The coordinates of a particle in the metric xy-plane are differentiable functions of time t with startfraction dx over dt endfraction equalsnegative 6 startfraction m over sec endfraction and startfraction dy over dt endfraction equalsnegative 4 startfraction m over sec endfraction . how fast is the particle's distance from the origin changing as it passes through the point (12,5)?

Explanation:

It is given that,

The coordinates of a particle in the metric xy-plane are differentiable functions of time t are given by :

Let D is the distance from the origin. It is given by :

Differentiate above equation wrt t as:

.............(1)

The points are given as, (12,5). Calculating D from these points as :

Put all values in equation (1) as :

So, the particle is moving away from the origin at the rate of 7.076 m/s. Hence, this is the required solution.

the small 0.38-kg slider is known to move from position a to position b along the vertical-plane slot. determine (a) the work done on the body by its weight and (b) the work done on the body by the spring. the distance r = 0.70 m, the spring modulus k = 154 n/m, and the unstretched length of the spring is 0.53 m

explanation:

-reverse card

it is given that trillions of microbes make up to 1% to 3% of the body mass.

let's take average of this percentage: 2%

consider the average mass of the human body as 70 kg.

then, trillions of microbes would have mass  

therefore, 100 trillion micro-organisms would weigh:

this is an approximate value and could change depending on the mass of the human body and percentage of the microbes present in it.

average mass per microorganism =