Jill jumped 6
1 answer:
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Answer:
31.76 ft and 58.64 ft
Step-by-step explanation:
The radius measures between 13 feet and 24 feet.
The wheel is able to turn 7π/9 radians before getting stuck.
We need to find the range of distances that the wheel could spin before getting stuck. That is, the length of arc.
Length of an arc is given as:
where θ = central angle = 7π/9 radians
r = radius of the circle
Therefore, for 13 feet:
For 24 feet:
The wheel could spin between 31.76 ft and 58.64 ft before getting stuck.
We know that
The Standard Form of a Quadratic Equation<span> looks like this
</span> ax²<span> + bx + c = 0
</span>
we have
<span>x -1 0 1 2 3
y -20 -6 2 4 0
for x=0 y=-6
then
</span> y=ax² + bx + c --------> -6=a*0² + b*0 + c ---------> c=-6
for y=0 x=3
then
y=ax² + bx + c-------> 0=a*3² + b*3 -6---------> 9a+3b=6----> equation 1
The Standard Form of a Quadratic Equation<span> looks like this
</span> ax²<span> + bx + c = 0
</span>
we have
<span>x -1 0 1 2 3
y -20 -6 2 4 0
for x=0 y=-6
then
</span> y=ax² + bx + c --------> -6=a*0² + b*0 + c ---------> c=-6
for y=0 x=3
then
y=ax² + bx + c-------> 0=a*3² + b*3 -6---------> 9a+3b=6----> equation 1
for x=2 y=4
then
y=ax² + bx + c-----> 4=a*2² + b*2 -6-----> 4=4a+2b-6-----> 4a+2b=10----> a=2.5-0.5b----> equation 2
I substitute 2 in 1
9*[2.5-0.5b]+3b=6------> 22.5-4.5b+3b=6------> 1.5b=16.5------> b=11
a=2.5-0.5*11------> a=2.5-5.5------> a=-3
The Standard Form of a Quadratic Equation is
ax² + bx + c = 0--------> -3x²+11x-6=0
the answer is
-3x²+11x-6=0
See the attached figure