Answer: The dimensions of the rectangle are
Length = 75 and Width = 63
Step-by-step explanation: We would start with the information about the sides of the rectangle which states that the length is twelve inches more than it's width. In other words, if the width is represented by the letter w, then the length will be w + 12.
Also the perimeter of a rectangle is given as
2(L + W) where L is the length and W is the width of the rectangle
Therefore
Perimeter = 2( {w +12} + w)
276 = 2(2w + 12)
276 = 4w + 24
Subtract 24 from both sides of the equation
252 = 4w
Divide both sides of the equation by 4
63 = w
Therefore the width of the rectangle is 63 and the length is 75 (63 + 12).
L = 75 inches
W = 63 inches
By using <span>Euler’s formula which state that:
e∧(iΘ) = cos Θ + i sin Θ
So, z₁ = 2 ( cos π/6 + i sin </span>π/6 ) = 2 e∧(i <span>π/6)
And </span><span>z₂ = 3 ( cos π/4 + i sin π/4 ) = 3 e∧(i <span>π/4)
Then </span></span>z₁ * z₂ = 2 e∧(i π/6) * <span>3 e∧(i π/4) = 6 </span><span>e∧[i (</span><span>π/6 + π/4)]
= </span><span>6 e∧(i 5<span>π/12)
= 6</span></span><span> ( cos 5π/12 + i sin 5π/12 )</span>
Answer:
The amount invested at 4.5% was 
The amount invested at 5% was 
Step-by-step explanation:
we know that
The simple interest formula is equal to
where
I is the Final Interest Value
P is the Principal amount of money to be invested
r is the rate of interest
t is Number of Time Periods
Let
x -----> the amount invested at 4.5%
9,000-x -----> the amount invested at 5%
in this problem we have
substitute
so
therefore
The amount invested at 4.5% was
The amount invested at 5% was
