9514 1404 393
Answer:
- 85°
- 60°
Step-by-step explanation:
1. Angle JKL is half the measure of the intercepted arc JK.
(1/2)JK = 1/2(360° -190°) = (1/2)(170°) = 85°
angle JKL is 85°
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2. The angle between tangents is the supplement of the intercepted arc.
angle JKL = 180° -(360° -240°)
angle JKL = 60°
Answer:
13
Step-by-step explanation:
Answer:
a. 12 feet b. 12 feet 0.5 inches c. 8.33 %
Step-by-step explanation:
a. How far out horizontally on the ground will it protrude from the building?
Since the rise to run ratio is 1:12 and the building is 12 inches off the ground, let x be the horizontal distance the ramp protrudes.
So, by ratios rise/run = 1/12 = 12/x
1/12 = 12/x
x = 12 × 12
x = 144 inches
Since 12 inches = 1 foot, 144 inches = 144 × 1 inch = 144 × 1 foot/12 inches = 12 feet
b. How long should the ramp be?
The length of the ramp, L is gotten from Pythagoras' theorem since the ramp is a right-angled triangle with sides 12 inches and 144 inches respectively.
So, L = √(12² + 144²)
= √[12² + (12² × 12²)]
= 12√(1 + 144)
= 12√145
= 12 × 12.042
= 144.5 inches
Since 12 inches = 1 foot, 144.5 inches = 144 × 1 inch + 0.5 inches = 144 × 1 foot/12 inches + 0.5 inches = 12 feet 0.5 inches
c. What percent grade is the ramp?
The percentage grade of the ramp = rise/run × 100 %
= 12 inches/144 inches × 100 %
= 1/12 × 100 %
= 0.0833 × 100 %
= 8.33 %
Answer:
Step-by-step explanation:
Mr. Rives' rotating sprinkler waters his lawn up to a radius of 7 feet. The formula for determining the area of a circle is expressed as
Area = πr²
Where
π is a constant whose value is 3.14.
r represents the radius if the circle.
The area covered by one of Mr. Rives' rotating sprinkler would be
3.14 × 7² = 3.14 × 49 = 153.86ft²
Therefore, the maximum area of lawn that two sprinklers can cover would be
153.86 × 2 = 307.72 ft²
Complete the square by adding the square of half of four to both sides (4)
x^2+y^2-4y+4=4
x^2+(y-2)^2=4
