Answer:
Part 1) The constant of variation is 
part 2) The equation is 
Step-by-step explanation:
we know that
A relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form 
or 
Let
x -----> the number of square feet
y -----> the number of square yards
Three square yards are equivalent to 27 square feet
so
we have the point (27,3)
Part 1) What is the constant of variation?
The constant of variation or proportionality is equal to
substitute the values
Simplify
Part 2) What is the equation representing the direct variation?
we know that
substitute the value of k
These triangles are congruent by AAS condition hence the statement is true
<span>Let L be the number of yards on a roll of lace ribbon.
Let S be the number of yards on a roll of satin ribbon.
We can set up two equations.
equation 1: 3L + 2S = 120 yards
equation 2: 2L + 4S = 160 yards
We can multiply (equation 1) by 2 and subtract (equation 2).
equation 1: 6L + 4S = 240 yards
equation 2: 2L + 4S = 160 yards
4L = 80 yards
L = 20 yards
equation 1: 3L + 2S = 120 yards
3(20 yards) + 2S = 120 yards
2S = 60 yards
S = 30 yards
There are 20 yards on a roll of lace ribbon.
There are 30 yards on a roll of satin ribbon.</span>
Answer:
Step-by-step explanation:
given is the Differential equation in I order linear as
Take Laplace on both sides
![L(y') +4L(y) = 48L(t)\\sY(s)-y(0) +4Y(s) = 48 *\frac{1}{s^2} \\Y(s) [s+4]=\frac{48}{s^2}+9\\Y(s) = \frac{1}{s^2(s+4)}+\frac{9}{s+4}](https://tex.z-dn.net/?f=L%28y%27%29%20%2B4L%28y%29%20%3D%2048L%28t%29%5C%5CsY%28s%29-y%280%29%20%2B4Y%28s%29%20%3D%2048%20%2A%5Cfrac%7B1%7D%7Bs%5E2%7D%20%5C%5CY%28s%29%20%5Bs%2B4%5D%3D%5Cfrac%7B48%7D%7Bs%5E2%7D%2B9%5C%5CY%28s%29%20%3D%20%5Cfrac%7B1%7D%7Bs%5E2%28s%2B4%29%7D%2B%5Cfrac%7B9%7D%7Bs%2B4%7D)
Now if we take inverse we get y(t) the solution
Thus the algebraic equation would be
Answer: ∠ACB ≅ ∠E'C'D'; translate point D' to point B
Step-by-step explanation:
That is just my best guess.
