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RideAnS [48]
3 years ago
6

1. The prism-shaped roof has equilateral triangular bases. Create an equation that models the height of one of the roof's triang

ular bases in terms of its sides. In your final answer, include all necessary calculations.
2. The prism-shaped roof has equilateral triangular bases. Use the model you created in question #1 to calculate the height of the roof, to the nearest tenth of a foot, if the side lengths each measure 25 feet. In your final answer, include all necessary calculations.

3. To determine the amount of roofing materials needed, the area of the roof's entire surface is calculated, including the ceiling of the garage. Considering the sketch of the roofing design, create a formula to model the area of the roof's entire surface. In your final answer, include all of your calculations.

4. The contractor in charge of the roofing project is trying to make the job the most cost effective for the homeowners. In order to cut back on the cost of supplies, he decides that a ceiling in the garage is not necessary. In other words, there will not be a barrier built between the garage and the roof. In two or more complete sentences, explain how these changes affect the model for the area of the roof's entire surface.

5. The contractor in charge of the roofing project is trying to make the job the most cost effective for the homeowners. In order to cut back on the cost of supplies, he decides that a ceiling in the garage is not necessary. In other words, there will not be a barrier built between the garage and the roof. Create a formula modeling the area of the roof’s surfaces that the contractor will be purchasing supplies for.

6. Use the formula you created in the previous question to calculate the area of the roof that the contractor will be purchasing supplies for, assuming that the side length of the triangular bases is 25 feet and the length of each rectangular face is twice its width.

Mathematics
2 answers:
Nat2105 [25]3 years ago
8 0

2. if a a=25 ft, then the height is  (ft)

3. one side of the prism (the roof) is a rectangle with dimensions a and l, so the area of one side is a*l the lateral Area of the roof is 3a*l

4. The total area was the 2 triangular surfaces + the 3 equal lateral rectangular surfaces. Now instead of 3 lateral triangular surfaces, we have 2.

So the total area found previously will be decreased by al

5. so the area now is

6. now a=25 and l=2a=50

Area=

=3041.3 (ft squared)

Mandarinka [93]3 years ago
7 0
1. Check picture 1. Let the one side of the triangle be a, drop one perpendicular, CD. Then triangle ADB is a right triangle, with hypothenuse a and one side equal to 1/2a. By the Pythegorean theorem, as shown in the picture, the height is \frac{ \sqrt{3} }{2} a

2. if a a=25 ft, then the height is \frac{ \sqrt{3} }{2} a=\frac{ \sqrt{3} }{2} *25= \frac{1.732}{2}*25= 21. 7 (ft)

3. consider picture 2. Let the length of the roof be l feet.

one side of the prism (the roof) is a rectangle with dimensions a and l, so the area of one side is a*l
the lateral Area of the roof is 3a*l

the area of the equilateral surfaces is 2*( \frac{1}{2} *a* \frac{ \sqrt{3} }{2}a )=\frac{ \sqrt{3} }{2} a^{2}

so the total area of the roof is \frac{ \sqrt{3} }{2} a^{2} +3al

4. The total area was the 2 triangular surfaces + the 3 equal lateral rectangular surfaces. Now instead of 3 lateral triangular surfaces, we have 2.
So the total area found previously will be decreased by al


5. so the area now is \frac{ \sqrt{3} }{2} a^{2} +2al

6. now a=25 and l=2a=50

Area=\frac{ \sqrt{3} }{2} a^{2} +2al=\frac{ \sqrt{3} }{2} * 25^{2}+2*25*50=25 ^{2}  (\frac{ \sqrt{3} }{2} +4)=625*4.866

=3041.3 (ft squared)

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Romashka-Z-Leto [24]

Answer:

k = 9

Step-by-step explanation:

Consider the pattern on the right side , that is

T_{k} = k(k + 2) + 1 = k² + 2k + 1

Equating

k² + 2k + 1 = 100 ( subtract 100 from both sides )

k² + 2k - 99 = 0 ← in standard form

(k + 11)(k - 9) = 0 ← in factored form

Equate each factor to zero and solve for k

k + 11 = 0 ⇒ k = - 11

k - 9 = 0 ⇒ k = 9

But k > 0 , then k = 9

5 0
2 years ago
Solve the triangle A=21 C=105 c=5
gregori [183]

Answer:

Granted that uppercase letters are the angles measurements and lowercase letters are the side lengths. I also was unable to round as I don't know to what decimal you need to round to.

First to find the measure of angle B, we must subtract A and C from 180

180-21-105=54

B=54

Next, we can use the law of sines in order to find the measures of a and b

As a reminder, The law of sines is

\frac{a}{sinA} =\frac{b}{sinB} =\frac{c}{sinC}

First, lets solve for b

\frac{b}{sin54}=\frac{5}{sin105} \\\\b=\frac{(5)sin54}{sin105}\\\\b=4.187780119

Next lets solve for a

\frac{a}{sin21}=\frac{5}{sin105} \\\\a=\frac{(5)sin21}{sin105}\\\\a=1.85504901

3 0
3 years ago
The figure below has a perimeter of 20 cm. Jinaiya wants to scale this figure by a factor of 0.75
Dmitrij [34]

Answer:

15cm

Step-by-step explanation:

scale factor =image diatace/object distance

0.75=x/20

0.75×20=x

15=x

: .x=15cm

4 0
3 years ago
-8x times 5 to the power of 3 would equal -1000x right?
marusya05 [52]
No. If you write it out, it would be -8*5 which is -40. (-40)^3 is -64000. So your answer would be -64000x
4 0
3 years ago
What is the measure of ZA?<br> A [?] degrees<br> 87°<br> 35<br> B<br> Enter
mamaluj [8]
Angle A is 58 degrees.

87 + 35 = 122
180 - 122 = 58
5 0
3 years ago
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