A man tied a rope to the top of a tree, which is 'x' m tall. The other end of the rope was tied to
2 answers:
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Check out the image attachment for the filled out table. There may be more than one way to fill out the table, but I did it in the way I learned in the past.
Let's work through the table one row at a time
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So we'll start with row 1
Row 1, column1: The value that goes here is 12 as each adult pays $12
Row 1, column2: You'll write 'a' without quotes here as there are 'a' adults ('a' is just a placeholder for a number)
Row 1, column3: Write 12*a or 12a here. Simply multiply the cost per adult ($12) with the number of adults (a).
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Now onto row 2
Row 2, column1: It costs $6 per young adult, so we write 6 here
Row 2, column2: There are y young adults. Write 'y' here without quotes
Row 2, column3: Write 6y here. Multiply the number of young adults with the price per young adult
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Now onto row 3
Now we add up the values per each column to get the column totals
Row 3, column1: The individual costs 12 and 6 add to 18. We won't use this value but it doesn't hurt to write it in. If it is confusing to add in, then just ignore this cell. The reason why we won't use this is because the number of adults (a) and young adults (y) is not necessarily the same. If we were guaranteed they were the same, then we could use this value. But again there's no guarantee. It's probably best to steer clear of this cell.
Row 3, column2: We have 'a' adults and 'y' young adults. So a+y people total. This total is 8 as we know a family of 8 had been registered. So we write 8 in this box as well. The two expressions a+y and 8 are equal to each other allowing us to form the first equation a+y = 8
Row 3, column3: The cost for all the adults is 12a dollars. Similarly it costs 6y dollars for just the young adults. Adding up the two subtotals we get 12a+6y as the total cost for everyone. We're told that the family paid a total of $66. So like with the previous box, we can equate the two expressions getting us the second equation to be 12a+6y = 66
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Again everything is summarized in the image attachment.
The two equations we pull away from that table are
a+y = 8
12a+6y = 66
which is the system of equations to set up
Let's work through the table one row at a time
------------------------------------------------------------------------------
So we'll start with row 1
Row 1, column1: The value that goes here is 12 as each adult pays $12
Row 1, column2: You'll write 'a' without quotes here as there are 'a' adults ('a' is just a placeholder for a number)
Row 1, column3: Write 12*a or 12a here. Simply multiply the cost per adult ($12) with the number of adults (a).
------------------------------------------------------------------------------
Now onto row 2
Row 2, column1: It costs $6 per young adult, so we write 6 here
Row 2, column2: There are y young adults. Write 'y' here without quotes
Row 2, column3: Write 6y here. Multiply the number of young adults with the price per young adult
------------------------------------------------------------------------------
Now onto row 3
Now we add up the values per each column to get the column totals
Row 3, column1: The individual costs 12 and 6 add to 18. We won't use this value but it doesn't hurt to write it in. If it is confusing to add in, then just ignore this cell. The reason why we won't use this is because the number of adults (a) and young adults (y) is not necessarily the same. If we were guaranteed they were the same, then we could use this value. But again there's no guarantee. It's probably best to steer clear of this cell.
Row 3, column2: We have 'a' adults and 'y' young adults. So a+y people total. This total is 8 as we know a family of 8 had been registered. So we write 8 in this box as well. The two expressions a+y and 8 are equal to each other allowing us to form the first equation a+y = 8
Row 3, column3: The cost for all the adults is 12a dollars. Similarly it costs 6y dollars for just the young adults. Adding up the two subtotals we get 12a+6y as the total cost for everyone. We're told that the family paid a total of $66. So like with the previous box, we can equate the two expressions getting us the second equation to be 12a+6y = 66
------------------------------------------------------------------------------
Again everything is summarized in the image attachment.
The two equations we pull away from that table are
a+y = 8
12a+6y = 66
which is the system of equations to set up
Answer:
The horizontal displacement is 11 units, the vertical displacement is 9 units, and the projection angle is 39.3 degrees.
Step-by-step explanation:
We can start using the definition of displacement in one dimension between any 2 points which is the difference between them, so we have
And apply it to get the horizontal and vertical displacements.
Once we have found them, we can use trigonometric functions to find the projection angle with respect the horizontal.
Linear displacements.
Using the definition of displacement, we can write the horizontal displacement as
So we can use the given points on the displacement formula
In the same manner we can look at the y components of those points to find the vertical displacement
Thus the horizontal displacement is 11 units and the vertical displacement is 9 units.
Projection angle.
The projection angle with respect the horizontal is the angle that is made between the line that connects the points P1 and P2 and the horizontal, so we can use the linear displacements previously found to write
Solving for the angle we get
Replacing values
Which give us
So the projection angle is 39.3 degrees.
Answer:
Step-by-step explanation:
we know that
The roots of the quadratic function (x-intercepts) are
x=-1 and x=5/3
so
we can write the equation of the parabola as
where
a is a coefficient
Remember that
The parabola pass through the point (5,40)
substitute the value of x and the value of y of the ordered pair in the quadratic equation and solve for a
x=5, y=40
substitute
apply distributive property
see the attached figure to better understand the problem
