Answer:
2 units
Step-by-step explanation:
The length of VW is just the distance between the two coordinates. You could use the distance formula, or an easier and faster way would be to recognize that since both points have the same y-coordinate, the distance between them will just be the distance of the x-coordinates. The absolute value of -4 and -2 is 2, so the length of VW is 2 units.
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1. Use p to find the circumference of a circle 2. Use p to find the area of a circle 3. Find the area of a parallelogram 4. Find the area of a triangle 5. Convert square units In Section 4.2, we again looked at the perimeter of a straight-edged figure. The distance around the outside of a circle is closely related to this concept of perimeter. We call the perimeter of a circle the circumference. 341 Example 1 Finding the Circumference of a Circle A circle has a diameter of 4.5 ft, as shown in Figure 2. Find its circumference, using 3.14 for p. If your calculator has a key, use that key instead of a decimal approximation for p. p The circumference of a circle is the distance around that circle. Definitions: Circumference of a Circle Let’s begin by defining some terms. In the circle of Figure 1, d represents the diameter. This is the distance across the circle through its center (labeled with the letter O, for origin). The radius r is the distance from the center to a point on the circle. The diameter is always twice the radius. It was discovered long ago that the ratio of the circumference of a circle to its diameter always stays the same. The ratio has a special name. It is named by the Greek letter p (pi). Pi is approximately , or 3.14 rounded to two decimal places. We can write the following formula. 22 7 O d Radius Diameter Circumference Figure 1 C pd (1) Rules and Properties: Formula for the Circumference of a Circle NOTE The formula comes from the ratio p C d 4.5 ft Figure 2 342 CHAPTER 4 DECIMALS © 2001 McGraw-Hill Companies C 2pr (2) Rules and Properties: Formula for the Circumference of a Circle Example 2 Finding the Circumference of a Circle A circle has a radius of 8 in., as shown in Figure 3. Find its circumference using 3.14 for p. From Formula (2), C 2pr 2 3.14 8 in. 50.2 in. (rounded to one decimal place) 8 in. Figure 3 NOTE Because d 2r (the diameter is twice the radius) and C pd, we have C p(2r), or C 2pr. CHECK YOURSELF 2 Find the circumference of a circle with a radius of 2.5 in. NOTE Because 3.14 is an approximation for pi, we can only say that the circumference is approximately 14.1 ft. The symbol means approximately. NOTE If you want to approximate p, you needn’t worry about running out of decimal places. The value for pi has been calculated to over 100,000,000 decimal places on a computer (the printout was some 20,000 pages long). CHECK YOURSELF 1 A circle has a diameter of inches (in.). Find its circumference. 3 1 2 Note: In finding the circumference of a circle, you can use whichever approximation for pi you choose. If you are using a calculator and want more accuracy, use the key. There is another useful formula for the circumference of a circle. p By Formula (1), C pd 3.14 4.5 ft 14.1 ft (rounded to one decimal place) AREA AND CIRCUMFERENCE SECTION 4.4 343 © 2001 McGraw-Hill Companies Example 3 Finding Perimeter We wish to build a wrought-iron frame gate according to the diagram in Figure 4. How many feet (ft) of material will be needed? The problem can be broken into two parts. The upper part of the frame is a semicircle (half a circle). The remaining part of the frame is just three sides of a rectangle. Circumference (upper part) Perimeter (lower part) 4 5 4 13 ft Adding, we have 7.9 13 20.9 ft We will need approximately 20.9 ft of material. 1 2 3.14 5 ft 7.9 ft 5 ft 4 ft Figure 4 NOTE Using a calculator with a key, 1 2 5 p p Sometimes we will want to combine the ideas of perimeter and circumference to solve a problem. CHECK YOURSELF 3 Find the perimeter of the following figure. 6 yd 8 yd The number pi (p), which we used to find circumference, is also used in finding the area of a circle. If r is the radius of a circle, we have the following formula.
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The length of hypotenuse of an isosceles right triangle with two equal legs each 4 cm is given by Pythagorean theorem as follows.
√42+42.
=√32.
=4√2.
4√2 cm.
Okay so first of all you are going to cross multiply, which is simply multiplying diagonally across so (6x×5 and 25×3) then you just answer each part and set them equal to each other so (30x=75). Then you just divide 30 on each side which ends up being (x=2.5)
