<u>Corrected Question</u>
Ping lives at the corner of 3rd Street and 6th Avenue. Ari lives at the corner of 21st Street and 18th Avenue. There is a gym 2/3 the distance from Ping's home to Ari's home. Where is the gym?
- 9th Street and 10th Avenue
- 12th Street and 12th Avenue
- 14th Street and 12th Avenue
- 15th Street and 14th Avenue
Answer:
(D)15th Street and 14th Avenue
Step-by-step explanation:
Ping's Location: (3rd Street, 6th Avenue)
Ari's Location: (21st Street, 18th Avenue)
The gym is at point P which is 
the distance from Ping's home to Ari's home.
That is, Point P divides the line segment in the ratio 2:1.
We use the section formula:
m:n=2:1, 
The gym is located at 15th Street and 14th Avenue.
X is greater than or equal to -200
<h2>
a. What is your equation?</h2>
This is a problem of projectile motion. A projectile is an object you throw with an initial velocity and whose trajectory is determined by the effect of gravitational acceleration. The general equation in this case is described as:
Where:
So:
Finally, the equation is:
<h2>b. How long will it take the rocket to reach its maximum height?</h2>
The rocket will reach the maximum height at the vertex of the parabola described by the equation 
. Therefore, our goal is to find 
at this point. In math, a parabola is described by the quadratic function:
So the x-coordinate of the vertex can be calculated as:
From our equation:
So:
So the rocket will take its maximum value after 1.99 seconds.
<h2>
c. What is the maximum height the rocket will reach?</h2>
From the previous solution, we know that after 1.99 seconds, the rocket will reach its maximum, so it is obvious that the maximum height is given by 
. Thus, we can find this as follows:
So the maximum height the rocket will reach is 66.68ft
<h2>
d. How long is the rocket in the air?</h2>
The rocket is in the air until it hits the ground. This can be found setting 
, so:
We can't have negative value of time, so the only correct option is 
and rounding to the nearest hundredth we have definitively:
A decimal equivalent to another decimal is the same number but with more zeros on the right hand side.
0.68 = 0.680 = 0.6800 = 0.68000 etc.
0.9 = 0.90 = 0.900 = 0.9000 = 0.90000 etc.
Just pick whichever two numbers you like :)
Answer: you would have to purchase $1300 of merchandise and the total yearly amount paid to the warehouse for each plan is $1210
Step-by-step explanation:
Let x represent the number of dollars of merchandise that you would have to purchase in a year to pay the same amount under both plans.
Plan A offers an annual membership fee of $300 and you pay 70%, of the manufacturers reccomended list price. This means that the total cost of using plan A would be
300 + 0.7x
Plan B offers an annual membership fee of $40 and you pay 90% of the manufacturers reccomended list price.
This means that the total cost of using plan B would be
40 + 0.9x
For both plans to be the same,
300 + 0.7x = 40 + 0.9x
0.9x - 0.7x = 300 - 40
0.2x = 260
x = $1300
The total yearly amount paid to the warehouse for each plan would be
40 + 0.9 × 1300 = $1210
