Answer:
A.) gf(x) = 3x^2 + 12x + 9
B.) g'(x) = 2
Step-by-step explanation:
A.) The two given functions are:
f(x) = (x + 2)^2 and g(x) = 3(x - 1)
Open the bracket of the two functions
f(x) = (x + 2)^2
f(x) = x^2 + 2x + 2x + 4
f(x) = x^2 + 4x + 4
and
g(x) = 3(x - 1)
g(x) = 3x - 3
To find gf(x), substitute f(x) for x in g(x)
gf(x) = 3( x^2 + 4x + 4 ) - 3
gf(x) = 3x^2 + 12x + 12 - 3
gf(x) = 3x^2 + 12x + 9
Where
a = 3, b = 12, c = 9
B.) To find g '(12), you must first find the inverse function of g(x) that is g'(x)
To find g'(x), let g(x) be equal to y. Then, interchange y and x for each other and make y the subject of formula
Y = 3x + 3
X = 3y + 3
Make y the subject of formula
3y = x - 3
Y = x/3 - 3/3
Y = x/3 - 1
Therefore, g'(x) = x/3 - 1
For g'(12), substitute 12 for x in g' (x)
g'(x) = 12/4 - 1
g'(x) = 3 - 1
g'(x) = 2.
Using 3.14 for PI.
The radius of a ball and the can is half the diameter = 1.25
The height of the can is the height of 3 diameters = 7.5
Volume of one tennis ball:
4/3 x PI x 1.25^3 = 8.18 cubic inches.
Volume of 3 tennis balls: 3 x 8.18 = 24.54 cubic inches.
Volume of can:
PI x 1.25^2 x 7.5 = 36.80 cubic inches.
Space = 36.80 - 24.54 = 12.26 cubic inches.
Answer:
<h3>
B. perimeter</h3>
Step-by-step explanation:
I think this would make the most sense.
Answer:
9 miles
Step-by-step explanation:
You need to get 27 minutes to 81 minutes so you multiply 27 by 3, and that is 81, so you simply multiply 3 by 3 and get 9! Hope this helps! ;)
(27 x 3) = 81
(3 x3) = 9