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anyanavicka [17]
3 years ago
7

3 times the sum of x and 6 equals 10 times the difference of x and 1.

Mathematics
1 answer:
o-na [289]3 years ago
4 0
3(x + 6) = 10(x - 1)
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What is the equation of this graphed line?
Soloha48 [4]
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Use the limit theorem and the properties of limits to find the limit.<br> Picture provided below
sashaice [31]

Answer:

b. 1/2

Step-by-step explanation:

lim        (x -3)(x +2)

x-->-∞    ---------------

              2x^2 + x +1

= lim        (x^2 -3x +2x - 6)

x-->-∞    -----------------------

              2x^2 + x +1

= lim        (x^2 -x - 6)

x-->-∞    -----------------------

              2x^2 + x +1

When we plug in x = -∞, we get indeterminate form.

Now we have to use the L'hospital rule.

d/dx (x^2 - x - 6) = 2x -1

d/dx (2x^2 + x + 1) = 4x + 1

Now apply the limit

lim            (2x - 1) / (4x + 1)

x--->-∞

Here we have to degree of the numerator and the denominator of the same. In this case, if x --> -∞, we get the result as the coefficient of the leading term as the result.

According to the rule, we get

= 2/4

Which can simplified as 1/2

The answer is 1/2

Hope this will helpful.

Thank you.

3 0
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What is the area of the largest rectangle with lower base on the x-axis and upper vertices on the curve y = 27 - x2?
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The answer is 54 square units.
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<span>then the vertex in quadratnt II is (-x,y) </span>
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<span>Area = xy </span>
<span>= x(27 - x</span>²<span>) </span>
<span>= -x</span>³<span> + 27x </span>
<span>d(area)/dx = 3x</span>²<span> - 27 </span><span>= 0 for a maximum of area </span>
<span>3x</span>²<span> = 3 x 3</span>² = <span>27 </span>
<span>x</span>²<span> = 9 </span>
<span>x = ±3 </span>
<span>y = 27-9 = 18 </span>
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