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Burka [1]
3 years ago
13

a river flows due south at 1.2 miles per hour. A swimmer attempting to cross the river heads due east swiming at 3 miles per hou

r relative to the water. In what direction should the swimmer head in order to arrive at a landing spot due east of his starting point
Mathematics
1 answer:
kotegsom [21]3 years ago
4 0

Answer:

The swimmer must move in the direction 338.2°

Step-by-step explanation:

Since the river flows due south at 1.2 miles per hour and the swimmer swims 3 miles per hour due east of the river, since their directions are perpendicular,  the resultant speed is the hypotenuse of the triangle formed by the two perpendicular directions.

The direction of the resultant speed is thus θ = tan⁻¹( vertical component/horizontal component) where vertical component = 1.2 mph due south = -1.2 mph and horizontal component = 3 mph due east = + 3 mph

So, θ = tan⁻¹(-1.2 mph/+ 3mph)

θ = tan⁻¹(-1.2/3)

θ = tan⁻¹(-0.4)

θ = -21.8°

θ = -21.8° + 360° (since we are in the fourth quadrant- between east and south)

θ = 338.2°

So, <u>the swimmer must move in the direction 338.2°</u>.

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MatroZZZ [7]

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This means 45 grams are equal to 45 ml's.

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2 years ago
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The base of a triangle is nine centimeters longer than the perpendicular height. If the area of the triangle is 180 square centi
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Answer:

<em>The base is 24 cm long.</em>

Step-by-step explanation:

<u>Equations</u>

Let's call

b= base of the triangle

h=height of the triangle

The base is 9 cm longer than the height, thus:

b = h + 9

The area of the triangle is:

\displaystyle A=\frac{bh}{2}

\displaystyle A=\frac{(h+9)h}{2}

And its value is 180:

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Multiplying by 2:

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The only valid positive solution is:

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