From the moment the friend passes the bicyclist, his friend covers a distance over time t of (3.63 m/s)*t.
The bicyclist covers a distance of 1/2*(2.11 m/s^2)*t^2. They meet when these distances are equal:
3.63 t = 1.055 t^2 ==> 1.055 t^2 - 3.63 t = 0
==> t = 0 s or t = 3.44 s
Triangle HAM looks like an isosceles triangle, and we know that in an isosceles triangle 2 of the angles are the same.
so :
180 - 106 = 74 ( sum of the other 2 angles )
74/2 = 37 ( sum of angle HMA / HAM )
angles on a straight line add up to 180.
180-37=143 ( angle x )
since triangle YMH is also an isosceles,
180-37=143
143/2=71.5 ( angle w )
Answer:
y
=
4
(
1
2
)
x
Explanation:
An exponential function is in the general form
y
=
a
(
b
)
x
We know the points
(
−
1
,
8
)
and
(
1
,
2
)
, so the following are true:
8
=
a
(
b
−
1
)
=
a
b
2
=
a
(
b
1
)
=
a
b
Multiply both sides of the first equation by
b
to find that
8
b
=
a
Plug this into the second equation and solve for
b
:
2
=
(
8
b
)
b
2
=
8
b
2
b
2
=
1
4
b
=
±
1
2
Two equations seem to be possible here. Plug both values of
b
into the either equation to find
a
. I'll use the second equation for simpler algebra.
If
b
=
1
2
:
2
=
a
(
1
2
)
a
=
4
Giving us the equation:
y
=
4
(
1
2
)
x
If
b
=
−
1
2
:
2
=
a
(
−
1
2
)
a
=
−
4
Giving us the equation:
y
=
−
4
(
−
1
2
)
x
However! In an exponential function,
b
>
0
, otherwise many issues arise when trying to graph the function.
The only valid function is
y
=
4
(
1
2
)
x
Answer:
f(x) = 25.50x Roberto can buy 7 video games
Step-by-step explanation:
Each game is $25.50 which in math means it has an "x"
So if x=1 then 25.50x says that 1 video game is $25.50
Set up the equation:
200 = 25.50x (divide both sides by 25.50 to isolate the x)
200/25.50 = 7.84
x = 7.84
You can't have 0.84 of a video game, so Roberto can only buy 7 of them.
The first blank on the left side should be 0 I think
