What is 8.0622577483 rounded to nearest tenth?

it is 8.1

Step-by-step explanation:

if u see u round over or add 1 to the number if the number that is next to the number ur rounding is 5 or higher. and u do nothing when it is less than 5.

the tenth place is where the the zero is 0.0

and the number after is 6, so it is greater than 5, so it increases

8.1

Step-by-step explanation:

To round to the nearest tenth (the first decimal place), look at the number in the hundredth (the second decimal place) and round up or down. Since the number in the hundredths is a six, you round up.

You round down if the number is less than 5 and up if it is equal to or greater than 5.

(a) Applying T to p(t) = 2 - t + t ² gives

T ( p(t) ) = (t - 2) (2 - t + t ²) = -4 + 4t - 3t ² + t ³

(b) T is a linear transformation if for any p(t) and q(t) in P₂ and complex scalars a and b, the image of any linear combination of p and q is equal to the linear combination of the images of p and q. In other words,

T ( a p(t) + b q(t) ) = a T ( p(t) ) + b T ( q(t) )

Let

p(t) = α₀ + α₁ t + α₂ t ²

q(t) = β₀ + β₁ t + β₂ t ²

Compute the images of p and q :

T ( p(t) ) = (t - 2) (α₀ + α₁ t + α₂ t ²)

… = -2α₀ + (α₀ - 2α₁) t + (α₁ - 2α₂) t ² + α₂ t ³

Similarly,

T ( q(t) ) = -2β₀ + (β₀ - 2β₁) t + (β₁ - 2β₂) t ² + β₂ t ³

Then

a T ( p(t) ) + b T ( q(t) ) = a (-2α₀ + (α₀ - 2α₁) t + (α₁ - 2α₂) t ² + α₂ t ³) + b (-2β₀ + (β₀ - 2β₁) t + (β₁ - 2β₂) t ² + β₂ t ³)

… = c₀ + c₁ t + c₂ t ² + c₃ t ³

where

c₀ = -2 (a α₀ + b β₀)

c₁ = a (α₀ - 2α₁) + b (β₀ - 2β₁)

c₂ = a (α₁ - 2α₂) + b (β₁ - 2β₂)

c₃ = a α₂ + b β₂

Computing the image of a p(t) + b q(t) would give the same result; just multiply it by t - 2 and expand. This establishes that T is indeed linear.

(c) Find the image of each vector in the basis for P₂ :

T (1) = (t - 2) × 1 = t - 2

T (t ) = (t - 2) t = t ² - 2t

T (t ²) = (t - 2) t ² = t ³ - 2t ²

Then