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frozen [14]
3 years ago
9

An anthropology graduate student measures the floor of a round hut and calculates that it has an area of 12.56 square meters. Wh

at is the floors diameter ?
Mathematics
1 answer:
STALIN [3.7K]3 years ago
4 0

Answer:

The diameter of the room is 4 m.

Step-by-step explanation:

Since the hut is round we can assume that the floor is a circle, so in order to find the diameter of the floor we need to use the circle's area which is given by:

circle area = π*r²

In this case we have the area of the floor, so we can solve for "r". We have:

12.56 = π*r²

π*r² = 12.56

r² = 12.56/π

r² = 12.56/3.14 = 4

r = sqrt(4) = 2 m

The diameter is 2*r so the diameter of this room is 4 m.

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Infinite number of solutions.

Step-by-step explanation:

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Let a matrix A=\left[\begin{array}{ccc}5&4&5\\1&1&2\\2&1&-1\end{array}\right] and B=\left[\begin{array}{ccc}-1\\1\\-3\end{array}\right]

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Apply R_1\rightarrow R_1-4R_2 and R_3\rightarrow R_3-2R_2

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

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\left[\begin{array}{ccc}1&0&1\\0&1&1\\0&0&-2\end{array}\right]:\left[\begin{array}{ccc}-5\\6\\1\end{array}\right]

Apply R_3\rightarrow- \frac{1}{2} and R_2\rightarrow R_2-R_3

\left[\begin{array}{ccc}1&0&1\\0&1&0\\0&0&1\end{array}\right]:\left[\begin{array}{ccc}-5\\\frac{13}{2}\\-\frac{1}{2}\end{array}\right]

Apply R_1\rightarrow R_1-R_3

\left[\begin{array}{ccc}1&0&0\\0&1&0\\0&0&1\end{array}\right]:\left[\begin{array}{ccc}-\frac{9}{2}\\\frac{13}{2}\\-\frac{1}{2}\end{array}\right]

Rank of matrix A and B are equal.Therefore, matrix A has infinite number of solutions.

Therefore, rank of matrix is equal to rank of B.

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