Simplify: 18 - ⎷81 + 9 · 3⁴ - (3 - 2 + 9) ÷ 2
1 answer:
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Answer:
Peculiar purples would be more abundant
Step-by-step explanation:
Given that eculiar Purples and Outrageous Oranges are two different and unusual types of bacteria. Both types multiply through a mechanism in which each single bacterial cell splits into four. Time taken for one split is 12 m for I one and 10 minutes for 2nd
The function representing would be
i) for I bacteria where t is no of minutes from start.
ii) for II bacteria where t is no of minutes from start. P0 is the initial count of bacteria.
a) Here P0 =3, time t = 60 minutes.
i) I bacteria P =
ii) II bacteria P =
b) Since II is multiplying more we find that I type will be more abundant.
The difference in two hours would be
c) i) for I bacteria where t is no of minutes from start.
ii) for II bacteria where t is no of minutes from start. P0 is the initial count of bacteria.
d) At time 36 minutes we have t = 36
Peculiar purples would be
The rate may not be constant for a longer time. Hence this may not be accurate.
e) when splits into 2, we get
where P0 is initial and t = interval of time
Answer:
30
Step-by-step explanation:
To find the determinant of a 3x3 matrix, you can use this method. (See picture.)
Start with the first number in the top row, and block off the row and column. A 2x2 matrix will be left. Find the determinant of this 2x2 matrix, and multiply it by the number in the top row.
Repeat for the other two numbers in the top row. Add the first result, subtract the second, and add the third.
det A = -2 [(3)(-5) − (a)(0)] − 2 [(0)(-5) − (a)(0)] + b [(0)(0) − (3)(0)]
det A = -2 (3)(-5) − 0 + 0
det A = 30
<h3>Answer: (a - 1)(2a² + a + 2)</h3>
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Explanation:
Use the rational root theorem to determine this list of possible rational roots: 1, -1, 1/2, -1/2
Plug each possible root one at a time into the original expression given. If the simplified result is 0, then that possible root is an actual root.
If we tried say a = -1, then,
2a³-a²+a-2 = 2(-1)³-(-1)²+(-1)-2 = -6
The result is not zero, so a = -1 is not an actual root.
But if we tried say a = 1, then,
2a³-a²+a-2 = 2(1)³-1²+1-2 = 0
We get 0 so a = 1 is an actual root. I'll let you try the other values, but you should find that a = 1 is the only rational root.
Since a = 1 is a root, this makes (a-1) to be a factor.
From here, use either synthetic or polynomial long division to determine the other factor. Refer to the diagram below for each method.
Regardless of which method you pick, the quotient is 2a² + a + 2 which is the other factor needed. The remainder of 0 tells us we have (a-1) as a factor. For more information, check out the remainder theorem.