1answer.
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
Monica [59]
3 years ago
15

A cold drink is poured out at 52°F. After 2 minutes of sitting in a 72°F room, its temperature has risen to 55°F. Find an equati

on for the drink's temperature at any time t. (t) =
Mathematics
1 answer:
I am Lyosha [343]3 years ago
7 0

Answer:

The model for the temperature of the drink can be written as

T=72-20e^{-0.08t}

Step-by-step explanation:

For a cold drink in a hotter room, we can say that the rate of change of temperature of the drink is proportional to the difference of temperature between the drink and the room.

We can model that in this way

\frac{dT}{dt}=k*(T_r-T)

If we rearrange and integrate

\int\frac{dT}{(T-Tr)} =-k*\int dt\\\\ln(T-T_r)=-kt+C1\\\\T-T_r=Ce^{-kt}\\\\T=T_r+Ce^{-kt}

We know that at time 0, the temperature of the drink was 52°F. Then we have:

T=T_r+Ce^{-kt}\\\\52=72+Ce^0=72+C\\\\C=-20

We also know that at t=2, T=55°F

T=T_r+Ce^{-kt}\\\\55=72-20e^{-k*2}\\\\e^{-k*2}=(72-55)/20=0.85\\\\-2k=ln(0.85)=-0.1625\\\\k=0.08

The model for the temperature of the drink can be written as

T=72-20e^{-0.08t}

You might be interested in
Write a piecewise-defined function that represents the graph?
kodGreya [7K]

Answer:

f(x) = { x, -5 ≤ x < 0 and 3x - 3, 1 ≤ x < 5

Step-by-step explanation:

The equation of one line is y = x

The equation of the other line is y = 3x - 3

Altogether,

f(x) = { x, -5 ≤ x < 0 and 3x - 3, 1 ≤ x < 5

4 0
2 years ago
Find the maximum rate of change of f(x,y) = x2y +2y
nevsk [136]

Answer:

Maximum rate of change at the point (-1,2) = √17

Direction is the direction of the gradient

Step-by-step explanation:

The gradient of a function (scalar or vectorial ) is a vector in the direction of maximum rate of change then

f( x,y ) =  x*2y  + 2y

grad    =  δ/δx i +  δ/δy j + δ/δz k

grad f(x,y)  = [ δ/δx i , δ/δy]  =  [ 2y , x+2 ]

at the point  ( -1 , 2 )

grad f(x,y)  = [4 , 1]

| grad f(x,y) |  =  √ (4)²  + (1)²   =  √17

4 0
3 years ago
Solve the following inequality for h then simplify <br> 8h-2&gt;3h+2
Nata [24]

Answer:

8h-3>3h +2

8h-3h>2+3

5h>5

h>1

don't forget to draw your number line

pls make me the brainliest

6 0
3 years ago
What is the solution or solutions to 5x-y=-6 and   -2x+y=3?
sladkih [1.3K]
I would reccomend the app photo math its really easy to use and it answers questions like this. 
4 0
3 years ago
Read 2 more answers
21.
jasenka [17]

Answer:

b = y intercept

Step-by-step explanation:

y = mx +b

This is the slope intercept form of a line

The m is the slope and the b is the y intercept

8 0
3 years ago
Other questions:
  • Write 0.0003532 in scientific notation. A. 3.532 × 105 B. 3.532 × 104 C. 3.532 × 10−4 D. 3.532 × 10−5
    12·1 answer
  • Hello please could you answer the questions in the attachment about arc length and the area of a sector. Please show full workin
    9·2 answers
  • Given: log2 = a, log7 = b. <br> Find: log56
    5·1 answer
  • Suppose a creditor offers you an agreement where the infest accrues as follows: I=Prt, where I is interest owed ($), P is the am
    12·1 answer
  • B is opposite __________.
    9·1 answer
  • 4 (2x + 1) — 5х + 3x +9
    8·1 answer
  • Who could help me please and thank you
    10·1 answer
  • Find the surface area of a cylinder with a height of 4 yd and a base radius of 3 yd.​
    13·1 answer
  • 2, 2, 2, 3, 4, 4, 11<br> What is the median of the seven data values shown
    9·2 answers
  • Y = 3x + 15<br> 3x + 3y = 9
    15·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!