Answer:
94.2 cubic mm
Step-by-step explanation:
The volume for a cylinder is
We can use 3.1415 for pi,
r = 5
h = 1.2
Filling in then:
and
so
Just multiply all those numbers together.
Rate of appreciation is based on an exponential function, i.e.
if r=rate of appreciation, after n years, the new value is
F=P(1+r)^n.
P=present worth
F=future worth.
Here,
P=126000
F=156000
n=8
so
156000=126000(1+r)^8
=>
(1+r)^8=(156000/126000)=26/21
=>
(1+r)=(26/21)^(1/8)=1.02706 (approx.)
=>
r=1.02706-1=0.02706, or
rate of appreciation is approximately 2.7%
Step-by-step explanation:
we have two lines you have to draw.
one is all in the bottom left quadrant (for x<=0) and one in the upper right quadrant (for x>5).
the easiest is for x>5. the line function is only
f(x) = y = 3
so, this is a horizontal line on the grid line for y = 3. it starts above x=5 and then goes all the way to the right ("to infinity and beyond !"). just, if possible, mark the starting point at x=5 as a little empty "circle" instead of a full dot, as x=5 is explicitly excluded (due to x>5).
and for x<=0 the line
f(x) = y = 4x - 3
goes sharp down but goes a little bit to the left the further down it goes. it starts with x=0, which gives y=-3 per the function.
so, the starting point (with a full dot, as x=0 is included) is (0,-3).
from there it goes sharp down and a little bit to the left.
for example the next point is for x=-1, which gives y=-7, so it is the point (-1,-7). x=-2 gives y=-11 and the point (-2,-11).
the line has to go through so these points and further down (again, "to infinity and beyond !"), as to move further left on the negative x-axis.
ANSWER
The equation of the new parabola is
EXPLANATION
The given parabola has equation:
If this parabola is reflected in the x-axis, its equation becomes :
When this parabola is scaled vertically by a factor of 5, the equation becomes,