So, to set up this equation, lets just say that Lucas did 5 hours of homework also. The ratio of Lucas's homework to video games is 60 minutes of homework/30 minutes of video games. If we converted the 5 hours into 300 minutes then you would multiply the 60 minutes by 5 and the 30 minutes by 5 also. You would get 300 minutes/150 minutes. Jonathan's ratio is every 5 hours of homework/3 hours of video games. We would convert this to minutes by taking both numbers and multiplying them by 60. We would get 300 minutes/180 minutes. Using this we know that Jonathan gets more time to play video games because every 5 hours of homework he gets 180 minutes of gaming and for Lucas, every 5 hours of homework he only gets 150 minutes of gaming. I hope that this helped you!

6 0

4 years ago

Determine the equation of the tangent of the hyperbola that is parallel to the given line:

marin [14]

The tangent line to the curve has slope equal to $\frac{\mathrm dy}{\mathrm dx}$ . Use implicit differentiation to find this derivative.

$9x^2-4y^2=32$

$\implies18x-16y\dfrac{\mathrm dy}{\mathrm dx}=0\implies\dfrac{\mathrm dy}{\mathrm dx}=\dfrac{-18x}{-16y}=\dfrac{9x}{8y}$

The given line in slope-intercept form is

$9x+2y-1=0\implies y=\dfrac{1-9x}2$

and has slope -9/2. Any line parallel to this one has the same slope. The tangent to the hyperbola has this slope at points (<em>x</em>, <em>y</em>) such that

$-\dfrac92=\dfrac{9x}{8y}\implies x=-4y$

Find the points on the hyperbola where this condition is met.

$9(-4y)^2-4y^2=140y^2=32\implies y^2=\dfrac{32}{140}\implies y=\pm\sqrt{\dfrac8{35}}\implies x=\pm4\sqrt{\dfrac8{35}}$

Then use the point-slop formula to build the equations of these tangents:

$y\mp\sqrt{\dfrac8{35}}=-\dfrac92\left(x\pm4\sqrt{\dfrac8{35}}\right)$

8 0

3 years ago

Whats the difference 5 2/7 - 3 4/7

umka21 [38]

$5 \frac{2}{7} - 3\frac{4}{7} =\frac{(5\times 7)+2}{7} -\frac{(3\times7)+4}{7} =\frac{37}{7} -\frac{25}{7} -\frac{37-25}{7} =\frac{12}{7}=\boxed{\bf{1\frac{5}{7}}}$

4 0

4 years ago