Solve the following inequality. Use interval notation.

Mathematics

1 answer:

Svetach [21]2 years ago

8 0

9514 1404 393

Answer:

(-∞, -1/3) U (3, ∞)

Step-by-step explanation:

The given inequality is equivalent to two inequalities (joined with OR).

-3x +7 ≥ 8 . . . . . . eliminate parentheses

-3x ≥ 1 . . . . . . . subtract 7

x ≤ -1/3 . . . . . divide by 3

3x ≥ 9 . . . . . add 1

x ≥ 3 . . . . . . divide by 3

Then the solution to the inequality is the union of these intervals:

x ∈ (-∞, -1/3) ∪ (3, ∞)

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Paul and jose are trying to measure the height of a tree. paul is standing 19m from the foot of the tree and measures the angle

Nina [5.8K]

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 $x$ .
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:
$cos(59)= \frac{19}{h}$
$h= \frac{19}{cos(59)}$
$h=36.9$
Now we can use the law of sines to find the distance $x$ between Paul and Jose:
$\frac{sin(43)}{36.9} = \frac{sin(16)}{x}$
$x= \frac{36.9sin(16)}{sin(43)}$
$x=14.9$

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:
$19m+14.9=33.9m$

We can conclude that Jose is 33.9m from the base of the tree.