The line defined by the equation 2y+3=-(2/3)(x-3) is tangent to the graph of g(x) at x=-3. What is the value of the limit as x a
1 answer:
<span>the limit as x approaches -3 of [g(x)-g(-3)]over(x+3) is the same as the derivative, or slope, of g(x) at the point x=-3, or g'(-3).
Since you are given the equation of the tangent line, the answer is just the slope of that line.
</span><span>2y+3=-(2/3)(x-3)
</span><span>6y+9=-2(x-3)
6y+9=-2x+6
6y=-2x-3
y= (-2x-3)/6
slope is -2/6 = </span>
Since you are given the equation of the tangent line, the answer is just the slope of that line.
</span><span>2y+3=-(2/3)(x-3)
</span><span>6y+9=-2(x-3)
6y+9=-2x+6
6y=-2x-3
y= (-2x-3)/6
slope is -2/6 = </span>
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Answer:
The time it takes to boil 2.2 litres of water is approximately 141 seconds
Step-by-step explanation:
The given parameters are;
The relationship of the variables, T and A is a proportional, therefore, we have;
T ∝ A, or T/A = k = Constant of proportionality
The time it takes to boil 2.8 liters of water = 180 seconds
∴ When A = 2.8 litres, T = 180 seconds, from which we have;
k = T/A = 180 s/(2.8 L) = 450/7 s/L
k = 450/7 s/L
When A = 2.2 litres, we have;
T/A = k
∴ T = k × A
Plugging in the value for both 'k', and 'A' when A = 2.2 litres, gives;
T = k × A = 450/7 s/L × 2.2 L = 990/7 s = 141. s
The time it takes to boil 2.2 litres of water, given a direct proportionality relation is, T = 141. seconds ≈ 141 seconds given to the nearest second.