Answer:
10x - 3y = -109 .
Step-by-step explanation:
x^2 + y^2 = 109
Implicit Differentiation:
2x + 2y.y' = 0
y' = -2x/2y = -x/y
So at the point (-10,3) the gradient of the tangent is -(-10)/3 = 10/3.
Equation of the tangent:
y - y1 = m(x - x1)
y - 3 = 10/3(x + 10)
y - 3 = 10/3 x + 100/3
3y - 9 = 10x + 100
-109 + 3y = 10x
10x - 3y = -109
Answer:
D. A travels 90 miles more
Step-by-step explanation:
The graph tells you Car A travels 140 miles on 5 gallons of gas. (There is a point marked there on the graph.)
The table tells you Car B travels 99 miles on 4.5 gallons of gas. When that is multiplied by 5/4.5 = 10/9 to get the equivalent for 5 gallons, we see that Car B could travel 10/9 × 99 = 110 miles on 5 gallons of gas.
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Already <em>on 5 gallons of gas</em>, Car A has traveled <em>30 miles farther</em>. The only sensible answer choice is ...
D. Car A travelled 90 miles more than Car B [when 15 gallons are used].
Answer:
257.5 mph
332.5 mph
Step-by-step explanation:
The initial distance between the two planes is 960 miles, while the final distance (after t=1.5 h) is 75 miles, so the total distance covered by the two planes in 1.5h is
miles
Calling v1 and v2 the velocities of the two planes, we have the following equations:
(1) 
--> velocity of plane 1 exceeds velocity of plane 2 by 75 mph
(2) 
--> the total distance covered by the two planes is 885 miles (t=1.5 h is the time, and the products v1 t and v2 t represent the distance covered by each plane)
Substituting t=1.5 h, the second equation becomes:
By substituting (1) into this last equation, we find:
And substituting this back into eq.(1), we find
So, the speeds of the two planes are
257.5 mph
332.5 mph
