Find two values of d such that the line 2x + y = d is tangent to the ellipse 4x2 + y2 = 36. find the points of tangency.

The solution for this problem would be:
slope must be [ - 2 ]...dy/dx = - 4x / y...= - 2 means y = 2x...thus 4 x² + [ 2x]² = 36 or 
x = ± 3 √2 / 2 and y = ± 3 √2 ---> d = ± 3 √2 ± 3 √2 = ± 6 √2 ...( 3√2 / 2 , 2√3 ) & ( - 3 √2 / 2 , - 3 √2 ) for negative slopes.

When rates are expressed as a quantity of 1, such as 2 feet per second or 5 miles per hour, they are called unit rates. if you have a multiple-unit rate such as 120 students for every 3 buses, and want to find the single-unit rate, write a ratio equal to the multiple-unit rate with 1 as the second term.