Scott ran 11 kilometers in nine days. One mile is approximately 1.6 kilometers. About how many miles did Scott run?

Mathematics

1 answer:

natita [175]3 years ago

3 0

Scott run 6.875 miles in nine days.

Step-by-step explanation:

Given,

Distance covered by Scott = 11 kilometer

1.6 kilometer = 1 mile

We will find the unit rate in terms of kilometer;

1 kilometer = $\frac{1}{1.6}\ miles$

11 kilometers = 11*unit rate of kilometer

11 kilometers = $11*\frac{1}{1.6}$

11 kilometers = 6.875 miles

Scott run 6.875 miles in nine days.

Keywords: unit rate, multiplication

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2 years ago

A triangle is inscribed in a circle. The vertices of the triangle divide the circle into three arcs of lengths 3, 4, and 5. What

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The area of the required triangle is <u>9/π²(3 + √3)</u> sq. units.

In the question, we are given that a triangle is inscribed in a circle. The vertices of the triangle divide the circle into three arcs of lengths 3, 4, and 5.

We are asked for the area of the triangle.

Now, the circumference of the circle = 3 + 4 + 5 = 12 units.

The formula for the circumference is 2πr, which gives is:

2πr = 12,

or, r = 6/π.

The length of the arcs are proportional to its central angle, making the angles: 3θ, 4θ, and 5θ, which needs to sum up to 360°, giving us θ = 360°/12 = 30°.

Thus, the three arcs subtends angles of θ₁ = 3θ = 90°,θ₂ = 4θ = 120°, and θ₃ = 5θ = 150°.

The area of the circle can be calculated as:

Area = (1/2)r² sin θ₁ + (1/2)r² sin θ₂ + (1/2)r² sin θ₃ = r²/2(sin θ₁ + sin θ₂ + sin θ₃).

Substituting the values, we get:

Area = 36/2π²(sin 90° + sin 120° + sin 150°),

or, Area = 36/2π²( 1 + √3/2 + 1/2),

or, Area = 9/π²(3 + √3).

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