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natima [27]
2 years ago
10

Civil engineer wants to estimate the maximum number of cars that can safely travel on a particular road at a given speed. He ass

umes that each car is 14 feet long, travels at speed S, and follows the car in front of it at a safe distance for that speed. He finds that the number N of cars that can pass a given spot per minute is modeled by the function
N=(89s)/(14+14(s/17)^2))

At what speed can the greatest number of cars travel safely on that road? Assume that the maximum possible speed of a car is less than 300.
Mathematics
1 answer:
pychu [463]2 years ago
5 0
N(s)= \frac{89s}{14+14( \frac{s}{17})^2 }
\\
\\N'(s)= (\frac{89s}{14+14( \frac{s}{17})^2 } )'= \frac{89\times 14(1+( \frac{s}{17})^2)-89s\times  \frac{28}{17} }{14^2(1+( \frac{s}{17})^2)} 
\\
\\N'(s)=0
\\
\\89\times 14(1+( \frac{s}{17})^2)-89s\times  \frac{28}{17}=0
\\
\\1+( \frac{s}{17})^2- \frac{2s}{17} =0
\\
\\289+s^2-34s=0
\\
\\s^2-34s+289=0
\\
\\(s-17)^2=0
\\
\\s=17

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Find the measures of the requested angles.
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Answer:

d. m<ABD = 50°, m<GBC = 47°, m<EBC = 50°, and m<DBG = 83°

Step-by-step explanation:

m<ABF = 47° (given)

m<FBE = 83°

✍️m<ABD + m<ABF + m<FBE = 180° (angles on straight line)

m<ABD + 47° + 83° = 180° (substitution)

m<ABD + 130° = 180°

Subtract 130 from each side

m<ABD = 180° - 130°

✅m<ABD = 50°

✍️m<GBC = m<ABF (vertical angles)

✅m<GBC = 47° (Substitution)

✍️m<EBC = m<ABD (Vertical angles)

✅m<EBC = 50° (substitution)

✍️m<DBG = m<FBE (vertical angles)

✅m<DBG = 83° (Substitution)

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If the conversion rate for Swiss francs is 1.68 francs = 1 U.S. dollar, then how many Swiss francs can be exchanged for $79.00 i
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The equation of the parabola in the vertex form is y =  (x - 3)^{2} - 5 with ( 3, -5) is the vertex of the parabola and 1 is the multiplier

In the above question, A parabolic equation is given as follows:

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The equation of the parabola in the vertex form is :

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where, ( 3, -5) is the vertex of the parabola and 1 is the multiplier

Hence, The equation of the parabola in the vertex form is y =  (x - 3)^{2} - 5 with ( 3, -5) is the vertex of the parabola and 1 is the multiplier

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brainly.com/question/21685473

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