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lys-0071 [83]
3 years ago
6

A triangle is inside a circle where the triangles base is on the circles diameter. What is the area of the shaded region where t

he base is 16 ft?
Mathematics
1 answer:
DaniilM [7]3 years ago
8 0
I believe it’s approximately 19.63
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If x=5 and y=−2, evaluate the following expression:10+5xy​
Fittoniya [83]

Answer:

-90

Step-by-step explanation:

10+5×5×(-2)

10+25×(-2)

10+(-100)

10-100

-90

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3 years ago
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Find a formula for the least squares solution of ax=b when the columns of a are orthonormal1 .
neonofarm [45]
Let \mathbf A be a rectangular m\times n matrix with column vectors \mathbf a_1,\ldots,\mathbf a_n, i.e.

\mathbf A=\begin{bmatrix}\mathbf a_1&\cdots&\mathbf a_n\end{bmatrix}

Then we have

\mathbf A^\top=\begin{bmatrix}\mathbf a_1&\cdots&\mathbf a_n\end{bmatrix}^\top

and the product of the two is

\mathbf A^\top\mathbf A=\begin{bmatrix}\mathbf a_1\cdot\mathbf a_1&\mathbf a_1\cdot\mathbf a_2&\cdots&\mathbf a_1\cdot\mathbf a_n\\\mathbf a_2\cdot\mathbf a_1&\mathbf a_2\cdot\mathbf a_2&\cdots&\mathbf a_2\cdot\mathbf a_n\\\vdots&\vdots&\ddots&\vdots\\\mathbf a_n\cdot\mathbf a_1&\mathbf a_n\cdot\mathbf a_2&\cdots&\mathbf a_n\cdot\mathbf a_n\end{bmatrix}

Because the columns of \mathbf A are orthonormal, we have

\mathbf a_i\cdot\mathbf a_j=\begin{cases}1&\text{for }i=j\\0&\text{for }i\neq j\end{cases}

which means \mathbf A^\top\mathbf A reduces to an n\times n matrix with ones along the diagonal and zero everywhere else, i.e.

\mathbf A^\top\mathbf A=\begin{bmatrix}1&0&\cdots&0\\0&1&\cdots&0\\\vdots&\vdots&\ddots&\vdots\\0&0&\cdots&1\end{bmatrix}=\mathbf I_n

where \mathbf I denotes the identity matrix. This means the solution to \mathbf{Ax}=\mathbf b is given by

\mathbf A^\top(\mathbf{Ax})=\mathbf A^\top\mathbf b\implies(\underbrace{\mathbf A^\top\mathbf A}_{\mathbf I})\mathbf x=\mathbf A^\top\mathbf b\implies\mathbf x=\mathbf A^\top\mathbf b
6 0
3 years ago
10) Solve the system by the elimination method. Check the solution.
Galina-37 [17]

Answer:

x =2, y = 2

Step-by-step explanation:

x + 2y = 6....(1) \\ -x + 5y = 8....(2) \\  adding \: equations \: (1) \: and \: (2) \\ x + 2y = 6\\ -x + 5y = 8 \\  -  -  -  -  -  -  -   \\ 7y = 14 \\ y =  \frac{14}{7}  \\ \huge \red{ \boxed{ y = 2}} \\ substituting \: y = 2 \: in \: equation \: (1) \\ x + 2 \times 2 = 6 \\ x + 4 = 6 \\ x = 6 - 4 \\\huge \purple{ \boxed{ x = 2}} \\  \\ \huge \orange{ \boxed{(x, \: y) = (2, \: 2)}}

8 0
3 years ago
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Angela uses 7 1/2 inches each of 6 different colors of embroidery floss to make one friendship. Each package of the floss contai
Soloha48 [4]

Answer:

She can make 41 bracelets!:D

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Use the following function rule to find f(r+4). simplify your answer .. f(n)=n+4
Fudgin [204]
N=54........................
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3 years ago
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