Answer:
Lateral areas have ratio of 4:1
Volumes have ratio of 8:1
Step-by-step explanation:
There is a rule in 3D geometry that when two solids are similar, and their edges are in the ratio of
, the ratio of any surface area type measure is always
this includes the lateral area, which is just a surface area minus the base, which is not important for this problem. The ratio of volumes of those similar solids is in the ratio of
.
Now, to solve this, we need to find the ratio of any corresponding length of these similar pyramids. We have both the heights, so if we form a ratio of
which if you simplify it, it is
, which is
. The ratio of the heights are
.
Now we can apply those rules to this ratio, the ratio of lateral areas would then be
, which is
. the ratio of volumes would be
, which is 
It says The temperature doubled
It means the temperature has been doubled ,
if earlier it was t , then now its 2t
Now in the question it says the the temperature doubled
And now the temperature is 32 degrees ,
so we double it to get the new temperature
and the double of 32 degrees is 64 degrees
So
The value of the expression when t = 32 degrees is 64 degrees
<h3>
Answer: 40 novels</h3>
================================================
Work Shown:
n = number of novels
(32 ebooks)/(n novels) = 4/5
32/n = 4/5
32*5 = n*4 ............ cross multiply
160 = 4n
4n = 160
n = 160/4 .............. dividing both sides by 4
n = 40
There are 40 novels.
Answer:
Step-by-step explanation:
The domain of all polynomials is all real numbers. To find the range, let's solve that quadratic for its vertex. We will do this by completing the square. To begin, set the quadratic equal to 0 and then move the -10 over by addition. The first rule is that the leading coefficient has to be a 1; ours is a 2 so we factor it out. That gives us:

The second rule is to take half the linear term, square it, and add it to both sides. Our linear term is 2 (from the -2x). Half of 2 is 1, and 1 squared is 1. So we add 1 into the parenthesis on the left. BUT we cannot ignore the 2 sitting out front of the parenthesis. It is a multiplier. That means that we didn't just add in a 1, we added in a 2 * 1 = 2. So we add 2 to the right as well, giving us now:

The reason we complete the square (other than as a means of factoring) is to get a quadratic into vertex form. Completing the square gives us a perfect square binomial on the left.
and on the right we will just add 10 and 2:

Now we move the 12 back over by subtracting and set the quadratic back to equal y:

From this vertex form we can see that the vertex of the parabola sits at (1,-12). This tells us that the absolute lowest point of the parabola (since it is positive it opens upwards) is -12. Therefore, the range is R={y|y ≥ -12}