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PSYCHO15rus [73]

3 years ago

6

Update for the first one

2 answers:

Zepler [3.9K]3 years ago

8 0

Answer is x+2.5 Hope it helped

PSYCHO15rus [73]3 years ago

7 0

Answer:

y = x + 2.5

Step-by-step explanation:

slope = (y2-y1)/(x2-x1) where the variables indicate the coordinates of the two points

slope = (2.5-1.5)/(0+1) = 1

equation = y-y1 = m(x-x1)

y - 2.5 = x

y = x + 2.5

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Let p0, p1, and p2 be the orthogonal polynomials described below, where the inner product on P4 is given by evaluation at -2, -1

Mamont248 [21]

Answer:

$\frac{51}{5}t$

Step-by-step explanation:

Let W = $(p_0, p_1, p_2)$ be orthogonal polynomials which is equal to $(4, 3t, t^2 -2)$ , which defines the inner products as

$(f,g)=f(-2)g(-2)+f(-1)g(-1)+f(0)g(0)+f(1)g(1)+f(2)g(2)$

Now, we find the orthogonal projection of $p=3t^3$ on W.

So the projection is

$Proj_W p = \frac{(p_0,p)}{(p_0,p_0)}p_0+\frac{(p_1,p)}{(p_1,p_1)}p_1+\frac{(p_2,p)}{(p_2,p_2)}p_2$

$(p_0,p)=p_0(-2)p(-2)+p_0(-1)p(-1)+p_0(0)p(0)+p_0(1)p(1)+p_0(2)p(2)$

$=4(-24)+4(-3)+4(0)+4(3)+4(24)=0$

$(p_0,p_0)=p_0(-2)p_0(-2)+p_0(-1)p_0(-1)+p_0(0)p_0(0)+p_0(1)p_0(1)+p_0(2)p_0(2)$

$=4(4)+4(4)+4(4)+4(4)+4(4)=80$

$(p_1,p)=p_1(-2)p(-2)+p_1(-1)p(-1)+p_1(0)p(0)+p_1(1)p(1)+p_1(2)p(2)$

$=(-6)(-24)+(-3)(-3)+0(0)+3(3)+6(24)=306$

$(p_1,p_1)=p_1(-2)p_1(-2)+p_1(-1)p_1(-1)+p_1(0)p_1(0)+p_1(1)p_1(1)+p_1(2)p_1(2)$

$=(-6)(-6)+(-3)(-3)+0(0)+3(3)+6(6)=90$

$(p_2,p)=p_2(-2)p(-2)+p_2(-1)p(-1)+p_2(0)p(0)+p_2(1)p(1)+p_2(2)p(2)$

$=2(-24)+(-1)(-3)+(-2)(0)+(-1)(3)+2(24)=0$

$(p_2,p_2)=p_2(-2)p_2(-2)+p_2(-1)p_2(-1)+p_2(0)p_2(0)+p_2(1)p_2(1)+p_2(2)p_2(2)$

$=(2)(2)+(-1)(-1)+(-2)(-2)+(-1)(-1)+2(2)=14$

Therefore,

$Proj_W p = \frac{(p_0,p)}{(p_0,p_0)}p_0+\frac{(p_1,p)}{(p_1,p_1)}p_1+\frac{(p_2,p)}{(p_2,p_2)}p_2$

$=\frac{0}{80}(4)+\frac{306}{90}(3t)+\frac{0}{14}(t^2-2)$

$=\frac{51}{5}t$

6 0

3 years ago

Complete the statements to find 8 divided by 0.01

Phoenix [80]

Use a calculator if you want to see how it works
8÷0.01=800

8 0

3 years ago

Which property was used to simplify the expression? <br> 3c+9+4c=3c+4c+9

xenn [34]

Answer:

It seems to be the Commutative Property of Addition,

Where the order of elements can be changed without affecting the sum.

But state that $3c+9+4c=3c+4c+9$ is an equation.

3 0

3 years ago

HELPP PLEASEEEEEE!!!!!

SSSSS [86.1K]

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I need help please, mutiply chose picking irrational number

aksik [14]

Here i hope this helps you with the problem

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