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Simora [160]
2 years ago
15

the grid below is made up of squares with sides of 1cm draw a rectangle with an area of 12 cm squared

Mathematics
1 answer:
Ann [662]2 years ago
4 0

Answer:

6 is length and 2 is width.

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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
Zoe just lit a new candle and then let it burn all the way down to nothing. The length
NikAS [45]

Answer: i thought you were telling people what was happening in your home not a question

Step-by-step explanation:

3 0
2 years ago
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Please tell me how o do this
larisa86 [58]

Answer:

you might have to use an app that scans that specific problem :)

Step-by-step explanation:

5 0
3 years ago
Find the average rate of change of the function f(x), represented by the graph, over the interval [0, 3]. Calculate the average
Over [174]

Answer:

[f(3) - f(0)]/(3-0)

[f(3) - f(0)]/3

7 0
3 years ago
64 ft of rope weighs 20 pounds 28 ft of rope weighs x pounds​
castortr0y [4]

Answer

89.6

Step-by-step explanation:

Each foot of rope weighs 3.2 so then mutiplied 3.2 by 28 and got that

4 0
3 years ago
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