Scientific notation : 7.88 × 105
The height will be 4 cm.
Explanation
<u />The volume of a cylinder is given by the formula V=πr²h. For a volume of 36π cm³ and a radius of 3 cm,
36π = π(3²)h
36π = 9πh
Divide both sides by 9π:
36π/9π = 9πh/9π
4 = h
Average rate of change over the interval <span><span>[a,b]</span>
</span> for <span><span>y=<span>f<span>(x)</span></span></span>
</span> is given by <span><span><span><span>f<span>(b)</span></span>−<span>f<span>(a)</span></span></span><span>b−a</span></span>
</span>
Hence, average rate of change of from <span><span>x=−2</span>
</span> to <span><span>x=6</span>
</span> i.e. over the interval <span><span>[−2,6]</span>
</span> for <span><span>y=<span>f<span>(x)</span></span>=<span>12</span><span>x2</span></span>
</span> is given<span><span> rate of change=<span><span><span>f<span>(6)</span></span>−<span>f<span>(−2)</span></span></span><span>6−<span>(−2)</span></span></span></span>
</span>
As <span><span><span>f<span>(−2)</span></span>=<span>12</span><span><span>(−2)</span>2</span>=2</span>
</span> and <span><span><span>f<span>(6)</span></span>=<span>12</span><span><span>(6)</span>2</span>=</span>
</span><span>rate of change=<span><span>18−2</span>8</span>=<span>162</span>=<span>2</span></span>
It would most likely take 3-4 hours, maybe even 5.
We are given with a function equal to f(x) = x^4. When the function is changed to -f(1/2x), the function changes to -f(1/2x) = (1/2 x)^4 equal to (-1/16 x^4). The graph of the function should be opening the opposite way and has a narrower plot. answer is C
