Flexural strength is a measure of a material's ability to resist failure in bending. The accompanying data are on flexural strength of concrete (in MegaPascal, MPa, where 1 Pa (Pascal) = 1.45 cross 10❝4 psi):

5.7 7.2 7.3 6.3 8.1 6.8 7.0 7.6 6.8 6.5 7.0 6.3 7.9 9.0
8.2 8.7 7.8 9.7 7.4 7.7 9.7 7.8 7.7 11.6 11.4 11.8 10.9
(a) Construct a stem-and-leaf display of the data. (Enter numbers from smallest to largest separated by spaces. Enter NONE for stems with no values.)

Stem   Leaf

5       |  7

6       | 3 3 5 8 8

7       | 0 0 2 3 4 6 7 7 8 8 9

8       | 1 2 7

9       | 0 7 7

10     | 9

11      | 4 6 8

Notation: 5|7 means 5.7 and 11|4. means 11.4

Step-by-step explanation:

For this case we have the following data:

5.7 7.2 7.3 6.3 8.1 6.8 7.0 7.6 6.8 6.5 7.0 6.3 7.9 9.0  8.2 8.7 7.8 9.7 7.4 7.7 9.7 7.8 7.7 11.6 11.4 11.8 10.9

The first step on this case is order the dataset on increasing way:

5.7  6.3  6.3  6.5  6.8  6.8  7.0  7.0  7.2  7.3  7.4  7.6  7.7  7.7  7.8  7.8  7.9  8.1  8.2  8.7  9.0  9.7  9.7 10.9 11.4 11.6 11.8

Then we can construct the stem leaf plot like this:

Stem   Leaf

5       |  7

6       | 3 3 5 8 8

7       | 0 0 2 3 4 6 7 7 8 8 9

8       | 1 2 7

9       | 0 7 7

10     | 9

11      | 4 6 8

Notation: 5|7 means 5.7 and 11|4. means 11.4

step-by-step explanation:

x^2 -12x + 36 + y^2 = 36

x^2 + y^2 = 12x

r^2 = 12rcos(theta)

r = 12 cos(theta)

point a is the center of the circle that passes through points e, f, and g and the center of the circle that passes through points x, y, and z.