Answer:
y = 9x + 10
Step-by-step explanation:
y = mx + b
Here, m is slope and b is y-intercept
y = 9x + 10
Using the Quadratic Function, Such Means x = - b + or - the square root of - 4 a c over 2 a.
After you do it you would get the answer :
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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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∠ KGH is equal to 77°. This is arrived at by using the knowledge of the total angles in Parallel Lines.
<h3>What are the total angles on a straight line?</h3>
According to the laws of lines and angles, the total number of angles that can exist on a straight line is 180°.
If ∠CED = 25° and ∠BFL = 78°, then: ∠KGH = 180-(25+78), which is equals 77°. This is because the total angles on a straight-line total 180°
<h3>What is ∠LKJ?</h3>
Recall that in angles in parallel lines:
- Corresponding Angles are always congruent,
- Alternate Angles are always congruent, and
- Interior According always sum up to 180°
Hence,
We can derive ∠LKJ because it is congruent with ∠BGJ.
To get ∠BGJ, we must get ∠LFH because both of them are interior angles and sum up to 180°.
To get ∠LFH, we must subtract ∠BFL from 180° because they are both angles on a straight line.
Hence ∠LFH = 180 - 78 = 102°
Recall that ∠LFH and ∠BGJ are interior angels. Hence
∠BGJ = 180 - 102 = 78°.
Since ∠BGJ is a corresponding ∠ with ∠LKJ, therefore
∠LKJ = 78°
<h3>
What is ∠ALM?</h3>
∠ALM is ∠BFL because they are both corresponding angles and are therefore congruent.
<h3>What are the solutions to section B?</h3>
- Because ∠ACB and ∠BAC are equal, therefore sides AB and BC are equal in length. We can tell that ∠ACB and ∠BAC are equal because the total angles in the triangle are equal to 180°
2. The name given to the triangle mentioned above is Obtuse
Triangle. This is because one of the angles exceeds 90°.
Learn more about angles in parallel lines at:
brainly.com/question/24607467
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Answer:
D pi/4, 3pi/4
Step-by-step explanation:
Differentiate the function then equal it to zero and solve for the interval (see attached workings)
