Answer:
A: the proposed route is 3.09 miles, so exceeds the city's limit
Step-by-step explanation:
The length of the route in grid squares can be found using the Pythagorean theorem on the two parts of the route. Let 'a' represent the length of the route to the park from the start, and 'b' represent the route length from the park to the finish. Then we have (in grid squares) ...
a^2 = (12-6)^2 +3^2 = 45
a = √45 = 3√5
and
b^2 = (6 -2)^2 +4^2 = 32
b = √32 = 4√2
Then the total length, in grid squares, is ...
3√5 + 4√2 = 6.7082 +5.6569 = 12.3651
If each grid square is 1/4 mile, then 12.3651 grid squares is about ...
(12.3651 squares) · (1/4 mile/square) = 3.0913 miles
The proposed route is too long by 0.09 miles.
Step-by-step explanation:
Let the height above which the ball is released be H
This problem can be tackled using geometric progression.
The nth term of a Geometric progression is given by the above, where n is the term index, a is the first term and the sum for such a progression up to the Nth term is
To find the total distance travel one has to sum over up to n=3. But there is little subtle point here. For the first bounce ( n=1 ), the ball has only travel H and not 2H. For subsequent bounces ( n=2,3,4,5...... ), the distance travel is 2×(3/4)n×H
a=2H..........r=3/4
However we have to subtract H because up to the first bounce, the ball only travel H instead of 2H
Therefore the total distance travel up to the Nth bounce is
For N=3 one obtains
D=3.625H
Answer:
B) -4 < y
Step-by-step explanation:
The lowest point on the y axis of the graph is -4 and everything else is higher
The number of bottles of soda purchased is 10 and the number of bottles of juice purchased is 4.
<u>Step-by-step explanation:</u>
Let us consider the soda bottles as x and juice bottles as y.
From the given data we can derive 2 equations,
35x+15y= 410. .....(1)
x=y+6. ....(2)
Substitute equation (2) in (1),
35(y+6)+15y=410.
35y+ 210+15y=410.
50y+210=410.
50y=410-210.
50y=200.
y=4.
Substitute y value in equation (2),
x=4+6.
x=10.
The number of bottles of soda purchased is 10 and the number of bottles of juice purchased is 4.
