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
Harrison plays a game in which he uses a net to catch balls that are randomly launched from holes in the ground. The height of o
aleksandr82 [10.1K]
3 sishsusbsusbsusnsjsnsn
7 0
3 years ago
What interest rate would produce an<br>interest amount of $450 if you invest $4800 for 5.5 years?​
V125BC [204]

Answer:

Im in 7th grade and I need some help on a math problem. can I post it?

3 0
3 years ago
An egg of a certain kind of insect called a Tachinidae is 0.00002 meters long. What is this length in scientific notation?
GaryK [48]
2.0x10^-5 or 2.0E-5 —this is because as a small decimal number, you move the decimal to the right five spaces and then add a negative to the decimal to indicate that when you translate back (from scientific notation to 0.00002) you will move the decimal to the left
6 0
3 years ago
Read 2 more answers
you pick a card at random without getting the first card back you pick a second card at random what is the probability of pickin
Keith_Richards [23]

We have to calculate the probability of picking a 4 and then a 5 without replacement.

We can express this as the product of the probabilities of two events:

• The probability of picking a 4

,

• The probability of picking a 5, given that a 4 has been retired from the deck.

We have one card in the deck out of fouor cards that is a "4".

Then, the probability of picking a "4" will be:

P(4)=\frac{1}{4}

The probability of picking a "5" will be now equal to one card (the number of 5's in the deck) divided by the number of remaining cards (3 cards):

P(5|4)=\frac{1}{3}

We then calculate the probabilities of this two events happening in sequence as:

\begin{gathered} P(4,5)=P(4)\cdot P(5|4) \\ P(4,5)=\frac{1}{4}\cdot\frac{1}{3}=\frac{1}{12} \end{gathered}

Answer: 1/12

8 0
1 year ago
Simplify. Assume that letters represent any real number.
TiliK225 [7]
\sqrt[5]{x^5}=x\\\\32^\frac{3}{5}=\left(32^\frac{1}{5}\right)^3=\left(\sqrt[5]{32}\right)^3=2^3=8
7 0
3 years ago
Read 2 more answers
Other questions:
  • An equation is given below.
    13·1 answer
  • Mrs. Lang asked these questions to her sixth-grade students. Which
    11·1 answer
  • Solve the following proble<br> 1. 3a + 1 = a +9
    13·1 answer
  • In 1929 Edwin Hubble investigated the claim that distance (explanatory) and radial velocity (response) of extragalactic nebulae
    12·1 answer
  • Wha do you see in this diagram
    10·1 answer
  • Can y’all help me with this it’s my last question?
    12·2 answers
  • (x^5 y)/(x^2 y^6) please help i dont understand this
    8·1 answer
  • Please help 15 points
    10·1 answer
  • Slope intercept form
    7·1 answer
  • Gas mileage is the number of miles you can drive on a gallon of gasoline. A test of a new car results in 510 miles on 20 gallons
    7·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!