The y-coordinate of the point that divides the directed line segment from J to K into a ratio of 5:1 is 0.
<h3>How to carry out division of line segments?</h3>
From the attached line segment graph, we see the coordinates as;
J (1, -10) and K (7, 2)
Let us assume that, point L divides the directed line segment from J to K into a ratio of 5:1.
From the properties of coordinate geometry we know that, the coordinates of point that divides the line joining (x₁, y₁), (x₂, y₂) in m:n, are;
[(mx₂ + nx₁)/(m + n)], [(my₂ + ny₁)/(m + n)]
Plugging in the relevant values gives;
[(5 * 7 + 1 * 1)/(5 + 1)], [(5 * 2 + 1 * -10)/(5 + 1)]
⇒ (6, 0)
Therefore, the y-coordinate of the point that divides the directed line segment from J to K into a ratio of 5:1 is 0.
Read more about division of line segments at; brainly.com/question/17374569
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The given radius is = 60 feet
The volume of the sphere is given by =
So we will find the volume of the sphere using radius as 60 and pi as 3.14
Volume = = 902059.20 cubic feet
As quarter of anything is defined as its one-fourth part, so here the volume of the quarter of sphere can be calculated by finding one fourth of the calculated volume.
So volume of quarter sphere =
= 225514.80 cubic feet
And rounding this to nearest whole number we get 225515 cubic feet as the answer.
Answer:
a) 1/2
b) 250
Step-by-step explanation:
The start of the question doesn't matter entirely, although is interesting to read. What we are trying to do is find the value for such that
is maximized. Once we have that
, we can easily find the answer to part b.
Finding the value that maximizes is the same as finding the value that maximizes
, just on a smaller scale. So, we really want to maximize
. To do this, we will do a trick called completing the square.
.
Because there is a negative sign in front of the big squared term, combined with the fact that a square is always positive, means we need to find the value of such that the inner part of the square term is equal to
.
.
So, the answer to part a is .
We can then plug into the equation for p to find the answer to part b.
.
So, the answer to part b is .
And we're done!