In a flight of 100km, an aircraft was slowed down due to bad weather. Its average speed for the trip was reduced by 200km/hr. And the time of flight increased by 30 minutes. The duration of the flight is

1 hour

Step-by-step explanation:

The formula for average speed is given as = Distance( km)  / Time(hours)

From the question

Average Speed = 200km/hr

Distance = 100km

Time is unknown, let us represent it as x

In the question, we are told the weather was bad and the time of the flight increased by 30minutes

Therefore, we would have algebraic equation

100/(x-200) - 100/x = 1/2

Find the LCM = x(x - 200)

100(x) - 100(x - 200) /(x) (x -200) = 1/2

100x - 100x - 20000/ x² - 200x = 1/2

-20000/x² - 200x = 1/2

Cross Multiply

-40000 = x² - 200x

x² - 200x + 40000 = 0

Looking at this quadratic equation, we can't use factorisation method to find the answer.

This signifies that the question is wrong.

Correct Question:

In a flight of 600km, an aircraft was slowed down due to bad weather. Its average speed for the trip was reduced by 200km/hr. And the time of flight increased by 30 minutes. The duration of the flight is

Step-by-step explanation:

The formula for average speed is given as = Distance( km)  / Time(hours)

From the question

Average Speed = 200km/hr

Distance = 600km

Time is unknown, let us represent it as x

In the question, we are told the weather was bad and the time of the flight increased by 30minutes

Therefore, we would have algebraic equation to find the speed of the journey as:

600/(x-200) - 600/x = 1/2

Find the LCM = x(x - 200)

600(x) - 600(x - 200) /(x) (x -200) = 1/2

600x - 600x + 120000/ x² - 200x = 1/2

240000/x² - 200x = 1/2

Cross Multiply

240000 = x² - 200x

x² - 200x - 240000 = 0

x² - 600x + 400x - 240000 = 0

x(x - 600) + 400( x - 600) = 0

(x - 600)(x + 400) = 0.

x - 600 = 0

x = 600 km/hr

x + 400 = 0

x = - 400 km/hr

Therefore, x = 600km/hr

Time = Distance / speed

Time = 600km/ 600km/hr

Time = 1 hour

Therefore, The duration of the flight is 1 hour.

b. an equilateral triangle inscribed in a circle

step-by-step explanation:

we are given the figure of two circles having a triangle inside.

now, we know that,

"when a figure is lying inside an another figure, then the outside figure is known as circumscribed figure and the figure lying inside is referred to as the inscribed figure".

as we see that, the circles are containing the triangle completely.

thus, the circles are the circumscribed figures and the triangle is the inscribed figure.

hence, we get, 'an equilateral triangle is inscribed in a circle'.