jboy314

Whoops i read the question wrong!  As far as similarity goes you need to focus on the shape rather than the size.  The simple way to think of similarity is to ask yourself if two shapes are the exact same shape even though they are different sizes.  If they are the exact same but one is just shrunk or expanded then they are similar. 

For a more formal definition, similar shapes must have congruent angles and proportional side lengths.

If they are not the same exact size and shape then it is not a rigid motion.

Rigid motion is something that preserves the size of an object. Think of a sheet of paper.  If you turn it or flip it over or move it it is essentially the same shape.  If you try to stretch the paper or fold it you change what the shape is so it is not a rigid motion. Since the two circles are not the same size then it is not a rigid motion.

This is a tangent problem.  Draw out your picture, a right triangle where the horizontal side is 5 and label the vertical side as x.  From the angle of 6 degrees the opposite side is x and the adjacent side is 5, thats why we use tangent.  Set up the problem as follows:

tan(6)=x/5

Multiply both sides by 5

5tan(6)=x

x=0.526 miles

This is an extention of the pythagorean theorem.

lets take the two smaller side lengths, square them, and add them together.  Then we will compare with the longest side squared to see if it fits the pythagorean theorem.

7^2 +10^2 =49+100=149

15^2=225

since 225 is not equal to 149 we have shown that this is not a right triangle.  Well then what is it!?

if we look closely at the form a^2+b^2=c^2 we see that in our case the right side of the equation is greater than the left side.  What this means is that the side that would have been the hypotenuse were this a right triangle is too long for it to be a right triangle.  That means that the angle which would normally be a right angle must be greater than a right angle to create this side which is longer than what they hypotenuse would need to be.  Therefore, it must be the case that this is an obtuse triangle.

Please note that if the part of the equation that is c^2 were less than the a^2+b^2 side then it would be acute.

Looks like i totally blew the first step in my own work by not using a substitution for dx!  wow!  Thanks!

1-10

3(-3)

27/(-3)

-100+91

the square root of 81 (kinda sorta)

Start by adding 1/2 to both sides so we would have

-1/5y=-3/7+1/2

We need a common denominator

(-1/5)y=-6/14+7/14

(-1/5)y=1/14

Multiply by -5

y=-5/14

Exactly!  It is always easy to turn a fraction into a decimal but sometimes it is very difficult and cumbersone to turn a decimal into a fraction.

It is always best to leave things in terms of fractions for a most exact answer.  The first thing that is tough about this is that you dont have a common denominator, so let's fix that!

We want out common denominator to be 30 here because it is easy to turn 3 and 5 into thirty with multiplication.  Multiply $${\frac{{\mathtt{2}}}{{\mathtt{3}}}}$$2/3 by 10/10 (which you should notice is legal because we are just multiplying by one) and multiply 4/5 by 6/6. This gives us a new expression

(20/30)x+(24/30)=-17/30

Let's subtract (24/30) from both sides to get  (20/30)x=-41/30

Now we can multiply both sides by 30 so that there are no longer any fractions

20x=-41   And now we divide by 20 to get x=-41/20 which is exactly the same as -2.05