justtryingtopass7
02.11.2020 •
Mathematics
Due to inclement weather, the pilot of a plane slows down the plane’s regular flying rate by 25%. This result to an additional 1.5 hours in covering the 3,000km distance to its regular time required for the trip. Find the regular rate of the trip.
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Ответ:
The regular speed or rate of the trip is 2111.1 km per hour.
Suppose that ; speed of plane is = S
Due to inclement weather the pilot slow down the plan rate by 25%
then new speed = S-25% of S = 0.75S
Time taken = t
New time taken = t+1.5 hours
Total distance covered = 3000 km
Initial speed of the plane was,
Time t can be written as,
So, the new speed will be,
So, the regular speed of the trip can be calculated as,
Solving further,
Therefore, the regular speed or rate of the trip is 2111.1 km per hour.
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Ответ:
Normal speed = 711.11 km/h (Approx)
Step-by-step explanation:
Assume;
Normal speed = x
New speed = x - 25% of x = 0.75 x
Time taken = t
New time taken = t + 1.5 hour
Total distance
Computation:
Total distance = 3,200 km
Speed = Distance/Time
x = 3200 / t
t = 3200/x
so,
0.75 x = 3200 / (t+1.5)
0.75 x = 3200 / (3200/x+1.5)
0.75 x = 3200 / [(3200 + 1,5x)x]
x = 711.11 km/h
Normal speed = 711.11 km/h (Approx)
Ответ:
a) 17.6cm and 22.4cm
b) the total area of the circle and the square can be maximum by differentiating and equating it to zero
Step-by-step explanation:
The length of the wire = 40
Let x be the circumference of the circle.
x = 2πr
r = x/2π (r = radius)
Let the perimeter of the square = (40-x)
4L = 40-x
Where L = lenght
L = (40-x)/4
Area of a circle = πr^2
A = π (x/2π)^2
A = π(x^2/(4π)^2)
A = x^2 / 4π
Area of a square = L^2
= [(40-x)/40]^2
= (x^2 - 80x +1600)/16
Total area = area of circle + area of square
= x^2/4π + (x^2 - 80x +1600)/16
= 0.0796x^2 + 0.0625x^2 - 5x + 100
A= 0.1421x^2 - 5x +100
Differentiate A with respect to x
dA/dx = 0.2842x -5
Total area is minimum when dA/dx = 0
0.2842x - 5 = 0
0.2842x = 5
x = 5/0.2842
x = 17.6cm
The circumference of the circle is 17.6cm
40-x = 40 - 17.6 = 22.4cm
The perimeter of the square is 22.4cm.
b) the total area of the circle and the square can be maximum by differentiating and equating it to zero