Jeriel decides to research the relationship between the length in inches and the weight of a certain species of catfish. He meas
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The answer is incomplete. Here is the complete question:
Jamie and Stella are saving money to sign up for a school trip to Washington, D.C. In order to sign up for the trip, they must pay $600 upfront. Jamie earns his money by washing cars for $25 each. Stella earns her money by making pecan pies for $15 each. Jamie earns more money than Stella does because Stella only has enough supplies to make 40 pies. let x represent the number of cars Jamie washes. Let y represent the number of pies Stella makes.
Part 1: Write a constraint (an inequality) to represent how much money Jamie needs for his trip.
Part 2: Write a constraint (an inequality) to represent how much money Stella needs for her trip.
Part 3: Write a constraint (an inequality) to represent the limitations of Stella's supplies.
Part 4: Can Stella afford to sign up for the trip with the money she earns? Explain your answer and show any work that might support your answer.
Answer:
Part 1:
Part 2:
Part 3:
Part 4: Yes, she makes exactly 600 dollars by making 40 pies.
Step-by-step explanation:
Given:
Total money needed for the trip is 600 dollars.
Money earnt by Jamie for washing one car is $25.
Money earnt by Stella for making one pie is $15.
Let represent the number of cars Jamie washes. Let
represent the number of pies Stella makes.
Part 1:
Since the cost for washing one car is $25
Therefore, the cost of washing cars is
.
Now, in order to sign up for the trip, money obtained from car washing must be greater than or equal to $600.
Therefore,
Part 2:
Since the cost for making one pie is $15
Therefore, the cost of making pies is
.
Now, in order to sign up for the trip, money obtained from pie making must be greater than or equal to $600.
Therefore,
Part 3:
As per the question, the maximum number of pies that Stella can make is 40. So, the value of can't exceed 40 and must be less than or equal to 40. Therefore,
Part 4:
Now, in order to sign up for the trip, Stella's total earning must be at least $600. So, is the minimum condition for signing up for the trip. Now, let us solve the above equation for
. This gives,
Therefore, minimum number of pies required for signing up for the trip is 40 and luckily that's the maximum supply Stella has for pies. Therefore, she can sign up for the trip by making all the 40 pies and earning a total of 600 dollars.
Answer:
The Line integral is π/2.
Step-by-step explanation:
We have to find a funtion f such that its gradient is (ycos(xy), x(cos(xy)-ze^(yz), -ye^(yz)). In other words:
we can find the value of f using integration over each separate, variable. For example, if we integrate ycos(x,y) over the x variable (assuming y and z as constants), we should obtain any function like f plus a function h(y,z). We will use the substitution method. We call u(x) = xy. The derivate of u (in respect to x) is y, hence
(Remember that c is treated like a constant just for the x-variable).
This means that f(x,y,z) = sen(x,y)+C(y,z). The derivate of f respect to the y-variable is xcos(xy) + d/dy (C(y,z)) = xcos(x,y) - ye^{yz}. Then, the derivate of C respect to y is -ze^{yz}. To obtain C, we can integrate that expression over the y-variable using again the substitution method, this time calling u(y) = yz, and du = zdy.
Where, again, the constant of integration depends on Z.
As a result,
if we derivate f over z, we obtain
That should be equal to -ye^(yz), hence the derivate of K(z) is 0 and, as a consecuence, K can be any constant. We can take K = 0. We obtain, therefore, that f(x,y,z) = cos(xy) - e^(yz)
The endpoints of the curve are r(0) = (0,0,1) and r(1) = (1,π/2,0). FOr the Fundamental Theorem for Line integrals, the integral of the gradient of f over C is f(c(1)) - f(c(0)) = f((0,0,1)) - f((1,π/2,0)) = (cos(0)-0e^(0))-(cos(π/2)-π/2e⁰) = 0-(-π/2) = π/2.