How do I find the area of the circular racetrack?

Mathematics

1 answer:

BabaBlast [244]3 years ago

6 0

Answer:

8483 ft²

Step-by-step explanation:

Subtract the area of the smaller circle from the area of the greater circle

Greater Circle area:

πr² = π × 140²

= 61583.2 ft²

Smaller Circle area:

= π × 130²

= 53099.8 ft²

Area of track:

61583.2 - 53099.8 = 8483.4ft²

= 8483ft² (to the nearest ft²)

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Poonam is five times as old as Shalini. The sum of their ages is 72

Elden [556K]

Answer:

Shalini = 12

Poonam = 60

Step-by-step explanation:

Let p = poonams age

Let s = shalini's age

p = 5s

p+s = 72

Substitute the first equation into the second equation

5s+s = 72

Combine like terms

6s= 72

Divide by 6

6s/6 = 72/6

s = 12

p = 5s =5*12 = 60

Shalini = 12

Poonam = 60

4 0

3 years ago

1. The height of a missile t seconds after it has been fired is given by h=4.9t^2+44.1t. How many seconds will it take for the r

asambeis [7]

Answer:

The rocket will take 4.5 seconds to reach its maximum height.

Step-by-step explanation:

The height of a missile t seconds after it has been fired is given by h=-4.9*t²+44.1*t

This function is a quadratic function of the form f (x) = a*x² + b*x + c. In this case a=-4.9, b=44.1 and c=0

To calculate how many seconds it will take for the rocket to reach its maximum height, I must calculate the maximum of the function. The maximum of a quadratic function is the vertex of the parabola. The x coordinate of the vertex will be simply: $x=\frac{-b}{2*a}$ . The y coordinate of the vertex corresponds to the function evaluated at that point.

In this case the x coordinate of the vertex corresponds to the t coordinate. In other words, by calculating the x coordinate of the vertex, you are calculating the maximum time t it will take for the rocket to reach its maximum height. So:

$t=\frac{44.1}{2*(-4.9)}$