if 5 cakes equal 3.50. we must divide 3.50 by 5 to see the price of just one cake. now since 3.50/5 is 0.70. we must multiply 0.70 by 7. since we have 7 cakes. now we get our simple answer of $4.90.
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the attachment shows a right triangle where arcsin(@) = 1/4. (the arcsin means find the angle whose sine is 1/4 as is done in the triangle.) the missing side, sqrt(15), shown in red, was determined by the pythagorean theorem.
then cos(@) = cos(arcsin(1/4)) = sqrt(15)/4
z = a+bi
the modulus is the sqrt ( a^2 +b^2)
and the argument (i call it theta) is equal to arctan (b/a)
we have z = 3-3i
we are looking for the argument of z
theta = arctan (-3/3)
= -45 degrees
they don't like negative arguments so add 360 degrees to it. it is the same value, we just loop once around the circle.
here's why to put something in standard form we simply use the equation y=mx+b. so we can't have anything but a coefficient of one for y. so we have to get everything to one side first and isolate y. now we did that our problem should look something like this: 2y=-x-8. so we divide the whole right hand side by 2, and we simply get: y=-1/2x-4.
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