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IrinaVladis [17]
3 years ago
14

If you look at a state map with a representative fraction scale of 1:500,000; the straight-line distance between two cities is e

qual to 12.7 inches on the map. Assuming that the representative fraction scale is also in inches, what is the ground distance between these two cities in miles?
Mathematics
1 answer:
Leya [2.2K]3 years ago
5 0

Answer:

Step-by-step explanation:

The scale factor is given as 1:500,000

i.e. original 500,000 is represented as 1 inch in the map

Hence if 12.7 inches on the map, this is a question of direct variation

So actual distance = 12.7(500000) = 6350000

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54 3/11 as a decimal
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54 3/11...

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What does n mean(mathematics)<br> ?
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Read 2 more answers
Suppose that θ is an acute angle of a right triangle and that sec(θ)=52. Find cos(θ) and csc(θ).
insens350 [35]

Answer:

\cos{\theta} = \dfrac{1}{52}

\csc{\theta} = \dfrac{52}{\sqrt{2703}}

Step-by-step explanation:

To solve this question we're going to use trigonometric identities and good ol' Pythagoras theorem.

a) Firstly, sec(θ)=52. we're gonna convert this to cos(θ) using:

\sec{\theta} = \dfrac{1}{\cos{\theta}}

we can substitute the value of sec(θ) in this equation:

52 = \dfrac{1}{\cos{\theta}}

and solve for for cos(θ)

\cos{\theta} = \dfrac{1}{52}

side note: just to confirm we can find the value of θ and verify that is indeed an acute angle by \theta = \arccos{\left(\dfrac{1}{52}\right)} = 88.8^\circ

b) since right triangle is mentioned in the question. We can use:

\cos{\theta} = \dfrac{\text{adj}}{\text{hyp}}

we know the value of cos(θ)=1\52. and by comparing the two. we can say that:

  • length of the adjacent side = 1
  • length of the hypotenuse = 52

we can find the third side using the Pythagoras theorem.

(\text{hyp})^2=(\text{adj})^2+(\text{opp})^2

(52)^2=(1)^2+(\text{opp})^2

\text{opp}=\sqrt{(52)^2-1}

\text{opp}=\sqrt{2703}

  • length of the opposite side = √(2703) ≈ 51.9904

we can find the sin(θ) using this side:

\sin{\theta} = \dfrac{\text{opp}}{\text{hyp}}

\sin{\theta} = \dfrac{\sqrt{2703}}{52}}

and since \csc{\theta} = \dfrac{1}{\sin{\theta}}

\csc{\theta} = \dfrac{52}{\sqrt{2703}}

4 0
3 years ago
Mr. Varga purchased candy boxes in the shape of a square pyramid for his kids for Valentine's Day.
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Answer:

yes  

Step-by-step explanation:

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3 years ago
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