Answer:
25151/100000
Step-by-step explanation:
Constant of proportionality is the constant value of the two proportional quantities, in this problem p and s, where 4 is the factor of proportionality because it is constant or k.
In simple terms, p is in direct proportion to s wherein the increase or decrease in value of s results to the increase or decrease in value of p with 4 the only factor remaining unchanged.
In the above problem, the number 4 is derived from the word square. We all know that a square has 4 sides of equal lengths, therefore, the perimeter is equivalent to the product of 4 and its lenght.
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
I would have to say that the angle is 61 degrees but this may not be correct so you know <span />
Answer:
y = cos (x + pi/6)
Step-by-step explanation:
We are told this is a translation. Look at the original graph which is dashed. That is the graph of y = cos x. Now look at the translated graph which is solid. Compared to the dashed graph, the solid line is translated to the left.
The question now is how much of a horizontal translation it has. The scale on the x axis can be determined. The period of the cosine function is 2pi. At x = 0, the graph of y = cos x has a maximum value. At x = 2pi, the graph has a maximum value again. From the highest point of he dashed graph to the next highest point, the distance along the x-axis must be 2pi. That means the second maximum we see at the right is at x = 2pi. Since the 2pi interval is divided into 12 equal spaces, that means each vertical line along the x-axis represents 2pi/12, or pi/6. Notice that the solid graph is pi/6 to the left of the dashed line, so the translation is pi/6 to the left, or -pi/6.
A horizontal translation is obtained when x is replaced by x - h.
cos x is the original function.
cos (x - h) is the translated function, where h is the translation.
Since the translation is -pi/6, then h = -pi/6
cos [x - (-pi/6)] = cos (x + pi/6)
G, the translated function has equation
y = cos (x + pi/6)
