t he number of views expected to be four weeks from now can
be calculated using the equation:
F = P ( 1+i)^n
Where F is the future views
P is the present views
i is the percent increase in views
n is the number of weeks
F = 15 ( 1+ 0.22)^4
F = 33 views
The blank is equal to 3/14
(a) By the fundamental theorem of calculus,
<em>v(t)</em> = <em>v(0)</em> + ∫₀ᵗ <em>a(u)</em> d<em>u</em>
The particle starts at rest, so <em>v(0)</em> = 0. Computing the integral gives
<em>v(t)</em> = [2/3 <em>u</em> ³ + 2<em>u</em> ²]₀ᵗ = 2/3 <em>t</em> ³ + 2<em>t</em> ²
(b) Use the FTC again, but this time you want the distance, which means you need to integrate the <u>speed</u> of the particle, i.e. the absolute value of <em>v(t)</em>. Fortunately, for <em>t</em> ≥ 0, we have <em>v(t)</em> ≥ 0 and |<em>v(t)</em> | = <em>v(t)</em>, so speed is governed by the same function. Taking the starting point to be the origin, after 8 seconds the particle travels a distance of
∫₀⁸ <em>v(u)</em> d<em>u</em> = ∫₀⁸ (2/3 <em>u</em> ³ + 2<em>u</em> ²) d<em>u</em> = [1/6 <em>u</em> ⁴ + 2/3 <em>u</em> ³]₀⁸ = 1024
There seems to be a problem with your question - AEC does not create a triangle while ADE does.
As for finding x
Draw an imaginary line from C to D. 3^2+4^2=5^2, so take the square root to find CD=5. Now we know that CA is also 5. To find x, x^2+3^2=5^2, or x^2+9=25. Subtract 9 from both sides to get 16, and take the square root of both sides to get x=4.
