If your brain is 0.4 m higher than your heart when you are standing, how much lower is your blood pressure at your brain than it is at your heart? The density of blood plasma is about 1025 kg/m3 and a typical maximum (systolic) pressure of the blood at the heart is 120 mg of Hg (= 16 kP = 1.6 × 104 N/m2). Give your answer in mg of Hg.

The correct answer is 88.84 mmHg.

Explanation:

The pressure differential between the brain and the heart while standing up will be 120 - rho × g (gravity) × h, here h is the distance from the brain to the heart. The h is 40 cm or 0.4 m.  

rho×g×h = 1060 kg/m³×9.8 m/s²×0.4m  

= 4155 Pa  

Now converting Pa to mmHg we get:  

4155 Pa × 760 mmHg / 1.01325 × 10⁵ Pa  

= 31.16 mmHg  

Thus, the pressure in the brain now is 120 - 31.16  

= 88.84 mmHg (hypotension)  

we have been given a quadratic function and we need to restrict the domain such that it becomes a one to one function.

we know that vertex of this quadratic function occurs at (5,2).

further, we know that range of this function is .

if we restrict the domain of this function to either or , it will become one to one function.

let us know find its inverse.

upon interchanging x and y, we get:

let us now solve this function for y.

hence, the inverse function would be if we restrict the domain of original function to and the inverse function would be if we restrict the domain to .