Answers:
Upper Limit = 2.55 cc
Lower Limit = 2.25 cc
cc stands for "cubic centimeters".
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Explanation:
The tolerance tells us how much we can go over or under our target. It's our margin of error. We add and subtract the tolerance (0.15) from the target we're trying to aim for (2.4)
So the lowest dosage allowed is 2.4-0.15 = 2.25 cc
The highest dosage allowed is 2.4+0.15 = 2.55 cc
The upper limit is 2.55 cc while the lower limit is 2.25 cc
On a number line, we would find that 2.4 is at the midpoint of 2.25 and 2.55; so its at the center of those lower and upper bounds. The distance from the center to each endpoint is the same. That distance would be the tolerance 0.15
Carry out the binomial expansion in the numerator:
Then the 9⁴ terms cancel each other, so in the limit we have
Since <em>h</em> is approaching 0, that means <em>h</em> ≠ 0, so we can cancel the common factor of <em>h</em> in both numerator and denominator:
Then when <em>h</em> converges to 0, each remaining term containing <em>h</em> goes to 0, leaving you with
or choice C.
Alternatively, you can recognize the given limit as the derivative of <em>f(x)</em> at <em>x</em> = 9:
We have <em>f(x)</em> = <em>x</em> ⁴, so <em>f '(x)</em> = 4<em>x</em> ³, and evaluating this at <em>x</em> = 9 gives the same result, 2916.
1 gallon of milk would be 16 cups :)
Step-by-step explanation:
#1.
(a + 2b)²
<em>Using identity (x + y)² = x² + 2xy + y², we get:</em>
= (a)² + (2b)² + 2 × (a) × (2b)
= a² + 4b² + 4ab
= a² + 4ab + 4b² Ans.
#2.
(5x - 3y)²
<em>Using identity (a - b)² = a² - 2ab + b², we get:</em>
= (5x)² + (3y)² - 2 × (5x) × (3y)
= 25x² + 9y² - 30xy
= 25x² - 30xy + 9y² Ans.
#3.
(3a + 4)(3a - 4)(9a² + 16)
<em>Using identity (x + y)(x - y) = x² - y², we get:</em>
= [(3a)² - (4)²][9a² + 16]
= (9a² - 16)(9a² + 16)
= (9a²)² - (16)²
= 81a⁴ - 256 Ans.
Answer:
4 and 7/8
Step-by-step explanation:
