Answer:
$24.35
Step-by-step explanation:
We will use the compound interest formula provided to solve this problem:
<em>P = initial balance</em>
<em>r = interest rate (decimal)</em>
<em>n = number of times compounded annually</em>
<em>t = time</em>
<em />
First, change 1% into a decimal:
1% -> -> 0.01
Since the interest is compounded monthly, we will use 12 for n. Lets plug in the values now:
Lastly, subtract <em>A </em>from the principal to get the interest earned:
Answer:
Step-by-step explanation:
Using the addition formulae for cosine
cos(x ± y) = cosxcosy ∓ sinxsiny
---------------------------------------------------------------
cos(120 + x) = cos120cosx - sin120sinx
= - cos60cosx - sin60sinx
= - cosx -
sinx
squaring to obtain cos² (120 + x)
= cos²x +
sinxcosx +
sin²x
--------------------------------------------------------------------
cos(120 - x) = cos120cosx + sin120sinx
= -cos60cosx + sin60sinx
= - cosx +
sinx
squaring to obtain cos²(120 - x)
= cos²x -
sinxcosx +
sin²x
--------------------------------------------------------------------------
Putting it all together
cos²x + cos²x +
sinxcosx +
sin²x +
cos²x -
sinxcosx +
sin²x
= cos²x + cos²x +
sin²x
= cos²x +
sin²x
= (cos²x + sin²x) =
Answer:
1.03
Step-by-step explanation:
To find the volume of a prism, find the area of the base and multiply it by the height.
The base is an octagon. The area is found . Substitute a = 0.5.
The volume is 1.21*2.5 = 3.025.
However, there are three holes drilled out half way which each have volume 0.06.
The volume is found as V = πr²h. Substitute r = 0.125 which is half the diameter of 0.25. Since they go half way, the height is h = 1.25.
V = π(0.125)²(1.25) = 0.06.
Since there are 3, they equal 3*0.06 = 0.18.
Subtract this from the volume.
1.21 - 0.18 = 1.03
