$2,000 - $23,75 = $1,976.25 / 8 = $<span>247.03 each</span>
When Area of rectangle is constant, then the length x is inversely proportional to the width y of the rectangle.
![x\propto \frac{1}{y}](https://tex.z-dn.net/?f=x%5Cpropto%20%20%5Cfrac%7B1%7D%7By%7D%20)
We know that the area of a rectangle is given by the product of the length and width of the rectangle.
Area = Length*Width
In this given problem,
The length of the rerectanglctangle is represented by x
and the width of the rectangle is represented by y
If the area of the rectangle is represented by A now.
So by the formula,
A = x*y
When A is constant then,
x = A/y
![\therefore x \propto \frac{1}{y}](https://tex.z-dn.net/?f=%5Ctherefore%20x%20%5Cpropto%20%5Cfrac%7B1%7D%7By%7D)
So from the above calculation we can conclude that about relation between length and width that,
"When Area of rectangle is constant, then the length x is inversely proportional to the width y of the rectangle."
Learn more about Area here -
brainly.com/question/25292087
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Answer: - 60i - 14j
Step-by-step explanation:
- 18i + 16j - 42i - 30j = - 60i - 14j
Answer:
![y(x)=x^2+5x](https://tex.z-dn.net/?f=y%28x%29%3Dx%5E2%2B5x)
Step-by-step explanation:
Given: ![y'=\sqrt{4y+25}](https://tex.z-dn.net/?f=y%27%3D%5Csqrt%7B4y%2B25%7D)
Initial value: y(1)=6
Let ![y'=\dfrac{dy}{dx}](https://tex.z-dn.net/?f=y%27%3D%5Cdfrac%7Bdy%7D%7Bdx%7D)
![\dfrac{dy}{dx}=\sqrt{4y+25}](https://tex.z-dn.net/?f=%5Cdfrac%7Bdy%7D%7Bdx%7D%3D%5Csqrt%7B4y%2B25%7D)
Variable separable
![\dfrac{dy}{\sqrt{4y+25}}=dx](https://tex.z-dn.net/?f=%5Cdfrac%7Bdy%7D%7B%5Csqrt%7B4y%2B25%7D%7D%3Ddx)
Integrate both sides
![\int \dfrac{dy}{\sqrt{4y+25}}=\int dx](https://tex.z-dn.net/?f=%5Cint%20%5Cdfrac%7Bdy%7D%7B%5Csqrt%7B4y%2B25%7D%7D%3D%5Cint%20dx)
![\sqrt{4y+25}=2x+C](https://tex.z-dn.net/?f=%5Csqrt%7B4y%2B25%7D%3D2x%2BC)
Initial condition, y(1)=6
![\sqrt{4\cdot 6+25}=2\cdot 1+C](https://tex.z-dn.net/?f=%5Csqrt%7B4%5Ccdot%206%2B25%7D%3D2%5Ccdot%201%2BC)
![C=5](https://tex.z-dn.net/?f=C%3D5)
Put C into equation
Solution:
![\sqrt{4y+25}=2x+5](https://tex.z-dn.net/?f=%5Csqrt%7B4y%2B25%7D%3D2x%2B5)
or
![4y+25=(2x+5)^2](https://tex.z-dn.net/?f=4y%2B25%3D%282x%2B5%29%5E2)
![y(x)=\dfrac{1}{4}(2x+5)^2-\dfrac{25}{4}](https://tex.z-dn.net/?f=y%28x%29%3D%5Cdfrac%7B1%7D%7B4%7D%282x%2B5%29%5E2-%5Cdfrac%7B25%7D%7B4%7D)
![y(x)=x^2+5x](https://tex.z-dn.net/?f=y%28x%29%3Dx%5E2%2B5x)
Hence, The solution is
or ![y(x)=x^2+5x](https://tex.z-dn.net/?f=y%28x%29%3Dx%5E2%2B5x)