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3/|2| > 1 Does it follow that 3 > 2^2?

It's good that you are checking whether the answer is reasonable. But in this case it's the diagram that's misleading you. The angle PQR is 150, but looks like it's 90. A better diagram would show the triangle PQR as one with a long base (PR) and a very short height, which, as you know, affects...

The solution looks good (didn't check the calculations). Why does the area seem too small?

Where is the question?

Ok. Please post a diagram with vertices marked so we can reference them.

I think it's possible. Is this a school assignment?

Sure, you can make whatever additional constructions you want and you can introduce whatever variables you want. But then you should post the diagram showing the constructions and your solution must include steps where all of your variables are expressed through values actually given in the problem.

What theta? Don't see any angles in the question. The distance is from point A to point P.

Math is very much black and white. But a problem needs to satisfy certain requirements to be considered a _math_ problem. If I write a math problem on a piece of paper and then erase 30% of it, is it still a math problem? How about a problem written in a language you don't know well?

Let's consider an easier problem. A line through point A(1, 2) intersects the line y=2x+3 at point P. Distance AP is given. Find the equation of the first line. How would you approach this problem?

If this is the exact problem statement then there is nothing to prove. 1 is a power of 2 and any number n is a sum of n 1s. I'm guessing they want distinct powers of 2.

Please do the following: Copy the diagram Draw additional segments so that all surfaces are divided into rectangles. For each rectangle write the expression for the area and draw an arrow from the expression to the rectangle Don't forget the surfaces not visible in the diagram (but they still...

Express a through c and b through c. Plug in the resulting expressions into the left side of the 3rd equality, simplify. Do you get 29/34? P.S. Is this standard notation not to use parentheses in a + b : b + c????

Using the diagram in post 20: tan\text{ θ} = \frac{4}{12} From the tangent of double angle identity: tan\text{ 2θ} = \frac{3}{4} Therefore ED = 12, area = 160.

Level 6: lost 2 points Level 7: lost 4 points Level 8: lost 6 points ... This is an arithmetic sequence (the difference between consecutive terms is constant). Look up the formula for the sum of such a sequence.

f(y)=(y-3)(y+1) means that for any valid input y the result of the function is (y-3)(y+1). We can name that input y, x, ABC, cow, etc.

There is only one machine - the function f. We are not "putting one machine into the other". We are putting different inputs into the same machine.

This is an animation, not a graph.

Not sure why the circle is necessary. Here's my diagram (hope I understand the problem correctly). You can set up a system of 3 equations with 3 variables (a, b, x) and solve it in wolframalpha.com. I'm getting x=63.3018. I used triangle similarity and the Pythagorean theorem. You can test the...

You need to split the remaining funds according to the 5 : 3 ratio. Divide the amount by 8 (5+3), take 5 "parts" and give the remaining 3 to the partner.