We have that
an=<span>10 * 5n---------------> an=50*n
then
for n=1
a1=50*1=50
</span>for n=2
a2=50*2=100
for n=3
a3=50*3=150
for n=4
a4=50*4=200<span>
the answer is
</span><span>the first four terms are [50,100,150,200]</span><span>
</span>
Looking at this problem in terms of geometry makes it easier than trying to think of it algebraically.
If you want the largest possible x+y, it's equivalent to finding a rectangle with width x and length y that has the largest perimeter.
If you want the smallest possible x+y, it's equivalent to finding the rectangle with the smallest perimeter.
However, the area x*y must be constant and = 100.
We know that a square has the smallest perimeter to area ratio. This means that the smallest perimeter rectangle with area 100 is a square with side length 10. For this square, x+y = 20.
We also know that the further the rectangle stretches, the larger its perimeter to area ratio becomes. This means that a rectangle with side lengths 100 and 1 with an area of 100 has the largest perimeter. For this rectangle, x+y = 101.
So, the difference between the max and min values of x+y = 101 - 20 = 81.
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Hello,
A: roots: -1,-3
a point (-2,1)
Vertex=((-2,1)
y=k*(x+1)(x+3) using roots
but k*(-2+1)(-2+3)=1==>k*(-1)*1=1==>k=-1
eq: y=-(x+1)(x+3)
==>y=-(x²+3x+x+3)
==>y=-x²-4x-3
y=k(x+2)²+1 if x=-1,y=0 ==>k*1+1=0==>k=-1
==>y=-(x+2)²+1
Answer :A--> R,K
B)
y=k(x+4)²-2 and k=-1/2
y=-1/2(x+4)²-2
y=-1/2x²-4x-10
answer B--> I,≈W if it is written -1/2*x² (square has been forgotten)
C:
y=2x²-16x+30
y=2(x-4)²-2
answer : C-->S,J
D:
y=-(x+3)(x+1)
y=-x²-4x-3
=-(x+2)²+1
answer D--> V,L
E:
Here there is a problem: or the graph is wrong, or 2 equations are missing!
y=1(x+1)(x-3) using roots
y=x²-2x-3 ≈ T si it were -2x and not +2x.
y=(x-1)²-4 ≈H is it were -1 in place of +1 [H:y=(x+1)²-4]
2x^3 + 9x - 8 - (4x^2 - 15x + 7)....distribute thru the parenthesis
2x^3 + 9x - 8 - 4x^2 + 15x - 7....combine like terms
2x^3 - 4x^2 + 24x - 15 <==
