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.
Eighty three thousand four hundred and seventy nine
Remember that c is the initial height. Since we the rocket is in a 99-foot cliff, c=99. Also, we know that the velocity of the rocket is 122 ft/s; therefore v=122
Lets replace the values into the the vertical motion formula to get:
Notice that the rocket hits the ground at the bottom of the cliff, which means that the final height is 99-foot bellow its original position; therefore, our final height will be h=-99
Lets replace this into our equation to get:
Now we can apply the quadratic formula
where a=-16, b=122, and c=198
or
or
or
Since the time can't be negative, we can conclude that the rocket hits the ground after 9 seconds.
Hence the correct answer is C) -23
Further explanation:
We have to put the values of m and n into both expression first separately and then multiply the answers.
Given expressions are:
The values are:
Putting the values in expression 1:
Putting the values of m and n in second expression
Multiplying both expressions:
Hence the correct answer is C) -23
Keywords: Polynomials, Putting values in expressions
Learn more about polynomials at:
#LearnwithBrainly
Answer:
1/14
Step-by-step explanation:
Odd numbers: 5, 7, 9
3/7 × 1/6
1/14