Answer:
Your answer is correct; 2:1
Step-by-step explanation:
Answer:
The first graph will be correct.
Step-by-step explanation:
The given inequality is y + 5 < x .......... (1)
Now, straight-line y + 5 = x will be the reference line of the solution of the given inequality (1).
Now, y + 5 = x
⇒ x - y = 5
⇒
......... (2)
This equation is in intercept form and the straight line will pass through the points (5,0) and (0,-5)
Now, point (5,0) does not satisfy inequality (1) and hence, the line (2) is not included in the solution of the inequality (1).
Now, (0,0) point is above the line (2), but (0,0) point also does not satisfy inequality (1) as
.
Therefore, the solution of the inequality is below the line (2) but not including the line.
Hence, the first graph will be correct. (Answer)
Answer: did you just put the direction man cause i dont see anything there?
Answer:
Step-by-step explanation:
Let W =
be orthogonal polynomials which is equal to
, which defines the inner products as
![$(f,g)=f(-2)g(-2)+f(-1)g(-1)+f(0)g(0)+f(1)g(1)+f(2)g(2)$](https://tex.z-dn.net/?f=%24%28f%2Cg%29%3Df%28-2%29g%28-2%29%2Bf%28-1%29g%28-1%29%2Bf%280%29g%280%29%2Bf%281%29g%281%29%2Bf%282%29g%282%29%24)
Now, we find the orthogonal projection of
on W.
So the projection is
![$Proj_W p = \frac{(p_0,p)}{(p_0,p_0)}p_0+\frac{(p_1,p)}{(p_1,p_1)}p_1+\frac{(p_2,p)}{(p_2,p_2)}p_2$](https://tex.z-dn.net/?f=%24Proj_W%20p%20%3D%20%5Cfrac%7B%28p_0%2Cp%29%7D%7B%28p_0%2Cp_0%29%7Dp_0%2B%5Cfrac%7B%28p_1%2Cp%29%7D%7B%28p_1%2Cp_1%29%7Dp_1%2B%5Cfrac%7B%28p_2%2Cp%29%7D%7B%28p_2%2Cp_2%29%7Dp_2%24)
![$(p_0,p)=p_0(-2)p(-2)+p_0(-1)p(-1)+p_0(0)p(0)+p_0(1)p(1)+p_0(2)p(2)$](https://tex.z-dn.net/?f=%24%28p_0%2Cp%29%3Dp_0%28-2%29p%28-2%29%2Bp_0%28-1%29p%28-1%29%2Bp_0%280%29p%280%29%2Bp_0%281%29p%281%29%2Bp_0%282%29p%282%29%24)
![$=4(-24)+4(-3)+4(0)+4(3)+4(24)=0$](https://tex.z-dn.net/?f=%24%3D4%28-24%29%2B4%28-3%29%2B4%280%29%2B4%283%29%2B4%2824%29%3D0%24)
![$(p_0,p_0)=p_0(-2)p_0(-2)+p_0(-1)p_0(-1)+p_0(0)p_0(0)+p_0(1)p_0(1)+p_0(2)p_0(2)$](https://tex.z-dn.net/?f=%24%28p_0%2Cp_0%29%3Dp_0%28-2%29p_0%28-2%29%2Bp_0%28-1%29p_0%28-1%29%2Bp_0%280%29p_0%280%29%2Bp_0%281%29p_0%281%29%2Bp_0%282%29p_0%282%29%24)
![$=4(4)+4(4)+4(4)+4(4)+4(4)=80$](https://tex.z-dn.net/?f=%24%3D4%284%29%2B4%284%29%2B4%284%29%2B4%284%29%2B4%284%29%3D80%24)
