Answer:
A.
Step-by-step explanation:
1. Write down the coordinates of the two points on the line.
(-4,-3) (-1,2)
2. Use the slope formula to find the slope.
Slope formula: y2-y1/x2-x1
2--3/-1--4
Slope: 5/3
Answer:
x = 60 cm
Step-by-step explanation:
using Pythagoras theorem which states that:-
Hypotenuse (h)² = perpendicular (p)² + base (b)²
100² = 80² + x²
100² - 80² = x²
10000 - 6400 = x²
3600 = x²
<u>x = 60 cm</u>
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:
x = 81/4
Step-by-step explanation:
multiply both sides by 4
4x + 15 = 96
subtract 15 from both sides
4x = 81
divide both sides by 4
x= 81/4
i hope that's right
Answer:
1545.66 rad/h
Step-by-step explanation:
We need to find the angular velocity in rad/hour when wind is moving with a speed of 4.1 rpm.
We know that,
1 revolution = 2π rad
1 hour = 60 minute
So,
So, the required angular velocity is 1545.66 rad/h.