well, we can check the units right off the grid.
so, below the x-axis, we have a rectangle, is a 10x3, so it has an area of 10*3.
above the x-axis we have a trapezoid, it has to parallel sides or bases, top is 6 units, bottom base is 10 units, and it has an altitude of 2.
we can just get the area of both, sum them up, and that's the area of the figure.
The way to solve the question is by dividing 2 and 32 = 16
2 ≤ 2w +4 ≤ 12
Subtract 4 from all 3 terms:
-2 ≤ 2w ≤ 8
Divide all 3 terms by 2:
-1 ≤ w ≤4
You can solve for the velocity and position functions by integrating using the fundamental theorem of calculus:
<em>a(t)</em> = 40 ft/s²
<em>v(t)</em> = <em>v </em>(0) + ∫₀ᵗ <em>a(u)</em> d<em>u</em>
<em>v(t)</em> = -20 ft/s + ∫₀ᵗ (40 ft/s²) d<em>u</em>
<em>v(t)</em> = -20 ft/s + (40 ft/s²) <em>t</em>
<em />
<em>s(t)</em> = <em>s </em>(0) + ∫₀ᵗ <em>v(u)</em> d<em>u</em>
<em>s(t)</em> = 10 ft + ∫₀ᵗ (-20 ft/s + (40 ft/s²) <em>u</em> ) d<em>u</em>
<em>s(t)</em> = 10 ft + (-20 ft/s) <em>t</em> + 1/2 (40 ft/s²) <em>t</em> ²
<em>s(t)</em> = 10 ft - (20 ft/s) <em>t</em> + (20 ft/s²) <em>t</em> ²
The answer is 75% because 150/200 converted to a percent is 75%
150/200= 0.75
0.75 x 100 = 75%
