Answer and Step-by-step explanation:
If my calculations are correct,
A. 17b = w
B. 867 = w
C. 3 bottles for 51 fluid ounces of water
For B and C, just plug in the values.
For A, it was 17 ounces for every bottle (b), so that's why it is multiplied together. This is then equal to w, the total volume of water in fluid ounces.
The slope is -0.25 or in fraction -1/4
Answer:
Step-by-step explanation:
So, our equation is:
In exponetial form, this looks like:
Now lets cube the 5:
Next, we can multiply the denominator on the right side by 5:
We need to now get x alone by adding 4 to both sides:
Finally, we divide by x's coefficent, 2, to get:
Hope this helps! :3
(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
No, because you can simplify it even more if you divide by 2.
2/2=1
and 6/2=3
2/6 in simplest form is 1/3.
