Answer:
10.5.
Step-by-step explanation:
By similar triangles:
IJ / 21 = 8 /(8+8) = 1/2
IJ / 21 = 1/2
IJ = 1/2 * 21
= 10.5.
The first figure has 3 angles, the second one has 4 angles, the third one has 5 angles so the next one will have 6 angles.
The violet figures inside stick with each side of the outer figures in the middle, so the last figure will look more less like in the attachment.
Step-by-step explanation:
Let the height above which the ball is released be H
This problem can be tackled using geometric progression.
The nth term of a Geometric progression is given by the above, where n is the term index, a is the first term and the sum for such a progression up to the Nth term is
To find the total distance travel one has to sum over up to n=3. But there is little subtle point here. For the first bounce ( n=1 ), the ball has only travel H and not 2H. For subsequent bounces ( n=2,3,4,5...... ), the distance travel is 2×(3/4)n×H
a=2H..........r=3/4
However we have to subtract H because up to the first bounce, the ball only travel H instead of 2H
Therefore the total distance travel up to the Nth bounce is
For N=3 one obtains
D=3.625H
You might have made an error the first time you solved for x. I got x = -0.5.
When you have your log base 4, the way you cancel that out is by making 4 the base on both sides, so you get 4^(log4) to reduce to 1, and you're left with:
2x + 3 = 4^(1/2) ... Simplify
2x + 3 = 2
2x = -1
x = -1/2
If you plug that back in, everything checks out. Maybe double check your use of logarithm/exponent properties?
