Space is a way of joining together points, lines, and

As part of a screening process, computer chips must be operated in an oven at 145 °C. Ten minutes after starting, the temperatur

Novosadov [1.4K]

Answer:

Step-by-step explanation:

I solved this using initial conditions and calculus, so I hope that's what you are doing in math. It's actually NOT calculus, just a concept that is taught in calculus.

The initial condition formula we need is

$y=Ce^{kt}$

Filling in our formula with the 2 conditions we are given:

$65=Ce^{10k}$ and $85=Ce^{15k}$

With those 2 equations, we have 2 unknowns, the C (initial value) and the k (the constant). We know that the initial value (or starting temp) for both conditions is the same, so we solve for C in one equation, sub it into the other equation and solve for k. If

$65=Ce^{10k}$ then

$\frac{65}{e^{10k}}=C$ which, by exponential rules is the same as

$C=65e^{-10k}$

Since that value of C is the same as the value of C in the other equation, we sub it in:

$85=65e^{-10k}(e^{15k})$

Divide both sides by 65 and use the rules of exponents again to get

$\frac{85}{65}=e^{-10k+15k}$ which simplifies down to

$\frac{85}{65}=e^{5k}$

Take the natural log of both sides to get

$ln(\frac{85}{65})=5k$

Do the log thing on your calculator to get

.2682639866 = 5k and divide both sides by 5 to find k:

k = .0536527973

Now that we have k, we sub THAT value in to one of the original equations to find C:

$65=Ce^{10(.0536527973)}$

which simplifies down to

$65=Ce^{.536527973}$

Raise e to that power on your calculator to get

65 = C(1.710059171) and divide to solve for C:

C = 38.01038064

Now sub in k and C to the final problem when t = 23:

$y=38.01038064e^{(.0536527973)(23)}$ which simplifies a bit to

$y=38.01038064e^{1.234014338}$

Raise e to that power on your calculator to get

y = 38.01038064(3.434991111) and

finally, the temp at 23 minutes is

130.565

6 0

3 years ago

In the diagram below, is the perpendicular bisector of JK. Which of the following statements must be true?

FinnZ [79.3K]

I need some details... If i can get a little more details with that "check all that apply" and i could get you an answer.

3 0

3 years ago

Solve the folowing equation for "n"<br> 6n - 4= 3n + 8

ipn [44]

Answer:

4/3

Step-by-step explanation:

6n - 4 = 3n + 8

6n - 3n = 8 + 4

3n = 4

n = 4/3

Goodluck with your schoolwork/homework.

---------------------------------------------------------------

apologies in advance for any errors or bad explanations.

4 0

4 years ago

Read 2 more answers

Help I’ll give 50 points<br> 12) 4x- y=8<br> 5x+y=1

Luba_88 [7]

12) 4x- y=8

5x+y=1

Correct.

4 0

3 years ago

True or false: Every sequence is either arithmetic or geometric. If this is true, explain. If false,

tiny-mole [99]

In an arithmetic sequence, the difference between consecutive terms is constant. In formulas, there exists a number $r$ such that

$a_{n+1}-a_n=r\quad \forall n\geq 1$

In an geometric sequence, the ratio between consecutive terms is constant. In formulas, there exists a number $r$ such that

$\dfrac{a_{n+1}}{a_n}=r\quad \forall n\geq 1$

So, there exists infinite sequences that are not arithmetic nor geometric. Simply choose a sequence where neither the difference nor the ratio between consecutive terms is constant.

For example, any sequence starting with

$1, 15, -3,\ldots$

Won't be arithmetic nor geometric. It's not arithmetic (no matter how you continue it, indefinitely), because the difference between the first two numbers is 14, and between the second and the third is -18, and thus it's not constant. It's not geometric either, because the ratio between the first two numbers is 15, and between the second and the third is -1/5, and thus it's not constant.

5 0

3 years ago