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3 years ago

Convert the mixed numbers into improper fractions. Convert the improper fraction to mixed Numbers.

Mathematics

1 answer:

Alexxx [7]3 years ago

6 0

Answer:

13) 23/4 14) 13/2 15) 6 1/2 16) 2 7/12

Step-by-step explanation:

13) (4 x 5) + 3 = 23 -> 23/4

14) (2 x 6) + 1 = 13 -> 13/2

15) 13/2 = 6.5, then take the number on the left of the decimal so, 6, as your whole number. After that, multiply it by the denominator so 6 x 2 = 12, then subtract the 12 with the numerator given in the improper fraction so, 13-12 = 1. The answer you get (which is 1 in this case) will be your numerator in for the mixed fraction. -> 6 1/2

Note: the denominator always stays the same

16) 31/12 = 2.58... take the 2 as your whole number.

2(whole number) x 12(denominator) = 24

31 - 24 = 7

= 2 7/12

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See below for the examples of sectors and arcs of a circle

<h3>Area of sector of a circle</h3>

The area of a sector is calculated as:

$A = \frac{\theta}{360} * \pi r^2$ ---- when the angle is in degrees

$A = \frac{\theta}{2} *r^2$ ---- when the angle is in radians

Take for instance, we have the following problems involving sector areas

Calculate the area of a sector where the radius of the circle is 7, and

The central angle is 30 degrees
The central angle is π/12 rad
The central angle is 90 degrees
The central angle is π/4 rad
The central angle is 180 degrees

Using the above formulas, the sector areas are:

1. $A = \frac{30}{360}* \frac{22}{7} * 7^2 = 12.83$

2. $A = \frac{\pi}{12} * 7^2 = 12.83$

3. $A = \frac{90}{360}* \frac{22}{7} * 7^2 = 38.5$

4. $A = \frac{\pi}{2} * 7^2 = 38.5$

5. $A = \frac{180}{360}* \frac{22}{7} * 7^2 = 77$

<h3>Examples of arc length</h3>

The length of an arc is calculated as:

$L= \frac{\theta}{360} * 2\pi r$ ---- when the angle is in degrees

$L = r\theta$ ---- when the angle is in radians

Take for instance, we have the following problems involving arc lengths

Calculate the length of an arc where the radius of the circle is 7, and

The central angle is 30 degrees
The central angle is π/12 rad
The central angle is 90 degrees
The central angle is π/4 rad
The central angle is 180 degrees

Using the above formulas, the arc lengths are:

1. $L = \frac{30}{360}* 2 * \frac{22}{7} * 7 = 3.7$

2. $L = \frac{\pi}{12} * 7 = 3.7$

3. $L = \frac{90}{360}*2 * \frac{22}{7} * 7 = 11.0$

4. $L = \frac{\pi}{4} * 7 = 11$

5. $L = \frac{180}{360}*2 * \frac{22}{7} * 7 = 22$

<h3>Examples of the arcs of a circle</h3>

The examples include:

A parabolic path
Distance in a curve
Curved bridges
Pizza
Bows

Convert the mixed numbers into improper fractions. Convert the improper fraction to mixed Numbers. ​

Convert the mixed numbers into improper fractions. Convert the improper fraction to mixed Numbers.