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
What is the slope of (-2,2) (-4,-4)
Flauer [41]

Answer:

3

Step-by-step explanation:

slope = (y2-y1)/(x2-x1)

(-4-2)/(-4--2)

-6/-2

3

7 0
2 years ago
Read 2 more answers
Please help ASAP! Only one question!!
levacccp [35]
It is negative because the plot is going down not up 
5 0
3 years ago
You and your best friend are meeting at
chubhunter [2.5K]

Answer:

  10.6 miles

Step-by-step explanation:

The corner where Starbucks is located could be considered to be the right angle in a right triangle having legs of 8 miles (distance to you) and 7 miles (distance to your friend). The straight-line distance (d) from you to your friend is the hypotenuse of that triangle. Its length can be found from the Pythagorean theorem.

  d² = 8² +7²

  d² = 64 +49 = 113

  d = √113 ≈ 10.6

You and your friend are about 10.6 miles from each other.

4 0
2 years ago
What is the answer to (-7) x (3) x (-4)
azamat

Answer:

The answer is 84

Step-by-step explanation:

(-7)*(3)*(-4)

negatives cancel out: 7*3*4

Simplify: 84

7 0
3 years ago
Read 2 more answers
The hours of daylight, y, in Utica in days x from January 1, 2013 can be modeled by the equation y = 2.89sin(0.0145x-1.40) + 10.
Pie

Answer:

9.3 hours

Step-by-step explanation:

Given

y = 2.89\sin(0.0145x-1.40) + 10.99.

Required

Hours of sunlight on Feb 21, 2013

First, calculate the number of days from Jan 1, 2013 to Feb 21, 2013

days = 52

So:

x = 52

So, we have:

y = 2.89\sin(0.0145x-1.40) + 10.99.

y = 2.89\sin(0.0145*52-1.40) + 10.99.

y = 2.89\sin(0.754-1.40) + 10.99.

y = 2.89\sin(-0.646) + 10.99.

y = 2.89*-0.6020 + 10.99.

y = -1.740 + 10.99.

y = 9.25

<em></em>y = 9.3<em> --- approximated</em>

8 0
2 years ago
Other questions:
  • Name the property illustrated by each statement​
    9·1 answer
  • there are 2,300 licensed dogs in clarkson. A random sample of 50 of the dogs in Clarkson shows that 8 have ID microchips implant
    11·2 answers
  • How do i do fifth grade divison
    15·1 answer
  • Find the area of this parallelogram. Be sure to include the correct unit in your answer.
    9·1 answer
  • Simplify to a single power of 4:4² x 4
    14·1 answer
  • Solve -4(3x – 7) = 40 for x.
    8·1 answer
  • Sofia is a helper for the kindergarten class and is in charge of picking a video for their end-of-year party. To choose which ty
    9·2 answers
  • Find the difference between (-11,-11) and (-12,-8) round answer to the nearest hundredth
    6·1 answer
  • Help ill give 5 stars if you get it correct
    14·2 answers
  • Solve pls brainliest
    11·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!