The rate at which a radioactive substance decay is proportional to the amount A(t) of the substance remaining at time t. At initial time of observation, the mass of this substance is 10g. Formulate the Initial-Value-Problem (IVP) for the amount A(t).

Step-by-step explanation:

Taking the integral of both sides

, where C=constant of integration.

Taking the exponents of both sides

Since the exponential of a constant is still a constant

At t=0, A(t)=10 g

Therefore the initial value problem is given as:

for the friend request.

when a figure, such as triangle (xyz) is reflected over the line y = x to create x'y'z' the x-coordinates and y-coordinates of the original image (pre-image) will be reversed for the image. (e.g., (x, y) > (y, x)) this means that the pre-image position of the x- and y-coordinates switch places which in turn provides a mirror like image of the original xyz.  

i notice that when i draw a line segment from x to x', that the points are parallel from each other -- they are exactly across from each other and do not intersect with any other points.  

yes, think i would see the same characteristic if you drew the line segment connecting y with the reflecting line and then y' with the reflecting line because of the essence of reflections. because it is a mirror image, each point was effected the same way which leads me to conclude that they same would apply to y and y'.