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Kazeer [188]
3 years ago
5

1. Determine if the polygons are similar.

Mathematics
1 answer:
nirvana33 [79]3 years ago
4 0
Yes they’re similar. The scale factor is 2:1
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In P2, find the change-of-coordinates matrix from the basis B = {1 − 3t 2 , 2 + t − 5t 2 , 1 + 2t} to the standard basis of P2.
Serjik [45]

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 :

M = \left[\begin{array}{ccc}1&2&1\\0&1&2\\-3&-5&0\end{array}\right]

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;

\left[\begin{array}{ccc}1&2&1\\0&1&2\\-3&-5&0\end{array}\right] \left[\begin{array}{ccc}D\\E\\F\end{array}\right] = \left[\begin{array}{ccc}D+2E+F\\E+2F\\-3D-5E\end{array}\right]

The change of coordinate matrix is therefore,

M = \left[\begin{array}{ccc}1&2&1\\0&1&2\\-3&-5&0\end{array}\right]

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]

3 0
2 years ago
Daisy has a marble collection in her room the ratio of blue marbles to red marbles are 4 : 7 if she has 24 blue marbles how many
Masteriza [31]

Answer:

The answer is 24:42

Step-by-step explanation:

All you have to do is multiply 7 by 6 because for every red marbles there are 6 marbles.

Hopes this helps!!

4 0
2 years ago
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Simplify the expression 14 + 5(x+3)-7
Alenkasestr [34]
14 + 5(x+3)-7
14 + 5x +15 -7
5x + 22
8 0
2 years ago
What is 812 divided by 14
Gnesinka [82]
58 is 812 divided by 14
4 0
3 years ago
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The volume V (in cubic feet) of a right cylinder with a height of 3 feet and radius r (in feet) is given by V=3πr2. Solve the fo
Kitty [74]

Answer:

r=\sqrt{\frac{V}{3\pi}}\\\\r\approx 5.00\ ft

Step-by-step explanation:

-The volume of a cylinder is given by the formula:

V=3\pi r^2

#We make r the subject of the formula:

V=3\pi r^2\\\\r^2=\frac{V}{3\pi}\\\\r=\sqrt{\frac{V}{3\pi}}

#We then substitute for the stated volume and solve for r:

r=\sqrt{\frac{V}{3\pi}}, V=236\\\\\therefore r=r=\sqrt{\frac{236}{3\pi}}\\\\r=5.00404\approx\ 5.00\ ft

Hence, the cylinder's radius is approximately 5.00 ft

5 0
3 years ago
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