Answer:
You could just replace all the given possible values of k in the inequality and see which ones are solutions, but let's solve this in a more interesting way:
First, remember how the absolute value works:
IxI = x if x ≥ 0
IxI = -x if x ≤ 0
Then if we have something like:
IxI < B
We can rewrite this as
-B < x < B
Now let's answer the question, here we have the inequality:
I-k -2I < 18
Then we can rewrite this as:
-18 < (-k - 2) < 18
Now let's isolate k:
first, we can add 2 in the 3 parts of the inequality:
-18 + 2 < -k - 2 + 2 < 18 + 2
-16 < -k < 20
Now we can multiply all sides by -1, remember that this also changes the direction of the signs, then:
-1*-16 > -1*-k > -1*20
16 > k > -20
Then k can be any value between these two limits.
So the correct options (from the given ones) are:
k = -16
k = -8
k = 0
Step-by-step explanation:
the distance of a vertex on the 2 outgoing sides to the touching points with the inscribed circle is the same for both sides.
and that applies to all 3 vertexes.
so, we know for the top left vertex the distance to both touching points is 4.
that means the distance to the touching points from the bottom left vertex is 7-4 = 3.
and that means that the distance to the touching points from the bottom right vertex is 16-3 = 13.
so, x = 13
it is the distance to one of the touching points for the bottom right vertex.
and the perimeter of the triangle is therefore
7 + 16 + (13 + 4) = 40
Answer:
A minimum of 16 rows are needed
Step-by-step explanation:
Here, we want to calculate the number of rows minimum that could seat 382 people in rows of 24 seats.
Mathematically, what we need to do here is to make a division.
We shall divide the number of people by the number of seats in a row so that we can get the number of rows needed.
Mathematically, that would be; 382/24 = 15 22/24
We are looking at a minimum number.
So we can see that 15 rows will be filled, with an extra 22 seats in the next row leaving only 2 seats in the next row unoccupied.
So we can see that the minimum number of rows required is 16 rows
Answer:
Given that:
and 
if a , a+ commutator, it obeys 
First find:
= 
Now;
=
therefore, which implies the operators a and a+ are commutators.
A sinusoid is cyclical and has a period or frequency.
y = sin x is a sinusoid, with a period of 2π.
y = √x is not a sinusoid.
y = cos x is a sinusoid with a period of 2π.
Answer: y = √x is not a sinusoid.
