Answer:
do you have a photo of the figure?
S(t) = -4.9t^2 + 19.6t + 24.5
when it reaches the ground s(t) = 0
so we have -4.9t^2 + 19.6t + 24.5 = 0
solve this for t:-
-4.9(t^2 - 4t - 5) = 0
(t + 1)(t - 5) = 0
so required time t = 5 seconds
answer 5 seconds
To get the points at which the two boats meet we need to find the equations that model their movement:
Boat A:
vertex form of the equation is given by:
f(x)=a(x-h)^2+k
where:
(h,k) is the vertex, thus plugging our values we shall have:
f(x)=a(x-0)^2+5
f(x)=ax^2+5
when x=-10, y=0 thus
0=100a+5
a=-1/20
thus the equation is:
f(x)=-1/20x^2+5
Boat B
slope=(4-0)/(10+10)=4/20=1/5
thus the equation is:
1/5(x-10)=y-4
y=1/5x+2
thus the points where they met will be at:
1/5x+2=-1/20x^2+5
solving for x we get:
x=-10 or x=6
when x=-10, y=0
when x=6, y=3.2
Answer is (6,3.2)
Given:
To find:
Solution:
We have, 
and 
.
Let the values of h and k are 2a and 5a respectively.
Let the values of x and y are 3b and 4b respectively.
We have,
It can be written as
On further simplification, we get
Now,
On further simplification, we get
Therefore, the ratio is 
.
