The distance from the center of earth to the dead spot.
The distance from the center of earth to the dead spot is .
The net gravitational force F acting on an object situated on imaginary line segment is drawn between the centers of the earth and the moon is , where is a constant and x is the distance of the object from the center of the earth, measured in thousands of miles.
The solution of a quadratic equation of the form can be obtained by using the quadratic formula .
Note that, no net gravitational force act between centre of the earth and dead spot. Therefore, .
Substitute for in the equation .
Simplify the above equation as follows.
Use the Quadratic formula to find the value of x.
Substitute for , for and for in the quadratic formula.
Simplify further as follows.
Note that, 268(000) miles is greater than the distance from the earth to the moon.
Thus, the distance from the center of earth to the dead spot is .
Subscribe to bartleby learn! Ask subject matter experts 30 homework questions each month. Plus, you’ll have access to millions of step-by-step textbook answers!