As part of a screening process, computer chips must be operated in an oven at 145 °c. ten minutes after starting, the temperature is 65 °c. after 15 minutes, the temperature is 85 °c.

what is the temperature after 23 minutes?

Step-by-step explanation:

This is an initial condition problem using natural logs to solve.  The formula for this is

where y is the temp after t time, e is Euler's number, C is the initial value, and k is the constant of proportionality.  We have 2 unknowns we need to solve for before we can answer the actual question about the temp after 23 minutes.  We also can come up with 2 equations to solve for these unknowns:

     and        

Since our initial value, C, is the same for both equations, we can solve for C in one of the equations and sub it into the other in order to solve for k:

If

, then

, which, equivalently, is

Subbing that value into the other equation:

Divide both sides by 65 to get

(that uses the fact that we are multiplying like bases together so we add their exponents), and

Now take the natural log of both sides to get

which simplifies to

so

k = .0536527973

Now we have our k value.  We can sub it into one of our equations to solve for C now:

and

Raise e to that power to get

65 = C(1.710059171) so

C = 38.01038064

Now we have enough info to solve for the temp after 23 minutes:

and

Raise e to that power to get

y = 38.01038064(3.434991111) so

y = 130.565 degrees after 23 minutes

16

step-by-step explanation:

2 x 40 = 80

80/5

= 16

mr. flanders’ class sold 47 doughnuts and   mr. rodriquez’s class sold 38 cartons of milk

step-by-step explanation:

let x be the number of doughnuts sold by mr. flanders’ class and y be the number of cartons sold by mr. rodriquez’s class.

1. together, the classes sold 85 items, then

x+y=85.

2. both classes earn earned $104.49 for their school. if doughnuts were sold for $1.35 each, then x doughnuts costed $1.35x. if cartons of milk were sold for $1.08 each, then y cartons costed $1.08y. hence,

1.35x+1.08y=104.49.

3. solve the system of two equations: