Answer:
Length = 2x + 5
Width = x + 3
Step-by-step explanation:
Area of rectangle = length × width
Expression for area of the rectangle = 2x² + 11x + 15
Factorising the quadratic expression
2x² + 11x + 15 = 2x² + 6x + 5x + 15 = (2x² + 6x) + (5x + 15) = 2x(x + 3) +5(x + 3) = (2x + 5)(x + 3)
Length = 2x + 5
Width = x + 3
At the start, the tank contains
(0.02 g/L) * (1000 L) = 20 g
of chlorine. Let <em>c</em> (<em>t</em> ) denote the amount of chlorine (in grams) in the tank at time <em>t </em>.
Pure water is pumped into the tank, so no chlorine is flowing into it, but is flowing out at a rate of
(<em>c</em> (<em>t</em> )/(1000 + (10 - 25)<em>t</em> ) g/L) * (25 L/s) = 5<em>c</em> (<em>t</em> ) /(200 - 3<em>t</em> ) g/s
In case it's unclear why this is the case:
The amount of liquid in the tank at the start is 1000 L. If water is pumped in at a rate of 10 L/s, then after <em>t</em> s there will be (1000 + 10<em>t</em> ) L of liquid in the tank. But we're also removing 25 L from the tank per second, so there is a net "gain" of 10 - 25 = -15 L of liquid each second. So the volume of liquid in the tank at time <em>t</em> is (1000 - 15<em>t </em>) L. Then the concentration of chlorine per unit volume is <em>c</em> (<em>t</em> ) divided by this volume.
So the amount of chlorine in the tank changes according to

which is a linear equation. Move the non-derivative term to the left, then multiply both sides by the integrating factor 1/(200 - 5<em>t</em> )^(5/3), then integrate both sides to solve for <em>c</em> (<em>t</em> ):


![\dfrac{\mathrm d}{\mathrm dt}\left[\dfrac{c(t)}{(200-3t)^{5/3}}\right]=0](https://tex.z-dn.net/?f=%5Cdfrac%7B%5Cmathrm%20d%7D%7B%5Cmathrm%20dt%7D%5Cleft%5B%5Cdfrac%7Bc%28t%29%7D%7B%28200-3t%29%5E%7B5%2F3%7D%7D%5Cright%5D%3D0)


There are 20 g of chlorine at the start, so <em>c</em> (0) = 20. Use this to solve for <em>C</em> :

![\implies\boxed{c(t)=\dfrac1{200}\sqrt[3]{\dfrac{(200-3t)^5}5}}](https://tex.z-dn.net/?f=%5Cimplies%5Cboxed%7Bc%28t%29%3D%5Cdfrac1%7B200%7D%5Csqrt%5B3%5D%7B%5Cdfrac%7B%28200-3t%29%5E5%7D5%7D%7D)
Answer:
The coordinates of other point are: (5,1)
Step-by-step explanation:
Given coordinates are:
M(x,y) = (2,4)
R(x_1,x_2) = (-1,7)
We have to find the coordinates of other point (x2,y2)
The formula for mid-point is given by:

Putting the values we get

Putting respective elements equal

Hence,
The coordinates of other point are: (5,1)
Hi there
let me help you out
The answer is 30
To find the answer you have to find the multiples of 2 and 5
2,4,6,8,10,12, 14,16,18,20,22,24,26,28,30,32,34,
5,10,15,20,25,30
30 comes in both time tables.
it also does not cross 34
hope this helps you