Answer:
Mark got 13 more points than Nick did
Step-by-step explanation:
Mark's score in all was: 487
Nick's score in all was: 474
<span>Surface Area =<span> (2 • <span>π <span>• r²) + (2 • <span>π • r • height)
</span></span></span></span></span>
<span>(2 • <span>π <span>• r²) is surface area of the "ends"
</span></span></span>
<span>(2 • <span>π <span>• r • height) is lateral area
</span></span></span>
<span>Lateral Area = 2 * PI * 2 * 7
</span>
<span>Lateral Area =28 * PI =
</span>
<span><span><span>87.9645943005 square inches</span></span></span><span><span><span>
</span>
</span>
</span>
Answer is B
Nothing to "solve" here. Just graph this absolute value function.
Note that if x=2 we get y = -4. Thus, (2,-4) is the vertex. Plot this point.
Now, starting from (2, -4), draw a line at a 45 degree angle to the horizontal.
Then draw a corresponding line on the other side of the y-axis. You're done!
Answer:
(8√2) / 15
Step-by-step explanation:
A curve bounded by the y-axis is represented by in terms of dy;

When the curve crosses the y-axis, x will be 0. In this case x is the function of t, so we have to solve for x(t) = 0;
0 = t^2 + 2t --- (1)
Solution(s) => t = 0, t = 2
dy = (1/2 * 1/√t)dt --- (2)
Our solutions (0, 2) are our limits. The area of the curve is in the form
, so now let's introduce the limits of integration, x(t) and dy/dt. Remember, dy/dt = (1/2 * 1/√t) (second equation). 1/2 * 1/√t can be rewritten as 1/2 * t^(-1/2)....
![A\:=\:\int _2^0\:\left(t^2-2t\right)\left(\frac{1}{2}t^{-\frac{1}{2}}\right)dt\\\\= \int _2^0\:\left(\frac{1}{2}t^{\frac{3}{2}}-t^{\frac{1}{2}}\right)dt\\\\= \left[\frac{t^{\frac{5}{2}}}{5}-\frac{2t^{\frac{3}{2}}}{3}\right]_2^0\\\\= 0\:-\:\left(\frac{4\sqrt{2}}{5}-\frac{4\sqrt{2}}{3}\right)\\\\= \frac{8\sqrt{2}}{15}](https://tex.z-dn.net/?f=A%5C%3A%3D%5C%3A%5Cint%20_2%5E0%5C%3A%5Cleft%28t%5E2-2t%5Cright%29%5Cleft%28%5Cfrac%7B1%7D%7B2%7Dt%5E%7B-%5Cfrac%7B1%7D%7B2%7D%7D%5Cright%29dt%5C%5C%5C%5C%3D%20%5Cint%20_2%5E0%5C%3A%5Cleft%28%5Cfrac%7B1%7D%7B2%7Dt%5E%7B%5Cfrac%7B3%7D%7B2%7D%7D-t%5E%7B%5Cfrac%7B1%7D%7B2%7D%7D%5Cright%29dt%5C%5C%5C%5C%3D%20%5Cleft%5B%5Cfrac%7Bt%5E%7B%5Cfrac%7B5%7D%7B2%7D%7D%7D%7B5%7D-%5Cfrac%7B2t%5E%7B%5Cfrac%7B3%7D%7B2%7D%7D%7D%7B3%7D%5Cright%5D_2%5E0%5C%5C%5C%5C%3D%200%5C%3A-%5C%3A%5Cleft%28%5Cfrac%7B4%5Csqrt%7B2%7D%7D%7B5%7D-%5Cfrac%7B4%5Csqrt%7B2%7D%7D%7B3%7D%5Cright%29%5C%5C%5C%5C%3D%20%5Cfrac%7B8%5Csqrt%7B2%7D%7D%7B15%7D)
Your solution is 8√2 / 15
Answer is 2 inches per hour.
12 inches/6 hours divided by 6 is 2 inches/ 1 hour.