Answer:
31.5 $
Step-by-step explanation:
First lets se how much 1 pound of pasta costs in the store. We do this dividing the price for 8 pounds over those 8 pounds:
12/8 = $1.5 each pound
As 21 pounds are needed:
$1.5 * 21 = $31.5
30 seconds for the whole length, so 1 min for 2 lengths meaning 2 • 10 = 20 lengths
You know that
so
.
Area of a shaded region is:
![$A=\int\limits_0^k\dfrac{y^2}{4}\,dy=\frac{1}{4}\int\limits_0^ky^2\,dy=\frac{1}{4}\left[\frac{y^3}{3}\right]_0^k=\frac{1}{4}\left[\frac{k^3}{3}-\frac{0^3}{3}\right]=\frac{1}{4}\cdot\dfrac{k^3}{3}=\boxed{\frac{k^3}{12}}](https://tex.z-dn.net/?f=%24A%3D%5Cint%5Climits_0%5Ek%5Cdfrac%7By%5E2%7D%7B4%7D%5C%2Cdy%3D%5Cfrac%7B1%7D%7B4%7D%5Cint%5Climits_0%5Eky%5E2%5C%2Cdy%3D%5Cfrac%7B1%7D%7B4%7D%5Cleft%5B%5Cfrac%7By%5E3%7D%7B3%7D%5Cright%5D_0%5Ek%3D%5Cfrac%7B1%7D%7B4%7D%5Cleft%5B%5Cfrac%7Bk%5E3%7D%7B3%7D-%5Cfrac%7B0%5E3%7D%7B3%7D%5Cright%5D%3D%5Cfrac%7B1%7D%7B4%7D%5Ccdot%5Cdfrac%7Bk%5E3%7D%7B3%7D%3D%5Cboxed%7B%5Cfrac%7Bk%5E3%7D%7B12%7D%7D%20)
so k:
![\dfrac{k^3}{12}=\dfrac{9}{4}\\\\\\k^3=\dfrac{9\cdot12}{4}\\\\\\k^3=9\cdot3\\\\k^3=3^3\quad|\sqrt[3]{(\ldots)}\\\\\boxed{k=3}](https://tex.z-dn.net/?f=%5Cdfrac%7Bk%5E3%7D%7B12%7D%3D%5Cdfrac%7B9%7D%7B4%7D%5C%5C%5C%5C%5C%5Ck%5E3%3D%5Cdfrac%7B9%5Ccdot12%7D%7B4%7D%5C%5C%5C%5C%5C%5Ck%5E3%3D9%5Ccdot3%5C%5C%5C%5Ck%5E3%3D3%5E3%5Cquad%7C%5Csqrt%5B3%5D%7B%28%5Cldots%29%7D%5C%5C%5C%5C%5Cboxed%7Bk%3D3%7D)
Answer: No
Step-by-step explanation:
The c kind of cut off, but you can use slopes to figure it out. The rule for a perpendicular slope is the opposite reciprocal. Assuming that C is the right angle, since right triangles typically work that way, we can figure out the slopes for ac and bc. The slopes are not reciprocals:
AC= -5/2
BC= -1/3
This isn't a right triangle because the lines are not perpendicular.
