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Semenov [28]
3 years ago
15

You want to build a wheelchair ramp leading up to your house. Your front door is 2 feet higher than the driveway and you would l

ike the grade of the ramp to be 7%. (a) What is the angle, θ, that the ramp forms with the driveway? (Round your answer to three decimal places.) s ° (b) How long does the driveway have to be to build this ramp? (Round your answer to two decimal places.) s ft (c) How long will the ramp be? (Round your answer to two decimal places.)

Mathematics
1 answer:
Alenkasestr [34]3 years ago
4 0

Answer: (a) The angle the ramp forms with the driveway, s° = 4.004° (3 d.p)

(b) The driveway has to be, s = 28.57 ft

(c) The ramp will be 28.64 ft long

Step-by-step explanation:

First key thing to know is that the %grade of a ramp = rise/ramp run

%grade of a ramp = 7% = 0.07

(Kindly find attached a diagram to assist with understanding).

Also note that, <em>the ramp run is not the same as the ramp length</em>

(a) the angle, θ, is the angle of slope between the driveway and the ramp,

tan θ = 0.07,

θ = tan⁻¹ 0.07 = 4.004° (3 d.p)

(b) the length of the driveway (s) is the same as the length of the ramp run, so, %grade of a ramp = rise/ramp run

0.07 = 2/s

s = 2/0.07 = 28.57 ft (2 d.p)

(c) the length of the ramp can be found by using Pythagoras' theorem,

L = ramp length =\sqrt{rise^{2} + ramprun^{2} }

L = \sqrt{2^{2} +28.571^{2} }

L = \sqrt{820.3041}

L = 28.64 ft (2 d.p)

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Step-by-step explanation:

The side of the square = 2x^2 y

Now, AREA OF THE SQUARE = SIDE x SIDE

⇒ Area of the square  is:

(2x^2 y) \times (2x^2 y)\\=   (2x^2 y)^2   = 4x^4y^2

So, the area of the square is  4x^4y^2

Now, to find the area when x = -2 and y = 2

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⇒The area of the square when x  = -2 and y = 2 is 256 sq. units.

5 0
2 years ago
Two consecutive integers have a product of 12. What is the initial equation that would be used
Triss [41]

Answer:

x(x+1) = 12

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8 0
2 years ago
Please help, i need answers asap
sukhopar [10]

Two angles are complementary if their sum is 90°, they are supplementary if their sum is 180.

With this definition, you can easily check all the couples:

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3 years ago
the cost of manufacturing a computer part is related to the quantity produced, x, during a production run. When 100 parts are pr
8_murik_8 [283]

Answer:

C = 9x -600

Step-by-step explanation:

When the number of parts produced goes up by 500 from 100 to 600, the cost goes up $4500 from 300 to 4800. Thus the average cost of producing a part is $4500/500 = $9.

If that were the total cost of producing a part, then the first 100 parts would cost $9×100 = $900. They only cost $300, so $600 must be subtracted from the value 9x to get the cost.

... C = 9x -600

_____

<em>Check</em>

100 parts cost 9·100 -600 = 300 . . . agrees with problem statement

600 parts cost 9·600 -600 = 4800 . . . agrees with problem statement

_____

<em>Comment on the problem statement</em>

The initial statement tells you "cost ... related to the quantity produced." The question then asks you to "find an equation ... relating quantity produced to cost." The latter statement suggests you want the independent variable to be <em>cost</em>, not quantity. Here, we have made <em>quantity</em> be the independent variable, as suggested by the use of C= in the answer form.

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The answer is B, because to circumscribe a quadrilateral the sum of each two opposite angles must be 180
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