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Zepler [3.9K]
3 years ago
9

A recommendation for wheelchair ramps is that the rise-to-run ratio be no greater than 1:12. This ensures that the ramps are nav

igable by people in wheelchairs. If a business needs to install a concrete ramp to the entrance of their building, which is 12 inches off the ground, how long should the ramp be and how far out horizontally on the ground will it protrude from the building? Give answers in feet and inches, such as 5 feet, 4 inches. What percent grade is the ramp?
Mathematics
1 answer:
patriot [66]3 years ago
6 0

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 %

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Answer:

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Step-by-step explanation:

The slope is the change in y divided by the corresponding change in x:

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The slope of the line is zero.

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3 years ago
A cube has a volume of 2197 m^3. Its surface is to be painted. Each can of paint covers about 40 m^2. How many cans of paint are
Gelneren [198K]
<em>Volume= a³</em>
<em>a=edge</em>
<em>2197 = a³</em>
<em>=> a=13 m</em>
<em>Surface area=6a²=6*13²=6*169=1014 m²</em>
<em>\frac{1014}{40} = 25,35 ≈ 26</em>
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3 years ago
Find the sum of the series given in sigma notation.
Kryger [21]

Answer:

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Step-by-step explanation:

n = 7

k = 6

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put k = 7 in above eq. for finding first term

 a2 = 3(7) - 2 = 21 - 2 = 19

 a3 = 3 (8) - 2 = 24 - 2 = 22

16, 19 , 22, ...  //Arithmetic series formation

a1 = 16 , a2 = 19

d = a2 - a1 = 19 - 16 = 3 //Difference of first two terms

Using sum forumula for arithmetic series

sum = \frac{n}{2}(2a1 + (n-1)d)

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4 0
3 years ago
Find the distance between points M (6,16) and Z (-1,14) to the nearest tenth, please help step by step
insens350 [35]
The distance between 2 points P(a, b) and Q(c,d) is given by the formula:

\displaystyle{d= \sqrt{(b-d)^2+(a-c)^2}, 


Apply the formula for the points M(6, 16) and Z(-1, 14):

\displaystyle{d= \sqrt{(16-14)^2+(6-(-1))^2}= \sqrt{2^2+7^2}= \sqrt{4+49}= \sqrt{53}\approx 7.28

which rounded to the nearest tenth is 7.3 (units)

Answer: 7.3 units
3 0
3 years ago
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djyliett [7]
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8 0
3 years ago
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