Mr. Gow needs to build a wheelchair access ramp for the school's auditorium. The ramp must rise a total of 3 feet to get from the ground to the entrance of the building. In order to follow the state building code, the angle formed by the ramp and the ground cannot exceed 4.75°. Mr. Gow plans from the planning department that call for the ramp to start 25 feet away from the building code?

a. Draw an appropiate diagram. Add all the measurements you can. What does Mr. Gow need to find?

b. According to the plan in part (a), what angle will the ramp make with the ground? Will the ramp be to code?

c. If Mr. Gow builds the ramp exactly to code, how long will the ramp be? In other words, at least how far from the building must the ramp start in order to∞ meet the building code? Show all work.

(NOT A MULTIPLE CHOICE)

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  a.  see below for diagram. Angle for the length; length for the angle

  b. 6.84°; not to code

  c. 36.1 ft

Step-by-step explanation:

a. The diagram is shown below. Mr. Gow needs to find the angle it makes in order to determine if it is up to code. Alternatively, Mr. Gow needs to find the required length for a ramp that meets code.

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b. The angle the ramp makes can be found using the tangent relation.

  Tan = Opposite/Adjacent

  tan(angle) = 3/25

  angle = arctan(3/25) ≈ 6.84°

The ramp will make a 6.84° angle with the ground. It will not meet code.

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c. We can find the distance from the building where the ramp must start using the same trig relation.

  tan(4.75°) = (3 ft)/(distance)

  distance = (3 ft)/tan(4.75°) ≈ 36.1 ft

The ramp must start 36.1 feet from the building to exactly meet code.

x = ±sqrt(10)

step-by-step explanation:

5 - 2x² = -15

subtract 5 from each side

5-5 - 2x² = -15-5

-2x^2   = -20

divide by -2 on each side

-2x^2   /-2= -20/-2

x^2 =10

take the square root on each side

sqrt(x^2 )=±sqrt(10)

x = ±sqrt(10)

check:

5 - 2x² = -15

+sqrt(10)

5 - 2(sqrt(10))² = -15

5 -2(10) = -15

5 -20 = -15

-15 = -15

-sqrt(10)

5 - 2(-sqrt(10))² = -15

5 -2(10) = -15

5 -20 = -15

-15 = -15