What is the volume of a cube with a cross section parallel to its base that has an area of 144 square inches?
1 answer:
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Answer: The determinant of the coefficient matrix is -15 and x = 3, y = 4, z = 1.
Step-by-step explanation: The given system of linear equations is :
We are given to find the determinant of the coefficient matrix and to find the values of x, y and z.
The determinant of the co-efficient matrix is given by
Now, from equations (ii) and (iii), we have
Substituting the value of y and z from equations (iv) and (v) in equation (i), we get
From equations (iv) and (v), we get
Thus, the determinant of the coefficient matrix is -15 and x = 3, y = 4, z = 1.
The given function is a quadratic equation. Any quadratic equation can be written in the form :
The given points can be taken as (2,23) ,(4,55) and(10,247)
We form three equations with the given points
For point (2,23 ) the equation is
23 = 4a + 2b + c
For point (4,55) the equation is
55 = 16a + 4b + c
For point (10,247) the equation is:
247 = 100a+10b+c.
Solving the three equations for a,b,c we have :
32 = 12a + 2b
16 = 6a + b
and,
192 = 84 a + 6b
32 = 14a + b
Solving for a,b,c we have:
a=2 b=4 c=7
The quadratic equation is c(x)=
When x=8
c(x)=]
Option C. $167 is the right answer.