Answer:
y= -⅓x +⅓
Step-by-step explanation:
The equation of a line is usually written in the form of y=mx+c, where m is the gradient and c is the y-intercept.
This form is also known as the point-slope form.
Since the slope is given to be -⅓, m= -⅓.
y= -⅓x +c
To find the value of c, substitute a pair of coordinates into the equation.
When x= -5, y=2,
2= -⅓(-5) +c
Thus, the equation of the line is y= -⅓x +⅓.
Answer:
The width of the computer compartment is 9 inches
The length of the computer compartment is 33 inches
The height of the computer compartment is 27 inches
Step-by-step explanation:
The given data on the rectangular prism compartment are;
The volume of the rectangular prism, V = 8019 cubic inches
The length of the compartment, l = 24 inches + The width, w
The height of the compartment, h = 18 inches + The width, w
Therefore, we have;
l = 24 + w
h = 18 + w
V = l × h × w
∴ V = (24 + w) × (18 + w) × w = w³ + 42·w² + 432·w = 8019
w³ + 42·w² + 432·w - 8019 = 0
By graphing the above function with MS Excel, we have one of the solution is w = 9
∴ (w - 9) is a factor of w³ + 42·w² + 432·w - 8019 = 0
Dividing, we get;
w² + 51·w + 891
w³ + 42·w² + 432·w - 8019 = 0
w³ - 9·w²
51·w² - 459·w
891·w
891·w + 8019
0
Therefore,
w³ + 42·w² + 432·w - 8019 = 0
w³ + 42·w² + 432·w - 8019 = (x - 9)·(w² + 51·w + 891) = 0
The determinant of the factor, w² + 51·w + 891 = 51² - 4×1×891 = -963, therefore, the it has complex roots
Therefore, the real solution of (x - 9)·(w² + 51·w + 891) = 0 is w = 9
The width of the computer compartment, w = 9 inches
The length of the computer compartment, l = 24 inches + 9 inches = 33 inches
The height of the computer compartment, h = 18 inches + 9 inches = 27 inches.