![$(p_1,p)=p_1(-2)p(-2)+p_1(-1)p(-1)+p_1(0)p(0)+p_1(1)p(1)+p_1(2)p(2)$](https://tex.z-dn.net/?f=%24%28p_1%2Cp%29%3Dp_1%28-2%29p%28-2%29%2Bp_1%28-1%29p%28-1%29%2Bp_1%280%29p%280%29%2Bp_1%281%29p%281%29%2Bp_1%282%29p%282%29%24)
![$=(-6)(-24)+(-3)(-3)+0(0)+3(3)+6(24)=306$](https://tex.z-dn.net/?f=%24%3D%28-6%29%28-24%29%2B%28-3%29%28-3%29%2B0%280%29%2B3%283%29%2B6%2824%29%3D306%24)
![$(p_1,p_1)=p_1(-2)p_1(-2)+p_1(-1)p_1(-1)+p_1(0)p_1(0)+p_1(1)p_1(1)+p_1(2)p_1(2)$](https://tex.z-dn.net/?f=%24%28p_1%2Cp_1%29%3Dp_1%28-2%29p_1%28-2%29%2Bp_1%28-1%29p_1%28-1%29%2Bp_1%280%29p_1%280%29%2Bp_1%281%29p_1%281%29%2Bp_1%282%29p_1%282%29%24)
![$=(-6)(-6)+(-3)(-3)+0(0)+3(3)+6(6)=90$](https://tex.z-dn.net/?f=%24%3D%28-6%29%28-6%29%2B%28-3%29%28-3%29%2B0%280%29%2B3%283%29%2B6%286%29%3D90%24)
![$(p_2,p)=p_2(-2)p(-2)+p_2(-1)p(-1)+p_2(0)p(0)+p_2(1)p(1)+p_2(2)p(2)$](https://tex.z-dn.net/?f=%24%28p_2%2Cp%29%3Dp_2%28-2%29p%28-2%29%2Bp_2%28-1%29p%28-1%29%2Bp_2%280%29p%280%29%2Bp_2%281%29p%281%29%2Bp_2%282%29p%282%29%24)
![$=2(-24)+(-1)(-3)+(-2)(0)+(-1)(3)+2(24)=0$](https://tex.z-dn.net/?f=%24%3D2%28-24%29%2B%28-1%29%28-3%29%2B%28-2%29%280%29%2B%28-1%29%283%29%2B2%2824%29%3D0%24)
![$(p_2,p_2)=p_2(-2)p_2(-2)+p_2(-1)p_2(-1)+p_2(0)p_2(0)+p_2(1)p_2(1)+p_2(2)p_2(2)$](https://tex.z-dn.net/?f=%24%28p_2%2Cp_2%29%3Dp_2%28-2%29p_2%28-2%29%2Bp_2%28-1%29p_2%28-1%29%2Bp_2%280%29p_2%280%29%2Bp_2%281%29p_2%281%29%2Bp_2%282%29p_2%282%29%24)
![$=(2)(2)+(-1)(-1)+(-2)(-2)+(-1)(-1)+2(2)=14$](https://tex.z-dn.net/?f=%24%3D%282%29%282%29%2B%28-1%29%28-1%29%2B%28-2%29%28-2%29%2B%28-1%29%28-1%29%2B2%282%29%3D14%24)
Therefore,
![$Proj_W p = \frac{(p_0,p)}{(p_0,p_0)}p_0+\frac{(p_1,p)}{(p_1,p_1)}p_1+\frac{(p_2,p)}{(p_2,p_2)}p_2$](https://tex.z-dn.net/?f=%24Proj_W%20p%20%3D%20%5Cfrac%7B%28p_0%2Cp%29%7D%7B%28p_0%2Cp_0%29%7Dp_0%2B%5Cfrac%7B%28p_1%2Cp%29%7D%7B%28p_1%2Cp_1%29%7Dp_1%2B%5Cfrac%7B%28p_2%2Cp%29%7D%7B%28p_2%2Cp_2%29%7Dp_2%24)
![$=\frac{0}{80}(4)+\frac{306}{90}(3t)+\frac{0}{14}(t^2-2)$](https://tex.z-dn.net/?f=%24%3D%5Cfrac%7B0%7D%7B80%7D%284%29%2B%5Cfrac%7B306%7D%7B90%7D%283t%29%2B%5Cfrac%7B0%7D%7B14%7D%28t%5E2-2%29%24)
![$=\frac{51}{5}t$](https://tex.z-dn.net/?f=%24%3D%5Cfrac%7B51%7D%7B5%7Dt%24)
the highest score is obviously going to be 2125 because that is 100%