A lithotriper is used to disentegrate kidney stones. The patient is placed within anelliptical device with the kidney centered at one focus, while ultrasound waves from the other focus hit the walls and are reflected to the kidney stone, shattering the stone. Suppose that the length of the major axis of the ellipse is 40 centimeters and the length of the minor axisis 20 centimeters. How far from the kidney stone should the electrode that sends the ultrasound waves be placed in order to shatter the stone?
A lithotriper is used to disentegrate kidney stones. The patient is placed within anelliptical device with the kidney centered at one focus, while ultrasound waves from the other focus hit the walls and are reflected to the kidney stone, shattering the stone. Suppose that the length of the major axis of the ellipse is 40 centimeters and the length of the minor axisis 20 centimeters. How far from the kidney stone should the electrode that sends the ultrasound waves be placed in order to shatter the stone?
Solution Summary: The author calculates the distance of the electrode from the kidney stone to disintegrate the stone using an elliptical device.
A lithotriper is used to disentegrate kidney stones. The patient is placed within anelliptical device with the kidney centered at one focus, while ultrasound waves from the other focus hit the walls and are reflected to the kidney stone, shattering the stone. Suppose that the length of the major axis of the ellipse is 40 centimeters and the length of the minor axisis 20 centimeters. How far from the kidney stone should the electrode that sends the ultrasound waves be placed in order to shatter the stone?
M = log
The formula
determines the magnitude of an earthquake,
where / is the intensity of the earthquake and S is the intensity of
a "standard earthquake." How many times stronger is an
earthquake with a magnitude of 8 than an earthquake with a
magnitude of 6? Show your work.
Now consider equations of the form ×-a=v
= √bx + c, where a, b, and c
are all positive integers and b>1.
(f) Create an equation of this form that has 7 as a solution and
an extraneous solution. Give the extraneous solution.
(g)
What must be true about the value of bx + c to ensure that
there is a real number solution to the equation? Explain.
The equation ×+ 2 = √3x+10 is of the form ×+ a = √bx + c, where a, b, and
c are all positive integers and b > 1. Using this equation as a
model, create your own equation that has extraneous solutions.
(d) Using trial and error with numbers for a, b, and c, create an
equation of the form x + a = √bx + c, where a, b, and c are all
positive integers and b>1 such that 7 is a solution and there
is an extraneous solution. (Hint: Substitute 7 for x, and
choose a value for a. Then square both sides so you can
choose a, b, and c that will make the equation true.)
(e) Solve the equation you created in Part 2a.
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, algebra and related others by exploring similar questions and additional content below.
Finding The Focus and Directrix of a Parabola - Conic Sections; Author: The Organic Chemistry Tutor;https://www.youtube.com/watch?v=KYgmOTLbuqE;License: Standard YouTube License, CC-BY