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
ad-work [718]
3 years ago
9

A small metal bar, whose initial temperature was 10° C, is dropped into a large container of boiling water. How long will it tak

e the bar to reach 70° C if it is known that its temperature increases 2° during the first second? (The boiling temperature for water is 100° C. Round your answer to one decimal place.) sec How long will it take the bar to reach 98° C? (Round your answer to one decimal place.)
Mathematics
1 answer:
IgorC [24]3 years ago
5 0

Answer

According to newton law of cooling

\dfrac{d T}{dt} = k (T - T_a)

and

T = Ce^{kt} + T_a

now At Ta = 100

T₀ = 10 °C

T₁ = 12° C

T(0) = Ce^{0} + T_a

10 = C + 100

C = -90

now,

12 = -90e^k + 100

e^k = \dfrac{88}{90}

k = ln{\dfrac{88}{90}}

at time equal to t

T(t) = 70

T(t) = -90 (\dfrac{88}{90})^t + 100

70 = -90(\dfrac{88}{90})^t + 100

(\dfrac{88}{90})^t = \dfrac{1}{3}

t\times ln(\dfrac{88}{90}) = ln(\dfrac{1}{3})

t = 48.88 s

hence, after 48.88 s the temperature of the body will be 70°C

b) time taken to reach 98°C

T(t) = -90 (\dfrac{88}{90})^t + 100

98 = -90(\dfrac{88}{90})^t + 100

(\dfrac{88}{90})^t = \dfrac{1}{45}

t\times ln(\dfrac{88}{90}) = ln(\dfrac{1}{45})

t = 390 s

hence, after 390 s the temperature of the body will be 98°C

You might be interested in
The graph of r = 1/ 1-5 sin theta is symmetric about the
Gnoma [55]

Answer:

A. y-axis only

Step-by-step explanation:

We have the graph of  as given below.

It can be seen that  passes through the points (0,0), (4,0) and (6,0).

Also, the graph is plotted in the 1st and 2nd quadrant symmetrically along the y-axis.

Hence, the axis of symmetry of  is the y-axis only.

7 0
3 years ago
Read 2 more answers
Triple a number, x, increased by 1 is between -20 and 10. What are the solutions for x?
Bumek [7]
Hello,
-20 \leq 3x+1 \leq 10\\
\Rightarrow\ -21 \leq 3x \leq 9\\
\Rightarrow\ -7 \leq x \leq 3\\

Sol=[-7\ 3]\ if\ x\ is\ a\ real.


3 0
3 years ago
Who drove the fastest? Select the correct answer. A Hector drove 205 miles in 5 hours. B Harlin drove 357 miles in 6 hours. C Ke
nikklg [1K]

Answer:

soooo it D

Step-by-step explanation:

you have to divide

A. h 205 divide by 5 =41 m

B. h 357 divide by 6= 59.5

C. k 419 divide by 7 = 59.8..............

D. s 508 divide by 8= 63.5

8 0
3 years ago
4) A window is in the form of a rectangle surmounted by a semicircle. The rectangle is of clear glass, whereas the semicircle is
lisov135 [29]

Answer:

l=0.1401P\\

w =0.2801P

where P = perimeter

Step-by-step explanation:

Given that a window is in the form of a rectangle surmounted by a semicircle.

Perimeter of window =2l+\pid/2+w

P= 2l+3.14 (w/2)+w

Or P = 2l+2.57w\\l = \frac{P-2.57w}{2}

To allow maximum light we must have maximum area

Area = area of rectangle + area of semi circle where rectangle width = diameter of semi circle

A=lw +\pi \frac{w^2}{8}

A=lw +\pi \frac{w^2}{8}\\A=w*\frac{P-2.57w}{2}+0.3925w^2\\2A= Pw-2.57w^2+(0.785w^2)\\2A' = P-5.14w+1.57 w\\2A" =-5.14+1.57

Hence we get maximum area when i derivative is 0

i.e. P-5.14w+1.57 w=0\\3.57w =P\\w = \frac{P}{3.57} =0.2801P

l = \frac{P-2.57w}{2}\\l = 0.1401P

Dimensions can be

l=0.1401P\\w =0.2801P

5 0
3 years ago
Rite an algebraic expression to represent "five plus the quotient of r and 14."
hichkok12 [17]
The answer is 3) 5+r/14

Let's go segment by segment:
<span>"five plus" means addition, so we have 5 +

</span><span>"the quotient of r and 14" is the division result, so sign / must be present: 14/r
</span>
Therefore "five plus the quotient of r and 14" is 5 + 14/r
4 0
3 years ago
Other questions:
  • Slope= 1/5, y-intercept=1
    6·1 answer
  • 3x+3y=12 how do I solve this for slope intercept form
    6·1 answer
  • Find m∠USW if m∠USW = 7x - 34 and m∠TSR = 4x + 9.
    7·1 answer
  • Determine the growth factor corresponding to 1% increase
    7·2 answers
  • This isosceles triangle has two sides of equal length, that are longer than the length of the base, b. The perimeter of the tria
    10·1 answer
  • image that you're doing an experiment to determine h9w the running speed of a hamster depends on the weight of the hamster. when
    9·1 answer
  • 55percent of her mony was spent for food. Express 55 percent as a decimal.
    9·2 answers
  • 1. What are the 3 different types of blood cells and what does each type of blood cell do?
    11·1 answer
  • Greg bought 18 4/5 gallons of gas. What decimal should the meter on the gas pump read?
    10·1 answer
  • someone pls help me :Jada and her sister went to the store together. After the store, Jada walked 9 blocks west to get a coffee
    9·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!