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
Pls help me answer this maths equation
Eva8 [605]

Jac fxddmcrrnfhthfjgjjfjffjfhfjthht tntnfntj4r

5 0
3 years ago
Read 2 more answers
What are the Answers to 1-10?
poizon [28]

Answer:

i can give u 2 10 and 7   acute, acute and straight

Step-by-step explanation:

4 0
3 years ago
Read 2 more answers
Use Cramers Rule to solve the system <br> 2x - 3y = 11<br> -6x + 8y = 34
Nastasia [14]

Step-by-step explanation:

given :

2x - 3y = 11

-6x + 8y = 34

find : the solutions of the system by using Cramers Rule.

solutions:

in the matrix 2x2 form =>

[ 2 -3] [x] [11]

=

[-6 8] [ y] [34]

D =

| 2 -3 |

|-6 8 |

= 8×2 - (-3) (-6)

= 16-18 = -2

Dx = | 11 -3 |

| 34 8 |

= 11×8 - (-3) (34)

= 88 + 102

= 190

Dy = | 2 11 |

|-6 34 |

= 2×34 - (-6) (11)

= 68 + 66

= 134

x = Dx/D = 190/-2 = -95

y = Dy/D = 134/-2 = -67

the solutions = {-95, -67}

8 0
3 years ago
Read 2 more answers
Please assist me with this problem: part 11​
Lady bird [3.3K]

Answer:

  a² = b² -w² +2wx

Step-by-step explanation:

The algebra is pretty straightforward. Expand the expression in parentheses and add x².

  b² -(w -x)² = e² = a² -x²

  b² -(w² -2wx +x²) = a² -x² . . . . . expand the square

  b² -w² +2wx -x² = a² -x² . . . . . . distribute the minus sign

  b² -w² +2wx = a² . . . . . . . . . . . . add x²

4 0
3 years ago
Given the function f defined by formula f(x)=2x+1 find the following f(4)
Nezavi [6.7K]
The correct answer you need will equal 9
6 0
3 years ago
Other questions:
  • Write the word sentence as an inequality and then solve the inequality: 4 less than a number is more than 15. PLEASE HELPP!!
    13·2 answers
  • What is the nth term of the geometric sequence that has a common ratio of 6 and 24 as it’s third term?
    11·1 answer
  • 5.1521, 5.4, 5.15, 5.015 least to greatest
    8·2 answers
  • 3. Solve the equation. -3 2/5 + b = 8 1/5
    11·2 answers
  • One circular table has a diameter of 9 ft, and another circular table has a diameter of 20 ft. How much greater is the area of t
    8·1 answer
  • A car advertisement states that a certain car can accelerate from rest to 70 km/h in 7 seconds. Find the cars average accelerati
    11·1 answer
  • Angle ACD is supplementary to angles ACE and BCD and congruent to angle BCE.
    13·2 answers
  • Choose Yes or No to tell if the number 102 will make each equation true.
    12·1 answer
  • Find the length of a segment in the coordinate plane with endpoints (-1 , 3) and (4 , -5).
    9·2 answers
  • 33. Construct a truth table to show that the following argument is valid.
    8·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!