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photoshop1234 [79]
3 years ago
14

Need help with this question ASAP! 20 points!

Mathematics
1 answer:
Delvig [45]3 years ago
4 0

Answer:

6√3

Step-by-step explanation:

Use the sin formula, which is sin = opp / hyp

sin 60 = x / 12

x = 12 sin 60

x = 6√3

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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
3 years ago
40 percent of students survey said that they are night owls . If 300 students said that they are night owls how many students we
sattari [20]

Based on the calculations that 300 is 40%, 375 is considered 50% or halfway.. in this case, we must multiply 375 by 2 and we will discover how many students were surveyed:

375 x 2 = 750

7 0
2 years ago
Help I need the intercept please.
Gnesinka [82]
The x-intercept would be (6,0)
8 0
2 years ago
Determine whether the equation below has a one solutions, no solutions, or an infinite number of solutions. Afterwards, determin
KengaRu [80]
Infinite number of solutions. x=4 and x=8
7 0
3 years ago
PLEASE HELP ASAP ILL REALLY APPRECIATE IT
sesenic [268]

Answer:

see below

Step-by-step explanation:

2.5 = 2 5/10 = 250%

40% = .40 = 40/100 = 4/10 =2/5

220% = 220/100 = 2 20/100 = 2 2/10 = 2 1/5

1/4 = 25/100 = 25%

4% = 4/100 = .04

3 0
3 years ago
Read 2 more answers
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