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AURORKA [14]
4 years ago
15

Find the following limit or state that it does not exist. ModifyingBelow lim With x right arrow minus 2 StartFraction 3 (2 x min

us 1 )squared minus 75 Over x plus 2 EndFraction
Mathematics
1 answer:
leva [86]4 years ago
6 0

Answer:

-60

Step-by-step explanation:

The objective is to state whether or not the following limit exists

                                \lim_{x \to -2}  \frac{3(2x-1)^2 - 75}{x+2}.

First, we simplify the expression in the numerator of the fraction.

3(2x-1)^2 -75 = 3(4x^2 - 4x +1) -75 = 12x^2 - 12x + 3 - 75 = 12x^2 - 12x -72

Now, we obtain

                         12(x^2-x-6) = 12(x+2)(x-3)

and the fraction is transformed into

                       \frac{3(2x-1)^2 - 75}{x+2} =  \frac{12(x+2)(x-3)}{x+2} = 12 (x-3)

Therefore, the following limit is

       \lim_{x \to -2}  \frac{3(2x-1)^2 - 75}{x+2} = \lim_{x \to -2}  12(x-3) = 12 \lim_{x \to -2} (x-3)

You can plug in -2 in the equation, hence

                        12 \lim_{x \to -2} (x-3) = 12 (-2-3) = -60

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Answer:

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<u>Part 2:</u> About 2.33 Rotations


Step-by-step explanation:


Part 1:

The arc length of a circle is given by the formula  s=r\theta

Where

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**The angle are in radians and we will use radian**

When smaller gear has made 1 complete rotations (2\pi radians), the arc length traveled is s=r\theta\\s=(3)(2\pi)\\s=6\pi


Now, what angle is swept by the larger circle when it travels 6\pi? Put in s=6\pi and r is 7 to find \theta:

s=r\theta\\6\pi=(7)\theta\\\theta= \frac{6\pi}{7}

** Since \pi radians is 180°, we plug in 180 into \pi and find the degree measure:

\frac{6\pi}{7}=\frac{6*180}{7}=154.3

Angle = 154.3°


Part 2:

In one complete rotation of the larger gear, it travels a distance of:

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We know that the smaller circle makes 1 rotation and travels s=r\theta=(3)(2\pi)=6\pi, so in 14\pi distance, it makes:

Rotations = \frac{14\pi}{6\pi}=\frac{14}{6}=2.33

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3 years ago
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madreJ [45]

Step-by-step explanation:

Changes made to your input should not affect the solution:

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Pull out like factors :

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Answer:

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Step-by-step explanation:

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3 years ago
Use the numbers 7,5,6, and 3 and only use each number once it has to equal 75. You may use addition, subtraction, multiplication
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Answer:

(7+5)*6+3=75

Step-by-step explanation:

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