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
vivado [14]
3 years ago
10

Between 0 degrees Celsius and 30 degrees Celsius, the volume V (in cubic centimeters) of 1 kg of water at a temperature T is giv

en approximately by the formula V=999.87−0.06426T+0.0085043T2−0.0000679T3 Find the temperature at which water has its maximum density. Temperature = degrees Celsius
Mathematics
1 answer:
Ira Lisetskai [31]3 years ago
3 0

Answer:

T = 3.967 C

Step-by-step explanation:

Density = mass / volume

Use the mass = 1kg and volume as the equation given V, we will come up with the following equation

D = 1 / 999.87−0.06426T+0.0085043T^2−0.0000679T^3

   = (999.87−0.06426T+0.0085043T^2−0.0000679T^3)^-1

Find the first derivative of D with respect to temperature T

dD/dT = \dfrac{70000000\left(291T^2-24298T+91800\right)}{\left(679T^3-85043T^2+642600T-9998700000\right)^2}

Let dD/dT = 0 to find the critical value we will get

\dfrac{70000000\left(291T^2-24298T+91800\right)}  = 0

Using formula of quadratic, we get the roots:

T =  79.53 and T = 3.967

Since the temperature is only between 0 and 30, pick T = 3.967

Find 2nd derivative to check whether the equation will have maximum value:

-\dfrac{140000000\left(395178T^4-65993368T^3+3286558821T^2+2886200857800T-121415215620000\right)}{\left(679T^3-85043T^2+642600T-9998700000\right)^3}

Substituting the value with T=3.967,

d2D/dT2 = -1.54 x 10^(-8)    a negative value. Hence It is a maximum value

Substitute T =3.967 into equation V, we get V = 0.001 i.e. the volume when the the density is the highest is at 0.001 m3 with density of

D = 1/0.001 = 1000 kg/m3

Therefore T = 3.967 C

You might be interested in
Find the missing lengths of the sides
SCORPION-xisa [38]
That's a 30-60-90 triangle, so the hypotenuse will always be 2x, the shorter leg will be x and the longer leg will be x√3. In this case, we are given the longer leg and we can deduce that x = 9. So, a = x = 9 and c = 2x = 18. Your answer is A, a = 9 yd, c = 18 yd.
8 0
3 years ago
Read 2 more answers
your employer has 600 business cards printed for you, and you give away 280 of them. To the nearest hundredth, what percent of t
arlik [135]
The number of cards left is 600-280=320.

So the 320 cards left are what percent? we count it like this:
\frac{320}{600}*100%= \frac{32}{60}*100%=\frac{32}{60}*100%=53.3..%

so the answer is 53.3%
4 0
3 years ago
Read 2 more answers
Anyone plz help I need it
son4ous [18]

Answer:

27.5 inches

Step-by-step explanation:

(68.1+11.2+x)/3=35.6

68.1+11.2+x=106.8

79.3+x=106.8

x=27.5

4 0
3 years ago
Karen has calls has 500 or 900 yards of thick soft wool, she has 200 feet at the strore they have 500 feet of wool. How many bal
Flauer [41]

Answer:

Yes.

Step-by-step explanation:

Because yes.

5 0
3 years ago
Pls help me! will give brainliest
Dimas [21]
Answer: (-1, 3)

Steps
X value to the left means add
X value to the right means subtract
Y value down means subtract
Y value up means add
3 0
3 years ago
Read 2 more answers
Other questions:
  • Please help me on this! Thank you!
    9·1 answer
  • What is the equation of the line that is parallel to the given
    15·1 answer
  • The number of home runs scored by a certain team in one baseball game is a random variable with the distribution x 0 1 2 P(x) 0.
    14·1 answer
  • Find the quotient of 4.13 × 10-8 and 0.04 × 10^5
    11·1 answer
  • Samantha’s rectangular gift is 10 inches. by 12 inches and is framed with a ribbon. She wants to use the same length of ribbon t
    11·2 answers
  • Identify the equivalent expression -4(b+2) - 3b
    13·1 answer
  • 23 clothespins are placed on a clothesline at 2-foot intervals. How far is it from the first clothespin to the last one
    8·1 answer
  • Triangle ABC has the following measurements.<br><br> m <br> write an equation and solve for x
    12·1 answer
  • Determine if parallel, perpendicular, or neither.<br><br> 3y+x=12 <br> -y=8x+1
    11·1 answer
  • T and F - question with a screenshot
    10·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!