What is the radius of a circle if its center is (-3,-2) and one point on the circle is (5,-2)?
1 answer:
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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.
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
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:
The graph with solution is shown below.
Step-by-step explanation:
We need to find the and
for given equation.
For , substitute
Considering inequality sign as equality and simplifying,
, point is
Similarly,
For , substitute
We get,
, point is
We locate this two points on the graph now and join them.
The joining line will be dotted as the inequality has just 'greater than' symbol. The region above the dotted line is the solution to graph.
To find the median of the data set, we must first order them from lowest to highest in increasing order. Let's rearrange them in that way:
{17, 23, 30, 40, 44, 44}
Then we begin by crossing one off from each side, until we get to the middle. However, we see that our middle here is both 30 and 40.
What we do in a case like this is add up the two numbers and divide by 2 (essentially find the mean of the two middlemost numbers). Let's do that now:
So now we know that the median of the set of data is 35.
{17, 23, 30, 40, 44, 44}
Then we begin by crossing one off from each side, until we get to the middle. However, we see that our middle here is both 30 and 40.
What we do in a case like this is add up the two numbers and divide by 2 (essentially find the mean of the two middlemost numbers). Let's do that now:
So now we know that the median of the set of data is 35.