Answer:
![\sqrt{-12} = 2\sqrt{3} i\\\sqrt{-9}= 3i\\3i * 2\sqrt{3}i = -6\sqrt{3](https://tex.z-dn.net/?f=%5Csqrt%7B-12%7D%20%3D%202%5Csqrt%7B3%7D%20i%5C%5C%5Csqrt%7B-9%7D%3D%203i%5C%5C3i%20%2A%202%5Csqrt%7B3%7Di%20%3D%20-6%5Csqrt%7B3)
Step-by-step explanation:
We know that
<span>diameter of the base of a cylindrical can= 4 in----------> r=2 in
h=6.5 in
</span>[surface area]=2*[pi*r²]+[2*pi*r*h]
then
[surface area]=2*[pi*2²]+[2*pi*2*6.5]=[ 25.13 ]+[ 81.68 ]=106.81 in²
the answer is 106.8 in²
It looks like the limit you want to compute is
![\displaystyle \lim_{x\to4} \frac{f(g(x)) - f(4)}{x-4}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Clim_%7Bx%5Cto4%7D%20%5Cfrac%7Bf%28g%28x%29%29%20-%20f%284%29%7D%7Bx-4%7D)
Since
, this limit corresponds exactly to the derivative of
at
. Recall that
![f'(a) = \displaystyle \lim_{x\to a} \frac{f(x) - f(a)}{x - a}](https://tex.z-dn.net/?f=f%27%28a%29%20%3D%20%5Cdisplaystyle%20%5Clim_%7Bx%5Cto%20a%7D%20%5Cfrac%7Bf%28x%29%20-%20f%28a%29%7D%7Bx%20-%20a%7D)
By the chain rule,
![(f\circ g)'(4) = f'(g(4)) \times g'(4) = f'(4) \times g'(4) = 3\times7 = \boxed{21}](https://tex.z-dn.net/?f=%28f%5Ccirc%20g%29%27%284%29%20%3D%20f%27%28g%284%29%29%20%5Ctimes%20g%27%284%29%20%3D%20f%27%284%29%20%5Ctimes%20g%27%284%29%20%3D%203%5Ctimes7%20%3D%20%5Cboxed%7B21%7D)
Since
exists,
is differentiable at
so it must be continuous.
Jane final solution is wrong due to the direction of the inequality sign
<h3>Solving linear equation</h3>
Linear equations are equation that has a leading degree of 1
Given the inequality below
-8x + 12x + 2 ≥ 62
Simplify to have
4x + 2 ≥ 62
Subtract 2 from both sides
4x + 2 - 2≥ 62 - 2
4x ≥ 60
Divide both sides by 4
4x/4≥ 60/4
x≥ 15
We can see that jane final solution is wrong due to the direction of the inequality sign
Learn more on inequality here: brainly.com/question/24372553
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