Answer:
(1, 3)
Step-by-step explanation:
You are given the h coordinate of the vertex as 1, but in order to find the k coordinate, you have to complete the square on the parabola. The first few steps are as follows. Set the parabola equal to 0 so you can solve for the vertex. Separate the x terms from the constant by moving the constant to the other side of the equals sign. The coefficient HAS to be a +1 (ours is a -2 so we have to factor it out). Let's start there. The first 2 steps result in this polynomial:
. Now we factor out the -2:
. Now we complete the square. This process is to take half the linear term, square it, and add it to both sides. Our linear term is 2x. Half of 2 is 1, and 1 squared is 1. We add 1 into the set of parenthesis. But we actually added into the parenthesis is +1(-2). The -2 out front is a multiplier and we cannot ignore it. Adding in to both sides looks like this:
. Simplifying gives us this:
On the left we have created a perfect square binomial which reflects the h coordinate of the vertex. Stating this binomial and moving the -3 over by addition and setting the polynomial equal to y:
From this form,
you can determine the coordinates of the vertex to be (1, 3)
Answer:
3.4
Step-by-step explanation:
83.3 divided by 24.5= 3.4
The Golden Ratio is a mathematical relationship that exists
in art, shapes, nature and the human body. The golden ratio can be present in
your body, from the length of your arms and legs when compared to your torso.
Fingers is another example because the length of our fingers, each section from
the tip of the base to the wrist is larger than the preceding.
The measurement of the human navel to the floor and to the
top of the head to the navel is also the Golden ratio. Plastic surgeons and
dental surgeons use it to reconstruct the human face. It also appears in everything
around us like in the nature and science. It appears on in flower petals
because it is believed that each petal is placed to so that each petal gets the
best exposure to sunlight. Dolphins, starfish, sea urchins and honeybees also
exhibit the proportion like humans. DNA molecules measures 34 angstroms by 21
angstroms at each full cycle of the double helix spiral, these two number are
successive numbers. I think that the Golden Ratio is just a freak coincidence
that happened.
Answer:
1.23625 rounded would be 1.24
