Which is the better deal 10 pens for 8.99 or 25 pens for 19.75
1 answer:
You might be interested in
Answer:
The three positions are not on the same line.
Step-by-step explanation:
We have three points: A:(3,2,0), B:(1,-1,2) and C:(5,5,2).
Let's build a vector that goes from one point to another; that vector will be the director of a line (if we draw a vector that goes from A to B, that vector will be the direction of the line that pass by A and B because it does not change). In order to build that vector, let's subtract B from A:
The equation of a line is:
Where p is every singular point of the line, is a particular point of the line (any that we are sure that it is on the line), r is the director vector and t is the independent variable.
Now we have the director vector: (2,3,-2), and we can verify that A and B are on the line:
Because there is a value for t that satisfies both A and B: If we do and t=0, we are going to obtain the point p=A; and if we do t=-1, we are going to obtain p=B. Let's see that:
If C is also in the same line, C must accomplish the equation: , so:
Let's simplify the equation writing the parametric equation, which is just to write the equation for each dimension:
You can verify that there is not a value of t that satisfies all three equations, so, the point C is not on the same line as A and B; which means that A, B and C are not on the same line.
So even postive integers are by defention in form 2k where k is a natural number so
let the sum of even integers to n=S
S=2(1+2+3+4+5+6+7+8+......+k-1+k
divide bith sides of equation 1 by 2
0.5S=1+2+3+4+5+...........+k-1+k
S=2(k+(k-1)+..............................+2+1)
divide both sides of equation 2 by 2
0.5S=k+k-1+..............................+2+1)
by adding both we will get
___________________________
S=(k+1)(k)
so the sum will be equal to
S=
so let us test the equation
for the first 3 even number there sums will be
2+4+6=12
by our equation 3^2+3=12
gave us the same answer so our equation is correct
let the sum of even integers to n=S
S=2(1+2+3+4+5+6+7+8+......+k-1+k
divide bith sides of equation 1 by 2
0.5S=1+2+3+4+5+...........+k-1+k
S=2(k+(k-1)+..............................+2+1)
divide both sides of equation 2 by 2
0.5S=k+k-1+..............................+2+1)
by adding both we will get
___________________________
S=(k+1)(k)
so the sum will be equal to
S=
so let us test the equation
for the first 3 even number there sums will be
2+4+6=12
by our equation 3^2+3=12
gave us the same answer so our equation is correct
Answer:
D. It will increase by 1%.
Step-by-step explanation:
Given
--- initial rate
--- final rate
Required
The effect on the GDP
To calculate this, we make use of:
This gives:
<em>This implies that the GDP will increase by 1%</em>