Any decimal number that is repeating can be written in the form <span>
</span> with b not equal to zero, so they are rational numbers.
The short answer is
yes, 0.6 repeating is a rational number.
Hope this helped :)
Answer:
Pendulum will swing by an angle 0.666π
Step-by-step explanation:
We have given arc = 
And length of the pendulum l = 150 cm
Length of the pendulum will be equal to radius of the pendulum so r = 150 cm
Arc is given by 
So 
So pendulum will swing by an angle 0.666π
Lets call x the amount of 18% solution and y the amount of 40% solution, and write as equations the info of the problem:
18x + 40y = 10(20)
x + y = 10
lets multiply the second equation by -18 and add to the first:
18x + 40y = 200
-18x -<span> 18y = -180
</span>----------------------
0 + 22y = 20
y = 20/22 = 10/11
and substitute in the original equation:
x <span>+ y = 10
</span>x = 10 - y
x = 10 - 10/11
x = 110/11 - 10/11
x = 100/11
so they have to use 100/11 liters of 18% solution and 10/11 liters of 40% solution
<span>To minimize the perimeter you should always have a square.
sqrt(289) = 17
The dimensions should be 17 X 17
To see , try starting at length 1, and gradually increase the length.
The height decreases at a faster rate than the length increases, up until you reach a square.
Or if you want to use algebra, Say the width is 17-x
Then the length is 289/(17-x)
Now, this is bigger than 17+x, as shown here:
289/(17-x) > 17+x
289 > 289 - x^2
which is true.
so the perimeter would be bigger than 2 * (17- x + 17 + x) = 2 * (2 * 17) = 4 * 17
Again, the dimensions should be a square. 17 X 17.</span>
Remember them is the best way to go.
draw the exact value triangles if you're unsure, but importantly, you just need to memorise these exact values.
