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VMariaS [17]
3 years ago
10

Find angle picture below

Mathematics
1 answer:
lesantik [10]3 years ago
4 0

Answer:

T = 67.5

V = 22.5

Step-by-step explanation:

The Sum of triangle angles = 180

180 = W + T + V

180 = 90 + 3X + X

X = 22.5

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Consider the linear transformation T from V = P2 to W = P2 given by T(a0 + a1t + a2t2) = (2a0 + 3a1 + 3a2) + (6a0 + 4a1 + 4a2)t
Svet_ta [14]

Answer:

[T]EE=\left[\begin{array}{ccc}2&3&3\\6&4&4\\-2&3&4\end{array}\right]

Step-by-step explanation:

First we start by finding the dimension of the matrix [T]EE

The dimension is : Dim (W) x Dim (V) = 3 x 3

Because the dimension of P2 is the number of vectors in any basis of P2 and that number is 3

Then, we are looking for a 3 x 3 matrix.

To find [T]EE we must transform the vectors of the basis E and then that result express it in terms of basis E using coordinates and putting them into columns. The order in which we transform the vectors of basis E is very important.

The first vector of basis E is e1(t) = 1

We calculate T[e1(t)] = T(1)

In the equation : 1 = a0

T(1)=(2.1+3.0+3.0)+(6.1+4.0+4.0)t+(-2.1+3.0+4.0)t^{2}=2+6t-2t^{2}

[T(e1)]E=\left[\begin{array}{c}2&6&-2\\\end{array}\right]

And that is the first column of [T]EE

The second vector of basis E is e2(t) = t

We calculate T[e2(t)] = T(t)

in the equation : 1 = a1

T(t)=(2.0+3.1+3.0)+(6.0+4.1+4.0)t+(-2.0+3.1+4.0)t^{2}=3+4t+3t^{2}

[T(e2)]E=\left[\begin{array}{c}3&4&3\\\end{array}\right]

Finally, the third vector of basis E is e3(t)=t^{2}

T[e3(t)]=T(t^{2})

in the equation : a2 = 1

T(t^{2})=(2.0+3.0+3.1)+(6.0+4.0+4.1)t+(-2.0+3.0+4.1)t^{2}=3+4t+4t^{2}

Then

[T(t^{2})]E=\left[\begin{array}{c}3&4&4\\\end{array}\right]

And that is the third column of [T]EE

Let's write our matrix

[T]EE=\left[\begin{array}{ccc}2&3&3\\6&4&4\\-2&3&4\end{array}\right]

T(X) = AX

Where T(X) is to apply the transformation T to a vector of P2,A is the matrix [T]EE and X is the vector of coordinates in basis E of a vector from P2

For example, if X is the vector of coordinates from e1(t) = 1

X=\left[\begin{array}{c}1&0&0\\\end{array}\right]

AX=\left[\begin{array}{ccc}2&3&3\\6&4&4\\-2&3&4\end{array}\right]\left[\begin{array}{c}1&0&0\\\end{array}\right]=\left[\begin{array}{c}2&6&-2\\\end{array}\right]

Applying the coordinates 2,6 and -2 to the basis E we obtain

2+6t-2t^{2}

That was the original result of T[e1(t)]

8 0
3 years ago
Plot the points (0,1), (-1,3), (2, -3) and describe the resulting graph.
ivanzaharov [21]

check the picture below.

6 0
3 years ago
Kayla has 18 bottles of bubbles. She wants to give 2 bottles to each of her 6 friends. How many bottles will she have left over?
MatroZZZ [7]

Answer: she would have 6 bottles left, (18/2)/6

Step-by-step explanation:

she has 18 bottles, when you divide it by two, she could give two bottles to 9 people. but, she only wants to give it to 6 friends. meaning that she would be left with 3 pairs of bubbles. as in, 6 bottles.

8 0
2 years ago
The area of Hawaii is 40.47x100 square kilometers. What is Hawaii's area?
Gemiola [76]

40.47×100=4047 so just multiply it and the the answer is 4047

7 0
3 years ago
Choose the equations that are not linear equations. - x - y = 2, x^2 + y = 4, x/2 - y^3 = 1, x = 5
tekilochka [14]

Answer:

  • x^2 + y = 4
  • x/2 - y^3 = 1

Step-by-step explanation:

Any equation with a product of variables, or with a variable in an exponent or denominator, is <em>not a linear equation</em>. Here, "product of variables" includes powers and roots—any expression with an exponent other than 1, or a total of exponents other than 1.

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3 years ago
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