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AKS 18/19 A travel agent is arranging a private cruise. The agent can arrange for, at most, 40 people to go on the trip. The tri

zlopas [31]

Answer:

M + W <= 40

M >= 12

M >= 15

Total profit = $26 * M + $14 * W

Step-by-step explanation:

Let the number of men be denoted by M

number of women be denoted by W

Maximum no of people that can go one trip = 40

Therefore representing it mathematically we have

M + W <= 40 -------------- CONSTRAINT 1

Minimum number of men needed on trip = 12

Therefore representing it mathematically we have

M >= 12 CONSTRAINT 2

Minimum number of women needed on trip = 15

Therefore representing it mathematically we have

M >= 15 CONSTRAINT 3

profit on 1 man = $26

profit on M men = $26 * M

profit on 1 woman = $14

profit on M men = $14 * W

Total profit combining for men and women =

$26 * M + $14 * W -------------CONSTRAINT 4

___________________________________________

writing together all the constraint

M + W <= 40

M >= 12

M >= 15

Total profit = $26 * M + $14 * W

4 0

3 years ago

The integral of (5x+8)/(x^2+3x+2) from 0 to 1

Lesechka [4]

Compute the definite integral:
integral_0^1 (5 x + 8)/(x^2 + 3 x + 2) dx

Rewrite the integrand (5 x + 8)/(x^2 + 3 x + 2) as (5 (2 x + 3))/(2 (x^2 + 3 x + 2)) + 1/(2 (x^2 + 3 x + 2)):
= integral_0^1 ((5 (2 x + 3))/(2 (x^2 + 3 x + 2)) + 1/(2 (x^2 + 3 x + 2))) dx

Integrate the sum term by term and factor out constants:
= 5/2 integral_0^1 (2 x + 3)/(x^2 + 3 x + 2) dx + 1/2 integral_0^1 1/(x^2 + 3 x + 2) dx

For the integrand (2 x + 3)/(x^2 + 3 x + 2), substitute u = x^2 + 3 x + 2 and du = (2 x + 3) dx.
This gives a new lower bound u = 2 + 3 0 + 0^2 = 2 and upper bound u = 2 + 3 1 + 1^2 = 6: = 5/2 integral_2^6 1/u du + 1/2 integral_0^1 1/(x^2 + 3 x + 2) dx

Apply the fundamental theorem of calculus.
The antiderivative of 1/u is log(u): = (5 log(u))/2 right bracketing bar _2^6 + 1/2 integral_0^1 1/(x^2 + 3 x + 2) dx

Evaluate the antiderivative at the limits and subtract.
(5 log(u))/2 right bracketing bar _2^6 = (5 log(6))/2 - (5 log(2))/2 = (5 log(3))/2: = (5 log(3))/2 + 1/2 integral_0^1 1/(x^2 + 3 x + 2) dx

For the integrand 1/(x^2 + 3 x + 2), complete the square:
= (5 log(3))/2 + 1/2 integral_0^1 1/((x + 3/2)^2 - 1/4) dx

For the integrand 1/((x + 3/2)^2 - 1/4), substitute s = x + 3/2 and ds = dx.
This gives a new lower bound s = 3/2 + 0 = 3/2 and upper bound s = 3/2 + 1 = 5/2: = (5 log(3))/2 + 1/2 integral_(3/2)^(5/2) 1/(s^2 - 1/4) ds

Factor -1/4 from the denominator:
= (5 log(3))/2 + 1/2 integral_(3/2)^(5/2) 4/(4 s^2 - 1) ds

Factor out constants:
= (5 log(3))/2 + 2 integral_(3/2)^(5/2) 1/(4 s^2 - 1) ds

Factor -1 from the denominator:
= (5 log(3))/2 - 2 integral_(3/2)^(5/2) 1/(1 - 4 s^2) ds

For the integrand 1/(1 - 4 s^2), substitute p = 2 s and dp = 2 ds.
This gives a new lower bound p = (2 3)/2 = 3 and upper bound p = (2 5)/2 = 5:
= (5 log(3))/2 - integral_3^5 1/(1 - p^2) dp

Apply the fundamental theorem of calculus.
The antiderivative of 1/(1 - p^2) is tanh^(-1)(p):
= (5 log(3))/2 + (-tanh^(-1)(p)) right bracketing bar _3^5

Evaluate the antiderivative at the limits and subtract. (-tanh^(-1)(p)) right bracketing bar _3^5 = (-tanh^(-1)(5)) - (-tanh^(-1)(3)) = tanh^(-1)(3) - tanh^(-1)(5):
= (5 log(3))/2 + tanh^(-1)(3) - tanh^(-1)(5)

Which is equal to:

Answer: = log(18)

6 0

3 years ago

Rosie wrote this expression to describe the amount she paid for each yoga class. 30 / m Which situation could be described by th

Zielflug [23.3K]

30/m would best describe situation D. Rosie has paid $30. Dividing it by <em>m</em> would mean she wants to know how many she can get out of that $30, which would imply she doesn't know how many classes she's bought.

4 0

3 years ago

Need help with #1 <br> Thank you.

lbvjy [14]

The answer should be B) if my math is correct

8 0

4 years ago

Two neighbors in a rural area want to know the dsitance between their homes in miles what should the mneighbors us as a conversi

lora16 [44]

They should use the conversion factor

1 mile = 5280 feet

To go from feet to miles, you divide by 5280

So,

4224 ft = 4224/5280 = 0.8 miles

The distance between their homes is exactly 0.8 miles

3 0

3 years ago