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
kipiarov [429]
3 years ago
9

The table shows the viscosity of an oil as a function of temperature. Identify a quadratic model for the viscosity, given the te

mperature. Then use the model to predict the viscosity of the oil at a temperature of 140°C.

Mathematics
1 answer:
777dan777 [17]3 years ago
8 0

Answer:

The viscosity at 140°C is predicted to be 7.2

Step-by-step explanation:

The function that model the relationship between viscosity and temperature = Quadratic model

The general form of a quadratic equation is y = a·x² + b·x + c

Therefore, we have;

When y = 10.8, x = 110, which gives;

10.8 = a·110² + b·110 + c = 12100·a + 110·b + c

10.8 = 12100·a + 110·b + c

When y =8.2, x = 130

8.2 = a· 130² + b· 130 + c = 16900·a + 130·b + c

8.2 = 16900·a + 130·b + c

When y = 160, x = 5.8

5.8 = a·160² + b·160 + c = 25600·a + 160·b + c

5.8 = 25600·a + 160·b + c

The three equations above can be listed as follows;

10.8 = 12100·a + 110·b + c

8.2 = 16900·a + 130·b + c

5.8 = 25600·a + 160·b + c

Solving using matrices gives;

\begin{bmatrix}12100 & 110 & 1\\ 16900 & 130 & 1\\ 25600 & 160 & 1\end{bmatrix} \begin{bmatrix}a\\ b\\ c\end{bmatrix} = \begin{bmatrix}10.8\\ 8.2\\ 5.8\end{bmatrix}

\begin{bmatrix}a\\ b\\ c\end{bmatrix} = -\dfrac{1}{3000}\begin{bmatrix}3 & -5 & 2\\ -867 & 1350 & -480\\ 62400 & -88000 & 28600\end{vmatrix} \begin{bmatrix}10.8\\ 8.2\\ 5.8\end{bmatrix}

From which we have;

a = 0.001, b = -0.37, c = 39.4

Substituting gives;

y = 0.001·x² - 0.37·x + 39.4

When x = 140

y = 0.962·140² - 0.37·140 + 39.4= 7.2

The viscosity at 140°C = 7.2.

You might be interested in
Factor −1/2−1/2 out of −1/2x+6.
pochemuha
That's unusual:  repetition:  -1/2 - 1/2.

Did you perhaps mean "Factor -1/2 out of (-1/2)x + 6?

Let's do that.  Let's rewrite 6 as (-1/2)(-12).

Then (-1/2)x + 6       (-1/2)x -(1/2)(-12)
         --------------  =  ------------------------  = x - 1/2
             -1/2                     -1/2

Hope that's what you wanted.  If not, please try to apply a similar approach to solving this particular problem.

3 0
3 years ago
Select the correct answer.<br> Which function is the inverse of ?
Artyom0805 [142]

<u>Answer:</u>

B.    f^{-1}(x) = \frac{x + 3}{9}

<u>Step-by-step explanation:</u>

let \space\ y = f(x)\\\\y = 9x -3\\

• Now make x the subject of the equation:

9x = y + 3\\\\x = \frac{y + 3}{9} \\

• Replace x with f⁻¹(x) and y with x:

f^{-1}(x) = \frac{x + 3}{9}

6 0
1 year ago
Read 2 more answers
What is the value of x?
Helga [31]

2x+20=3x-30

x=50

2x+20=3x-30

x=50

2x+20=3x-30

x=50

2x+20=3x-30

x=50

7 0
3 years ago
Evaluate [(21 + 6) − 3^2] ÷ 9 ⋅ 2.
Vlada [557]
 [(21 + 6) − 3^2] ÷ 9 ⋅ 2=[(27) − 9] ÷ 9 ⋅ 2
=18 ÷ 9 ⋅ 2
= 2 . 2
= 4
6 0
3 years ago
Read 2 more answers
40 + x + 25= 180
sveta [45]

\qquad\qquad\huge\underline{{\sf Answer}}♨

Let's solve ~

\qquad \sf  \dashrightarrow \:40 + x + 25 = 180

\qquad \sf  \dashrightarrow \:x + 65 = 180

\qquad \sf  \dashrightarrow \:x = 180 - 65

\qquad \sf  \dashrightarrow \:x = 115

I hope you understood the procedure, please let me know if you have any doubts

6 0
2 years ago
Other questions:
  • What is 2x -5/3 = 3.
    11·1 answer
  • The expected rainfall, in inches, for a city for the month of July is given by the inequality |x − 4.25| ≤ 0.15. Find the city’s
    13·2 answers
  • Please help ASAP! Will give BRAINLIEST! Please read the question THEN answer correctly! No guessing.
    6·2 answers
  • Draw the standard normal distribution curve
    6·1 answer
  • What is the value of y in this triangle?
    15·2 answers
  • Answer and question is in the pictures.
    11·1 answer
  • NEED HELP ASAP!
    14·1 answer
  • Quadrilateral OPQR is inscribed in circle N, as shown below. Which of the following
    15·1 answer
  • ¿Cuál es el mínimo común múltiplo de 36, 48 y 72?
    8·1 answer
  • 8h 39min<br> + 3h 25min<br> ------------------<br> h min
    10·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!