Solving for x.
Since x<span> is on the right-hand side of the </span>equation<span>, switch the sides so it is on the left-hand side of the </span>equation<span>.
</span><span>0.04<span>x2</span>−8.504x+25302=c
</span>Simplify the quadratic and set<span> the right side equal to </span><span>0.
</span><span>0.04<span>x2</span>−8.504x+25302−c=0
</span>Use the standard form of the quadratic <span>(<span><span>a<span>x2</span>+bx+c</span>)</span></span><span> to find </span><span>a,</span><span>b,</span><span> and </span>c<span> for this quadratic.
</span><span>a=0.04,</span><span>b=−8.504,</span><span>c=25302−1c
</span>Use the quadratic formula<span> to find the </span>solutions<span>.
</span><span>x=<span>−b ± </span></span>√<span><span> <span><span>b2</span>−4ac /</span> </span><span>2a
</span></span>Substitute in the values of <span><span>a=0.04</span>,</span><span><span>b=−8.504</span>,</span><span> and </span><span><span>c=25302−1c</span>.
</span>x=<span>−(−8.504) ±</span>√<span><span>(−8.504<span>)2</span>−4(0.04)(25302−1c)/</span><span>2(0.04)
</span></span>
<span>Simplify.
</span>x=<span>8.504 ±</span>√<span><span>(−8.504<span>)2</span>−4(0.04)(25302−1c)/</span><span>2(0.04)
</span></span>
Simplify the section inside the radical<span>.
</span>x=<span>8.504 ± </span>√<span><span><span>−3976.001984+0.16c</span>/</span><span>2(0.04)
</span></span>
Simplify the denominator<span> of the </span>quadratic formula<span>.
</span>x=<span>8.504 ±</span>√<span><span>−3976.001984+0.16c/</span>0.08
</span>
Answer:
x=8.504 ±√−3976.001984+0.16c/0.08
Yes it can hold up to a little over 4 liters
37/100. Easiest way possible
We know that
Applying the law of cosines
<span>c²=a²+b²-2*a*b*cos C
</span>in this problem
a=176.27 miles
b=222.34 miles
C=38.59°
c=<span>the distance between the planes
so
</span>c²=176.27²+222.34²-2*176.27*222.34*cos 38.59°----> c²=19239.15
<span>c=138.71 miles
the answer is
138.71 miles
</span>
