Answer:
Presumably this is a multiple choice question, and without seeing the potential answers, we can't tell you which ones are correct.
A few things can however be said about this function:
1) It describes a parabola that extends upward infinitely. We can see this because it's in the classic format ax² + bx + c, and all terms are positive.
2) We can find the x-intercepts by solving for zero. In this case we can do that by factoring it:
x² + 9x + 18 = 0
x² + 3x + 6x + 18 = 0
x(x + 3) + 6(x + 3) = 0
(x + 6)(x + 3) = 0
So the x intercepts occur at (-6, 0) and (-3, 0)
3) we can find its vertex by taking its derivative and solving for zero:
f'(x) = 2x + 9
0 = 2x + 9
x = -4.5
We can then plug that coordinate into the original function to find the y coordinate:
f(x) = x² + 9x + 18
f(-4.5) = 20.25 - 40.5 + 18
= -2.25
So the vertex is at (-4.5, -2.25)
4) As mentioned, the derivative of f(x) is f'(x) = 2x + 9. The integral is:
x³ / 3 + 9x² / 2 + 18x + C
The volume of a cylinder is calculated from the product of its base area and the height. The base area is equal to the area of a circle which is expressed as A = πr^2 where r is one half the diameter and the radius of the circular base. So, the volume of a cylinder is equal to:
Volume of cylinder = π(r^2)h
r = D/2 = 3.5 in / 2 = 1.75 in
h = 12 in
Volume of cylinder = π((1.75 in)^2)( 12 in )
Volume of cylinder = 147π/4 in^3 or 115.45353 in^3
Therefore, the volume of the cylinder given its specifications would be equal to 115.45 cubic inches.
The answer is: " 19 " .
_____________________
Explanation:
To solve:
_____________________
Given:
" 4² + 6 ÷ 2 " ;
We solve using "PE MD AS" (mnemonic device for order of operations in order of consideration); which stands for:
"Please Excuse My Dear Aunt Sally (or Aunt Susan)" ;
Alternately: "BE MD AS"
" Be Excused My Dear Aunt Sally (or Aunt Susan)" .
"Parentheses {alternative version: "Brackets" ; in which "Parentheses can be considered "Brackets" ; yet in reality, Brackets would come before Parentheses}, then Exponents, then "Multiplication then Division (from left to right as they occur in the problem) , then "Addition then Subtraction (from left to right as they occur in the problem) .
_____________________
As such:
Given: " 4² + 6 ÷ 2 " , we have:
"exponents", "addition" and "division" ;
So we can rewrite the problem as:
" (4²) + (6 ÷ 2) =
(4 * 4) + (3) =
(16) + (3) = 19 .
_______________________
The answer is: " 19 " .
_____________________
11x + y = -28
Make sure to always remember that you can't have any fractions or decimals in standard form.
Standard form is basically
Ax + By = C