Answer:
Step-by-step explanation:
The best way to do this is to first remove the parenthesis by distributing the negative into them. Then we will group the like terms together, moving their respective signs with them, then we will simplify. For the first one, after distributing the negative into the parenthesis (remember that a negative in front of a set of parenthesis containing a polynomial changes the signs in front of each term within the polynomial; negatives become positives and positives become negatives):
and then grouping like terms next to each other:
(this step is not completely necessary; I just encourage new learners to do it so as to not miss any of the like terms)
The above then simplifies to
The next one, after distributing the negative into the parenthesis:
and then grouping like terms next to each other (remember to move their signs with them!):
which simplifies to
Now for the last one:
and
which simplifies to
Answer:
Totalitarianism goes to C, Fascism goes to B, Communism goes to D, and Constitutional Monarchy goes to A
Step-by-step explanation:
Thats the way it works
A.) To find the maximum height, we can take the derivative of h(t). This will give us the rate at which the horse jumps (velocity) at time t.
h'(t) = -32t + 16
When the horse reaches its maximum height, its position on h(t) will be at the top of the parabola. The slope at this point will be zero because the line tangent to the peak of a parabola is a horizontal line. By setting h'(t) equal to 0, we can find the critical numbers which will be the maximum and minimum t values.
-32t + 16 = 0
-32t = -16
t = 0.5 seconds
b.) To find out if the horse can clear a fence that is 3.5 feet tall, we can plug 0.5 in for t in h(t) and solve for the maximum height.
h(0.5) = -16(0.5)^2 + 16(-0.5) = 4 feet
If 4 is the maximum height the horse can jump, then yes, it can clear a 3.5 foot tall fence.
c.) We know that the horse is in the air whenever h(t) is greater than 0.
-16t^2 + 16t = 0
-16t(t-1)=0
t = 0 and 1
So if the horse is on the ground at t = 0 and t = 1, then we know it was in the air for 1 second.
Quintet is what a stanza containing five lines is called.
