There are 5 soft pretzels shared equally between 8 people. What fraction of a soft pretzel does each person receive?
1 answer:
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Complete Question:
In P2, find the change-of-coordinates matrix from the basis B = {1 − 3t² , 2+t− 5t² , 1 + 2t} to the standard basis C = {1, t, t²}. Then, write t² as a linear combination of the polynomials in B.
Answer:
The change of coordinate matrix is :
U = t² = 3 [1 − 3t²] - 2 [2+t− 5t²] + [1 + 2t]
Step-by-step explanation:
Let U = {D, E, F} be any vector with respect to Basis B
U = D [1 − 3t²] + E [2+t− 5t²] + F[1 + 2t]..............(*)
U = [D+2E+F]+ t[E+2F] + t²[-3D-5E]...................(**)
In Matrix form;
The change of coordinate matrix is therefore,
To find D, E, F in (**) such that U = t²
D + 2E + F = 0.................(1)
E + 2F = 0.........................(2)
-3D -5E = 1........................(3)
Substituting eqn (2) into eqn (1 )
D=3F...................................(4)
Substituting equations (2) and (4) into eqn (3)
-9F+10F=1
F = 1
Put the value of F into equations (2) and (4)
E = -2(1) = -2
D = 3(1) = 3
Substituting the values of D, E, and F into (*)
U = t² = 3 [1 − 3t²] - 2 [2+t− 5t²] + [1 + 2t]
The measure of each exterior angle is 60° and the polygon has 6 sides ⇒ 4th answer
Step-by-step explanation:
In a regular n-side polygon:
- All sides are equal in lengths
- All angles are equal in measure
- The measure of each interior angle =
- The measure of each exterior angle =
- The sum of interior angle and exterior angle at a vertex is 180°
∵ The measure of an interior angle of a regular polygon is 120°
∵ The sum of interior angle and exterior angle at a vertex = 180°
∴ The measure of each exterior angle = 180 - 120
∴ The measure of each exterior angle = 60°
∵ The measure of each exterior angle =
- Substitute the measure of the exterior angle by 60
∴
- By using cross multiplication
∴ 60 n = 360
- Divide both sides by 60
∴ n = 6
∴ The polygon has 6 sides
The measure of each exterior angle is 60° and the polygon has 6 sides
Learn more:
You can learn more about polygons in brainly.com/question/6281564
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