The domain is the set of all the values of X therefore it would be D.
Let <span>RR</span> be the radius of the sphere and let <span>hh</span> be the height of the cylinder centered on the center of the sphere. By the Pythagorean theorem, the radius of the cylinder is given by
<span><span><span>r2</span>=<span>R2</span>−<span><span>(<span>h2</span>)</span>2</span>.</span><span><span>r2</span>=<span>R2</span>−<span><span>(<span>h2</span>)</span>2</span>.</span></span>
The volume of the cylinder is hence
<span><span>V<span><span>=π<span>r2</span>h</span><span>=π<span>(<span>h<span>R2</span>−<span><span>h3</span>4</span></span>)</span>.</span></span></span><span><span>V<span>=π<span>r2</span>h</span></span><span>=π<span>(<span>h<span>R2</span>−<span><span>h3</span>4</span></span>)</span>.</span></span></span>
Differentiating with respect to <span>hh</span> and equating to <span>00</span> to find extrema gives
<span><span><span><span><span>dV</span><span>dh</span></span>=π<span>(<span><span>R2</span>−<span><span>3<span>h2</span></span>4</span></span>)</span>=0</span><span>∴<span>h0</span>=<span><span>2R</span><span>3‾√</span></span></span></span><span><span><span>dV</span><span>dh</span></span>=π<span>(<span><span>R2</span>−<span><span>3<span>h2</span></span>4</span></span>)</span>=0∴<span>h0</span>=<span><span>2R</span>3</span></span></span>
The second derivative of the volume with respect to <span>hh</span> is negative if <span><span>h>0</span><span>h>0</span></span> such that the volume is maximal at <span><span>h=<span>h0</span></span><span>h=<span>h0</span></span></span>. Substituting gives
<span><span><span>V<span>max</span></span>=<span><span>4π<span>R3</span></span><span>3<span>3‾√</span></span></span>.</span></span>
Answer:
698 fishes
Step-by-step explanation:
Generally, we can represent an exponential growth function as;
y = a•(1 + r)^t
originally, there were 3 fishes
The original value in this case means a = 3
After 6 weeks, there were 31
31 in this case is y
r is the increase percentage or rate
t is the time
So, we have it that;
31 = 3•(1 + r)^6
31/3 = (1 + r)^6
10.33 = (1 + r)^6
ln 10.33 = 6 ln (1 + r)
ln 10.33/6 = ln (1 + r)
e^0.3892 = (1 + r)
1 + r = 1.476
r = 1.476-1
r = 0.476 or 47.6%
So the growth percentage or rate is 47.6%
For 14 weeks, we simply have the value of t as 14;
So ;
y = 3•(1 + 0.476)^14
y = 3(1.476)^14
y = 698 fishes
ANSWER :
The values of x are -8 and 8
EXPLANATION :
From the problem, we have the equation :
Add 47 to both sides :
Take the square root of both sides :
Answer:
8 feet tall
Step-by-step explanation:
Divide 816 by 102 to get 8 feet.