The point G on AB such that the ratio of AG to GB is 3:2 is; G(4.2, 2)
How to partition a Line segment?
The formula to partition a line segment in the ratio a:b is;
(x, y) = [(bx1 + ax2)/(a + b)], [(by1 + ay2)/(a + b)]
We want to find point G on AB such that the ratio of AG to GB is 3:2.
From the graph, the coordinates of the points A and B are;
A(3, 5) and B(5, 0)
Thus, coordinates of point G that divides the line AB in the ratio of 3:2 is;
G(x, y) = [(2 * 3 + 3 * 5)/(2 + 3)], [(2 * 5 + 3 * 0)/(2 + 3)]
G(x, y) = (21/5, 10/5)
G(x, y) = (4.2, 2)
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the answer is 6/1 and 6/1 simply divide and put the answer over one
The firts thig we are going to do is create tow triangles using the angles of elevation of Paul and Jose. Since the problem is not giving us their height we'll assume that the horizontal line of sight of both of them coincide with the base of the tree.
We know that Paul is 19m from the base of the tree and its elevation angle to the top of the tree is 59°. We also know that the elevation angle of Jose and the top of the tree is 43°, but we don't know the distance between Paul of Jose, so lets label that distance as

.
Now we can build a right triangle between Paul and the tree and another one between Jose and the tree as shown in the figure. Lets use cosine to find h in Paul's trianlge:



Now we can use the law of sines to find the distance

between Paul and Jose:



Now that we know the distance between Paul and Jose, the only thing left is add that distance to the distance from Paul and the base of the tree:

We can conclude that Jose is 33.9m from the base of the tree.
Answer: cotθ
<u>Step-by-step explanation:</u>
tanθ * cos²θ * csc²θ
= 
= 
= cotθ
Answer: B
<u>Step-by-step explanation:</u>
The parent graph is y = x²
The new graph y = -x² + 3 should have the following:
- reflection over the x-axis
- vertical shift up 3 units
Answers:
- a. Quadrant II
- b. negative
- c.

- d. C
- e.

<u>Explanation:</u>

a) Quadrant 2 is: 
b) In Quadrant 2, cos is negative and sin is positive, so tan is negative
c)
= 
d) the reference line is above the x-axis so it is negative --> 
e) 
<em>1452 feet</em>
- Step-by-step explanation:
<em>1 hour = 60min×60sec = 3600 sec</em>
<em>1 miles = 5280 feet</em>
<em>22 miles = 22×5280ft = 116160 ft</em>
<em />
<em>3600sec ................. 116160 ft</em>
<em>45sec ................................ x ft</em>
<em>x = 45×116160/3600</em>
<em>= 5227200/3600</em>
<em>= 1452 feet</em>