A total of $10,000 is invested at an annual interest rate of 3%. Find the balance after 5 years if the interest is compounded a) quarterly and b) continuously.

Step-by-step explanation:

We will need 2 different equations for this problem. For compounding a certain number of times a year, the formula is

so let's do that first. Filling in we get

and simplifying a bit gives us

and a bit more,

and then

A(t) = 10000(1.161184142) so

A(t) = 11611.84

Then for the compounding continuously, the formula is

and simplify a bit to\

Now raise e to the power of .15 on your calculator to get

A(t) = 10000(1.161834243) so

A(t) = 11618.34

Not too much of a difference between the 2 values at the end.

the figures below are made out of circles, semicircles, quarter … find the area and the perimeter of each figure and give your answers as a completely simplified exact value in terms of π (no approximations). remember that we'll also have to cut whatever areas we get in half, since we're only dealing im pretty sure that is the right answer

step-by-step explanation:

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'.