answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
LuckyWell [14K]
2 years ago
10

Jane wishes to bake an apple pie for dessert. The baking instructions say that she should bake the pie in an oven at a constant

temperature of 230◦C. Being a mathematician, she knows that the temperature T of the pie after t minutes of baking will be given by T(t) = 230 − Ae−kt , where A and k are constants. After 18 minutes of baking she notices that the temperature of the pie is 138◦C, while after 36 minutes it is 184◦C. Determine the constants A and k.
Mathematics
1 answer:
Viktor [21]2 years ago
7 0

Answer:

Therefore k= \frac{ln2 }{18}, A=184

Step-by-step explanation:

Given function is

T(t)=230 -e^{-kt}

where T(t) is the temperature in °C and t is time in minute and A and k are constants.

She noticed that after 18 minutes the temperature of the pie is 138°C

Putting T(t) =138°C and t= 18 minutes

138=230 -Ae^{-k\times 18}

\Rightarrow  -Ae^{-18k}=138-230

\Rightarrow  Ae^{-18k}=92 .....(1)

Again after 36 minutes it is 184°C

Putting T(t) =184°C and t= 36 minutes

184=230-Ae^{-k\times 36}

\Rightarrow Ae^{-36k}=230-184

\Rightarrow Ae^{-36k}=46.......(2)

Dividing (2) by (1)

\frac{Ae^{-36k}}{Ae^{-18k}}=\frac{46}{92}

\Rightarrow e^{-18k}=\frac{46}{92}

Taking ln both sides

ln e^{-18k}=ln\frac{46}{92}

\Rightarrow -18k =ln (\frac12)

\Rightarrow -18k= ln1-ln2

\Rightarrow k= \frac{ln2 }{18}

Putting the value k in equation (1)

Ae^{-18\frac{ln2}{18}}=92

\Rightarrow A e^{ln2^{-1}}=92

\Rightarrow A.2^{-1}=92

\Rightarrow \frac{A}{2}=92

\Rightarrow A= 92 \times 2

⇒A= 184.

Therefore k= \frac{ln2 }{18}, A=184

You might be interested in
Madelyn buys 3 bottles of orange juice at the corner store for a total cost of $2.31.
Tom [10]

Answer:

$0.77

Step-by-step explanation:

To find how much each bottle of juice costs, divide 2.31 by 3:

2.31/3

= 0.77

So, each bottle of juice is $0.77

5 0
2 years ago
Read 2 more answers
The table represents the height of a ball thrown up from the roof of a building, h(t), in meters, t seconds after it is thrown u
Anna [14]
• The ball is at the same height as the building between 8 and 10 seconds after it is thrown. TRUE - the height is zero somewhere in that interval, hence the ball is the same height from which it was thrown, the height of the roof of the building.

• The height of the ball decreases and then increases. FALSE - at t=2, the height is greater than at t=0.

• The ball reaches its maximum height about 4 seconds after it is thrown. TRUE - the largest number in the table corresponds to t=4.

• The ball hits the ground between 8 and 10 seconds after it is thrown. FALSE - see statement 1.

• The height of the building is 81.6 meters. FALSE - the maximum height above the building is 81.6 meters. Since the ball continues its travel to a distance 225.6 meters below the roof of the building, the building is at least that high.


1. TRUE
2. False
3. TRUE
4. False
5. False
9 0
2 years ago
Read 2 more answers
MO, MN, and ON are the midsegments of △JKL. What is the perimeter of △JKL? 6 9.5 11.5 19
ipn [44]
Answer is 19  just got it right 
6 0
2 years ago
Read 2 more answers
For a certain type of copper wire, it is knownthat, on the average, 1.5 flaws occur per millimeter.Assuming that the number of f
mario62 [17]

Answer:

The probability that no flaws occur in a certain portion of wire of length 5 millimeters =  1.1156 occur / millimeters

Step-by-step explanation:

<u>Step 1</u>:-

Given data A copper wire, it is known that, on the average, 1.5 flaws occur per millimeter.

by  Poisson random variable given that λ = 1.5 flaws/millimeter

Poisson distribution P(X= r) = \frac{e^{-\alpha } \alpha ^{r} }{r!}

<u>Step 2:</u>-

The probability that no flaws occur in a certain portion of wire

P(X= 0) = \frac{e^{-1.5 } \(1.5) ^{0} }{0!}

On simplification we get

P(x=0) = 0.223 flaws occur / millimeters

<u>Conclusion</u>:-

The probability that no flaws occur in a certain portion of wire of length 5 millimeters = 5 X P(X=0) = 5X 0.223 = 1.1156 occur / millimeters

5 0
2 years ago
Philip wants to give $260 to United Way, but he wants to give it over the coming year. If he signs up to have a regular amount w
Temka [501]

Answer:

D. 5$

Step-by-step explanation:

So, since he wants to save up the whole year, that would be 365 days. And, he wants to collect some money after then end of each <em>week</em>, and a week is 7 days, so you'd divide 365/7. This would give you about 52 weeks he'll set aside money for United Way. Therefore, you'd divide $260/52 weeks, to get a total of $5 each week.

6 0
2 years ago
Read 2 more answers
Other questions:
  • Find the surface area of a triangular prism that has the following dimensions. Use the formula SA = 2 B + Ph . B = 84 mm 2 P = 5
    10·1 answer
  • HIJK is a parallelogram because the midpoint of both diagonals is ____ which means the diagonals bisect each other.
    11·2 answers
  • How long is a distance of 8 km if measured on a map with a scale of 1:50,000
    10·1 answer
  • 16 tons 400 pounds divided by 5
    14·1 answer
  • William has eight more nickels than dimes in his pocket for a total of $2.50
    14·1 answer
  • Help Please! Giving 98 points!
    8·1 answer
  • Estimate the value 9.9 squared times 1.79 and the square root of 97.5 divided by 1.96
    6·1 answer
  • What is the constant of proportionality in the equation y = StartFraction x over 9 EndFraction? 0 StartFraction 1 over 9 EndFrac
    5·2 answers
  • It has been suggested that night shift-workers show more variability in their output levels than day workers. Below, you are giv
    5·1 answer
  • The third term of an A.P is 4m - 2n. If the ninth term of the progression is 2m - 8n. Find the common difference in terms of m a
    15·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!