The difference between 8 and n looks like,
8 - n
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:
259.6 ft/sec
Step-by-step explanation:
it is a universal standard that acceleration due to gravity is 32ft/sec^2.
Now it can be verified by equation,
V(f) = V(i)+at (1st equation of motion derived by Newton's three laws of motion)
where,
V(f) is final velocity
V(i) is initial velocity
a is acceleration which is constant and have value 32ft/sec^2
t is time which is given as 7.8 seconds
In the given case, initial velocity that is V(i) will be 0ft/sec. Because, on dropping, object will start to move under the influence of gravity from zero speed.
So,
V(f) = 0 +(32) (7.8)
V(f) = 249.6 ft/sec
Now the condition is given that you have to add a constant 10 to the answer.
so, V(f) = 249.6 + 10
V(f) = 259.6 ft/sec
17.5 because 140 divided by 35 is 17.5 and so is 70 divided by 35.
