The problem is attached as word document file with all mathematical expressions and pic.

Problem: For continuous wave Doppler ultrasound the transmitting and receiving transducers are usually mounted next to each other i.e. with approximately zero angular separation. However, it is possible to have the transmitter and receiver at different angles to the vessel. Use the configuration shown below to derive the Doppler frequency as a function of: a) The angle between the transducers b) The angle the transducers make with the flow vector. What combination of values of and produce the largest Doppler frequency, what values the smallest? Set equal to . For what range of values of does the Doppler frequency exceed 90% of the maximum Doppler frequency.

Radioactive decay

Radioactice substances decay exponentially. The amount of radium present at an time t obeys the law Q(t)= Qoe^-kt, where Qo. is the initial amount present and k is a suitable positive constant. The half-life of a radioactive substance is the time required for a given amount to be reduced by one-half. Now, it is known that the half-life of radium is approximately 1600 years. Suppose initially there are 200 miligrams of pure radium. Find the amount left after t years. What is the amount left after 800 years?

MATLAB code

i have a matlab code for a skull filled wth solid water and i want to put air at the places of Acoustic neuromata i.e. in sinus region and near the ears(and rest of skull will remain as it is i.e. filled with with solid water ) See attached matlab code and word file for help

MATLAB code

Using given geometry code...

wht is the radius of skull if....

What is the radius of the skull if the skull has dimensions 200*200*200 and where will its centre of gravity be?