St=d
s=d/t
t=d/s
so we have several things:
distance of alfredo
speed of alfredo
time of alredo
distance of louisa
speed of louisa
time of louisa
we will represen them as follows
distance of alfredo=d1
speed of alfredo=s1
time of alredo=t1=2=t2
distance of louisa=d2
speed of louisa=s2
time of louisa=t2=2=t1
d=distance
t=time
total d=15 miles
t=2 hours
they both walk towards each other
louisa's speed is 1 mile per hour more than Alfredo so s2=s1+1
so we also have
d1+d2=15
s2=s1+1
t1=t2=2
we want to solve for s1 and s2
d=st
d1=(s1)(2)
d2=(s2)(2)
subsitute s1+1 for s2
d2=(s1+1)(2)
put back ino equation
(s1)(2)+(s1+1)(2)=15
distribute
2s1+2s1+2=15
2(s1)+2(s1)+2=15
add like terms
4(s1)+2=15
subtract 2 from both sides
4(s1)=13
divide both sides by 4
s1=13/4=3 and 1/4 mph
s2=s1+1
s2=3 and 1/4
s2=4 and 1/4 mph
check
d=st
t=2
alfredo's distance=(3 and 1/4) times 2=6 and 1/2
louisa's distance=(4 and 1/4) times 2=8 and 1/2
6 and 1/2+8 and 1/2=6+1/2+8+1/2=14+1=15
Alfredo's walking speed=3 and 1/4 miles per hour
Louisa's walking speed=4 and 1/4 miles per hour
aka
Alredospeed=3.25 mph
Louisaspeed=4.25 mph
60 = a * (-30)^2
a = 1/15
So y = (1/15)x^2
abc)
The derivative of this function is 2x/15. This is the slope of a tangent at that point.
If Linda lets go at some point along the parabola with coordinates (t, t^2 / 15), then she will travel along a line that was TANGENT to the parabola at that point.
Since that line has slope 2t/15, we can determine equation of line using point-slope formula:
y = m(x-x0) + y0
y = 2t/15 * (x - t) + (1/15)t^2
Plug in the x-coordinate "t" that was given for any point.
d)
We are looking for some x-coordinate "t" of a point on the parabola that holds the tangent line that passes through the dock at point (30, 30).
So, use our equation for a general tangent picked at point (t, t^2 / 15):
y = 2t/15 * (x - t) + (1/15)t^2
And plug in the condition that it must satisfy x=30, y=30.
30 = 2t/15 * (30 - t) + (1/15)t^2
t = 30 ± 2√15 = 8.79 or 51.21
The larger solution does in fact work for a tangent that passes through the dock, but it's not important for us because she would have to travel in reverse to get to the dock from that point.
So the only solution is she needs to let go x = 8.79 m east and y = 5.15 m north of the vertex.
Answer:
the awnser I got is 279
Step-by-step explanation:
if it's wrong I'm so sorry I'm not the best at math >-<
Answer:
1
Step-by-step explanation:
of course the answer is one but you can't write it in exponential form because a regular keyboard doesn't contain it