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Oksanka [162]
3 years ago
10

Nathaniel's car used 10 gallons to travel 360 miles. How far can he travel on 16 gallons?

Mathematics
2 answers:
SCORPION-xisa [38]3 years ago
8 0

Answer:

576 miles

Step-by-step explanation:

If Nathaniel's car uses 10 gallons to travel 360 miles, then the car can drive 36 miles per 1 gallon (360/10=36).

If he has 16 gallons and he can drive 36 miles per gallon, he can travel 576 miles (36*16=576).

velikii [3]3 years ago
5 0

Answer:

16 gallons will get you 576 miles

Step-by-step explanation:

We use ratios to solve this question

10 gallons : 360 miles

Divide both sides by 10 to find 1 gallon

1 gallon:36 miles

multiply both sides by 16

16 gallons : 576 miles

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Prove 2/sqrt3cosx+sinx=sec(pi/6-x)
dlinn [17]

Thus L.H.S = R.H.S that is 2/√3cosx + sinx  = sec(Π/6-x) is proved

We have to prove that

2/√3cosx + sinx  = sec(Π/6-x)

To prove this we will solve the right-hand side of the equation which is

R.H.S = sec(Π/6-x)

          = 1/cos(Π/6-x)

[As secƟ = 1/cosƟ)

           = 1/[cos Π/6cosx + sin Π/6sinx]

[As cos (X-Y) = cosXcosY + sinXsinY , which is a trigonometry identity where X = Π/6 and Y = x]

           = 1/[√3/2cosx + 1/2sinx]

            = 1/(√3cosx + sinx]/2

            = 2/√3cosx + sinx

    R.H.S = L.H.S

Hence 2/√3cosx + sinx  = sec(Π/6-x) is proved

Learn more about trigonometry here : brainly.com/question/7331447

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