Answer:
Step-by-step explanation:
We are required to represent the expression given in the standard form to the quadratic form
Given
let us square the given expression
f(x)=(x+3)(x+3)
open brackets
sum the similar terms
Volume = are base*height
32 = x^2*h --> h = 32/x^2
surface area = 4x(32/x^2) + x^2
SA = 128/x + x^2
SA' = -128/x^2 + 2x = 0
2x = 128/x^2
2x^3 = 128
x^3 = 64
x = 4
surface area minimized when length of base is 4 in.
hope this help
Make note of the coefficients in the first and fourth equations. They've been conveniently picked so that subtracting one equation from the other eliminates every variable but <em>t</em>. We have
(3<em>r</em> + 2<em>s</em> + <em>t</em> + 2<em>u</em> + 3<em>v</em>) - (3<em>r</em> + 2<em>s</em> + 3<em>t</em> + 2<em>u</em> + 3<em>v</em>) = 7 - 17
-2<em>t</em> = -10
<em>t</em> = 5
Answer: it depends on how big each bowl could be. depending on how big the diameter of the bowl is, we can figure out what the radius is, and then we could multiply that by pi squared, which gets you the area of the circle. Then we could figure out how much larger the large bowl is than the smaller bowl with the diameter knowledge that we gained.
So, for example, there was a bowl like this: (|||) (imagine that is a full circle) and that would be... about 9 in. across. imagine the smaller bowl is about 3in. across. then, we could figure out the radius by finding the middle, and expand the middle to the edge of the bowl. then, whatever the radius is, we could multiply that by 8, and get the total diameter of the bowl in inches. with that knowledge, we should be able to know the area of the bowl, by getting the diameter, and multiplying it by pi squared which equals 9.42, and then you multiply that by the radius and the diameter to get the area of the bowl.
that is how you could figure out how much bigger the large bowl is than the smaller bowl.
<h3>
You need to add 4 to both sides</h3>
The x term has a coefficient of 4. Take half of this to get 2, then square it to get 4. This is the value we add to both sides to get x^2+4x+4 = 5. Note how x^2+4x+4 factors into (x+2)^2
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Another example: Let's say we started with x^2+6x = 1. To complete the square, we need to add 9 to both sides. I start with 6 (the x coefficient) and cut that in half to get 3, then I squared that to get 9. So we add 9 to both sides getting x^2+6x+9 = 10 which becomes (x+3)^2 = 10
