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
PolarNik [594]
3 years ago
7

An object is heated to 100°. It is left to cool in a room that

Mathematics
1 answer:
stepladder [879]3 years ago
3 0

Answer:

Step-by-step explanation:

Use Newton's Law of Cooling for this one.  It involves natural logs and being able to solve equations that require natural logs.  The formula is as follows:

T(t)=T_{1}+(T_{0}-T_{1})e^{kt} where

T(t) is the temp at time t

T₁ is the enviornmental temp

T₀ is the initial temp

k is the cooling constant which is different for everything, and

t is the time (here, it's in minutes)

If we are looking first for the temp after 20 minutes, we have to solve for the k value.  That's what we will do first, given the info that we have:

T(t) = 80

T₁ = 30

T₀ = 100

t = 5

k = ?

Filling in to solve for k:

80=30+(100-30)e^{5k} which simplifies to

50=70e^{5k} Divide both sides by 70 to get

\frac{50}{70}=e^{5k} and take the natural log of both sides:

ln(\frac{5}{7})=ln(e^{5k})

Since you're learning logs, I'm assuming that you know that a natural log and Euler's number, e, "undo" each other (just like taking the square root of something squared).  That gives us:

-.3364722366=5k

Divide both sides by 5 to get that

k = -.0672944473

Now that we have a value for k, we can sub that in to solve for T(20):

T(20)=30+(100-30)e^{-.0672944473(20)} which simplifies to

T(20)=30+70e^{-1.345888946}

On your calculator, raise e to that power and multiply that number by 70:

T(20)= 30 + 70(.260308205) and

T(20) = 30 + 18.22157435 so

T(20) = 48.2°

Now we can use that k value to find out when (time) the temp of the object cools to 35°:

T(t) = 35

T₁ = 30

T₀ = 100

k = -.0672944473

t = ?

35=30+100-30)e^{-.0672944473t} which simplifies to

5=70e^{-.0672944473t}

Now divide both sides by 70 and take the natural log of both sides:

ln(\frac{5}{70})=ln(e^{-.0672944473t}) which simplifies to

-2.63905733 = -.0672944473t

Divide to get

t = 39.2 minutes

You might be interested in
Find the value of x if 196^×=14​
castortr0y [4]

Answer:

x = \frac{1}{2}

Step-by-step explanation:

Note that \sqrt{196} = 14

Expressed in exponent form as

196^{\frac{1}{2} } = 14, thus

x = \frac{1}{2}

7 0
3 years ago
Please hurry up H. E. L. P
pickupchik [31]
GOING ACROSS

First: 2/4
Second: 5/6
Third: 5/6
Fourth: 2/4
Fifth: other
4 0
2 years ago
Read 2 more answers
The graph of the function f(x) =x^2 is shown on the grid below. Graph the function g(x) =(x-2)^2 -4 in the interactive graph.
Anastasy [175]

Answer:

shift it down by 4 units

Step-by-step explanation:

by the placement of the -4 it can be determined that you would shift it according to the y axis

The formula a(x-h)^2 + k = y

h represents change in x, k represents change in y

-k means shift down

5 0
3 years ago
Help, please in this problem
Nikolay [14]

Answer:

x=9.768

y=6.972

Step-by-step explanation:

For this problem we have to use the trig relationships of cos and sin to figure out the lengths. Cos is equal to adjacent/hypotenuse so we can set it as x/r=.814 and since r is equal to 12 we can do 12 times .814 to get x.

We do a similar process for sin but sin is equal to opposite/hypotenuse so we can set up the equation y/r=.581 and we simply multiply both sides by 12 to get 12*.581 to get y.

Also for future reference adjacent and hypotenuse are based on the angle at use, since ∅ is on the bottom left x is the adjacent side and y is the opposite side.

3 0
2 years ago
Calls to a customer service center last on average 1.4 minutes with a standard deviation of 1.7 minutes. An operator in the call
igomit [66]

Answer:

the expected total amount of time in minutes is 88.4

Step-by-step explanation:

The computation of the expected total amount of time in minutes is given below:

= Standard deviation × needed to answer calls each day

= 1.7 × 52

= 88.4

hence, the expected total amount of time in minutes is 88.4

8 0
3 years ago
Other questions:
  • What is the solution to 2x-8 < 12?
    8·1 answer
  • Ally is making a scale diagram of her classroom. She uses a scale factor of 3 centimeters per foot to draw the diagram. The actu
    8·1 answer
  • If the area of a triangle is 9.3 square meters and the base measurement
    10·2 answers
  • A spinner with 5 equal sections is spent 80 times. It lands on “A” 11 times. How many more times does it need to be spent and ha
    7·1 answer
  • How would I graph this y=1/3x+2,y=-x-2
    6·1 answer
  • Yes i am stupid . please help me.. i have 3 more assignments in this class XD 24-(4x-5)=23
    5·1 answer
  • The Panthers scored 13 more points than the Giants. The total of their scores was 47. How many points did each team score?
    6·1 answer
  • A carnival charges $5 to enter, and $2 per ride. If you paid a total of $23, which of
    10·1 answer
  • Hey guys please solve this for me!!
    12·1 answer
  • Please help! Im in in a quiz.​
    13·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!