Calculus module 7 dbq

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1. Filling in the table is just a matter of plugging in the given values into the ODE :

2. I've attached what the slope field should look like. Basically, sketch a line of slope equal to the value of at the labeled point (these values are listed in the table).

3. This ODE is separable. We have

Integrating both sides gives

With the initial condition , we take and to solve for :

Then the particular solution is

4. First, solve the ODE (also separable):

Integrating both sides gives

Given that , we can solve for :

Then use the other condition, , to solve for :

Then the particular solution is

Now, you want to know the temperature after an additional 30 minutes, i.e. 60 minutes after having placed the lemonade in the fridge. According to the particular solution, We have

5. You want to find such that :

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'.

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