5)}
So C is the correct option.
Answer:
0
Step-by-step explanation:
∫∫8xydA
converting to polar coordinates, x = rcosθ and y = rsinθ and dA = rdrdθ.
So,
∫∫8xydA = ∫∫8(rcosθ)(rsinθ)rdrdθ = ∫∫8r²(cosθsinθ)rdrdθ = ∫∫8r³(cosθsinθ)drdθ
So we integrate r from 0 to 9 and θ from 0 to 2π.
∫∫8r³(cosθsinθ)drdθ = 8∫[∫r³dr](cosθsinθ)dθ
= 8∫[r⁴/4]₀⁹(cosθsinθ)dθ
= 8∫[9⁴/4 - 0⁴/4](cosθsinθ)dθ
= 8[6561/4]∫(cosθsinθ)dθ
= 13122∫(cosθsinθ)dθ
Since sin2θ = 2sinθcosθ, sinθcosθ = (sin2θ)/2
Substituting this we have
13122∫(cosθsinθ)dθ = 13122∫(1/2)(sin2θ)dθ
= 13122/2[-cos2θ]/2 from 0 to 2π
13122/2[-cos2θ]/2 = 13122/4[-cos2(2π) - cos2(0)]
= -13122/4[cos4π - cos(0)]
= -13122/4[1 - 1]
= -13122/4 × 0
= 0
The mistake is n third line - adding 3w
96 + 2w =2(80 - 3w)
96 + 2w = 160 - 6w
+ 6w + 6w
96 + 8w = 160
- 96 -96
8w = 64
w = 8 weeks answer
Answer
P = 147 million
Step by step explanation
P = Po r^t -------------(1)
Po initial population, r = rate, t = number of years
Here P = 139, Po = 134, t = 10.
Now plug in these values into the formula and find the rate r.
139 = 134r^10
r^10 = 139/134
r = (139/134)^1/10
Now we got r, now plug in the equation (1)
Let's find the population in the year 2014, here t = 24
P = 134 (139/134)^(24/10)
P = 134(139/134)^(2.4)
P = 134*1.1
P = 147.4
P = 147 million
The country's population in 2014 is 147 million (estimation).
Thank you.
