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Vladimir79 [104]
3 years ago
14

A truck driver who covers the interstate in 4 1/2hours traveling at the posted speed of 55 mph. If the speed limit is raised to

65 mph, how much time will the same trip require
Mathematics
1 answer:
kotegsom [21]3 years ago
6 0

Answer: The same trip will require 3.8 hours.

Step-by-step explanation:

Since we have given that

Time = 4\dfrac{1}{2}=\dfrac{9}{2}

Speed = 55 mph

So, distance would be

Speed\times time=55\times 4.5=247.5\ miles

If the speed limit = 65 mph

So, time will be

\dfrac{247.5}{65}=3.8\ hours

Hence, the same trip will require 3.8 hours.

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Step-by-step explanation:

In right triangle MNP, MP = 4 cm, m∠N = 90°, m∠P = 21°

By the sine definition,

\sin \angle P=\dfrac{\text{Opposite leg}}{\text{Hypotenuse}}=\dfrac{MN}{MP}\\ \\MN=MP\sin \angle P\\ \\MN=4\sin 21^{\circ}\approx 1.43\ cm

Now, consider right triangle HMN (it is right because NH is an altitude). By the cosine definition,

\cos \angle M=\dfrac{\text{Adjacent leg}}{\text{Hypotenuse}}=\dfrac{MH}{MN}\\ \\MH=MN\cos \angle M

In the right triangle, two acute angles are always complementary, so

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Thus,

MH=1.43\cos 69^{\circ}\approx 0.51\ cm

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