4x^2 + 5xy - y^2 = 6
Implicitly differentiating both sides,
4(2x) + 5(x y' + y) - 2yy' = 0

where y' = dy/dx

8x + 5xy' +5y -2yy' = 0

combining y' terms
y' (5x-2y) +8x +5y = 0

y'(5x-2y) = -(8x+5y)

dy/dx = -(8x+5y)/(5x-2y)
or
dy/dx = (8x+5y)/(2y-5x)

5 0

3 years ago

Please round to the nearest tenth if possible.

Butoxors [25]

$\bf \cfrac{64~\underline{mi}}{\underline{hr}}\cdot \cfrac{\underline{hr}}{60~sec}\cdot \cfrac{5200~ft}{\underline{mi}}\implies \cfrac{64\cdot 5200~ft}{60~sec}\implies \cfrac{16640~ft}{3~sec}
\\\\\\
\approx 5546.67\frac{ft}{sec}\\\\
-------------------------------\\\\
\cfrac{6000~\underline{lbs}}{\underline{day}}\cdot \cfrac{ton}{2000~\underline{lbs}}\cdot \cfrac{7~\underline{day}}{week}\implies \cfrac{6000\cdot 7~ton}{2000~week}\implies 21.00\frac{ton}{week}$

$\bf -------------------------------\\\\
\cfrac{2~\underline{lbs}}{\underline{week}}\cdot \cfrac{16~oz}{\underline{lbs}}\cdot \cfrac{\underline{week}}{7~day}\implies \cfrac{2\cdot 16~oz}{7~day}\implies \cfrac{32~oz}{7~day}\approx 4.57\frac{oz}{day}$

8 0

3 years ago