Option C: is the value of a and b
Explanation:
Given that the expression
We need to determine the value of a and b
Let us consider the term and take the prime factorization of the term 648
Thus, we have,
648 divides by 2,
324 divides by 2,
162 divides by 2,
81 divides by 3,
27 divides by 3,
9 divides by 3,
Thus, we have,
Therefore, equating the powers of 2 and 3, we get,
Hence, the value of a and b is 3 and 4
Thus, Option C is the correct answer.
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.
