http://www.mathsisfun.com/definitions/coordinates.html

]]>I am not able to visualize it.]]>

Chris]]>

It does look complex. I didn't find the diagram helpful and some of the translation had me mystified for a while, so I made my own diagram:

I've shown lines at the front in thick ink, ones that would be hidden in thin ink and construction lines dotted. Alongside, I've drawn the cross-sectional shape. It is a kite.

Is the problem complete? Well you have enough information to make a wire model so I think the answer is YES.

Can I do it? Well let's see.

(i) AC is the projection of A'C onto the base, so that perpendicular property must follow as AC is perpendicular to BD.

(ii) To get the true angle between two intersecting planes first find the line of intersection. Then a line perpendicular to this in each plane. Then the angle between those lines.

In this case BD is the line of intersection. EC' and EA' are lines in the planes so find the angle C'EA'. You will need trigonometry to find the lengths of C'E, A'E and A'C', then use the cosine rule.

(iii) When the lines are in different planes you need to translate one line until it has crosses the other line, and then calculate the angle between those lines.

In this case translate AD across the base until the new A coincides with B. So draw a line BF, parallel to AD with F on DC. The angle required is angle FBC'. Again use trigonometry to find the lengths of the three sides in triangle FBC' and again the cosine rule.

Hope that helps.

Bob

]]>http://www.mathisfunforum.com/viewtopic.php?id=21327

Post 2 has the problem and post 7 has an outline of my solution.

Bob

]]>Welcome to the forum.

Is this what you were trying to draw?

As you know 5 out of the 6 measurements in this triangle, there are many ways you could do this. I think the simplest is to use the sine rule:

Bob

]]>Bob

]]>Let y = cos(tan(sin(x))).

Establish the following properties:

(1) y is an even function.

(2) y = 1 when x = 0

(3) y is periodic.

(4) y > 0 for all x.

(5) There exists an x = k so that y is symmetrical in that line. (There are many but find the lowest > 0 )

(6) y is decreasing between x = 0 and x = k

(7) The line y = x cuts the curve once between x = 0 and x = k

(8) This intersection gives the value of the constant. The other properties should be sufficient to show it is unique.

Hint: Use the MIF function grapher to see what the graph of y looks like.

Bob

]]>This problem is typical of olympiad inequality problems requiring quick manipulations using algebra rather than calculus. Thus, applying AMâ€“GM, we have

It is easily seen that in the interval the expression attains a maximum at , the maximum being . Hence the minimum of in that interval is and so:]]>To solve this I think you set up the equations by how they dissociate...then I am pretty sure you can use the Ksp to solve for the individual values...

Get the molar mass to convert to g/l...and I am lost...lol sorry

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