Answer: 12/5 or 2 2/5
2 divide 5=2/5
2/5 times 6 = 12/5
or 2 2/5
Answer:
![\huge\boxed{\sf x = 12 }](https://tex.z-dn.net/?f=%5Chuge%5Cboxed%7B%5Csf%20x%20%3D%2012%20%7D)
Step-by-step explanation:
Opposite sides and angles of a parallelogram are equal.
So,
3x - 1 = 35
Add 1 to both sides
3x = 35 + 1
3x = 36
Divide 3 to both sides
x = 36 / 3
x = 12
![\rule[225]{225}{2}](https://tex.z-dn.net/?f=%5Crule%5B225%5D%7B225%7D%7B2%7D)
Hope this helped!
<h3>~AH1807</h3>
Answer: Level of the liquid dropping at 28.28 inch/second when the liquid is 2 inches deep.
Step-by-step explanation:
Since we have given that
Height = 9 inches
Diameter = 6 inches
Radius = 3 inches
So, ![\dfrac{r}{h}=\dfrac{3}{9}=\dfrac{1}{3}\\\\r=\dfrac{1}{3}h](https://tex.z-dn.net/?f=%5Cdfrac%7Br%7D%7Bh%7D%3D%5Cdfrac%7B3%7D%7B9%7D%3D%5Cdfrac%7B1%7D%7B3%7D%5C%5C%5C%5Cr%3D%5Cdfrac%7B1%7D%7B3%7Dh)
Volume of cone is given by
![V=\dfrac{1}{3}\pi r^2h\\\\V=\dfrac{1}{3}\pi \dfrac{1}{9}h^2\times h\\\\V=\dfrac{1}{27}\pi h^3](https://tex.z-dn.net/?f=V%3D%5Cdfrac%7B1%7D%7B3%7D%5Cpi%20r%5E2h%5C%5C%5C%5CV%3D%5Cdfrac%7B1%7D%7B3%7D%5Cpi%20%5Cdfrac%7B1%7D%7B9%7Dh%5E2%5Ctimes%20h%5C%5C%5C%5CV%3D%5Cdfrac%7B1%7D%7B27%7D%5Cpi%20h%5E3)
By differentiating with respect to time t, we get that
![\dfrac{dv}{dt}=\dfrac{1}{27}\pi \times 3\times h^2\dfrac{dh}{dt}=\dfrac{1}{9}\pi h^2\dfrac{dh}{dt}](https://tex.z-dn.net/?f=%5Cdfrac%7Bdv%7D%7Bdt%7D%3D%5Cdfrac%7B1%7D%7B27%7D%5Cpi%20%5Ctimes%203%5Ctimes%20h%5E2%5Cdfrac%7Bdh%7D%7Bdt%7D%3D%5Cdfrac%7B1%7D%7B9%7D%5Cpi%20h%5E2%5Cdfrac%7Bdh%7D%7Bdt%7D)
Now, the liquid drips out the bottom of the filter at the constant rate of 4 cubic inches per second, ie ![\dfrac{dv}{dt}=-4\ in^3](https://tex.z-dn.net/?f=%5Cdfrac%7Bdv%7D%7Bdt%7D%3D-4%5C%20in%5E3)
and h = 2 inches deep.
![-4=\dfrac{1}{9}\times \pi\times (2)^2\dfrac{dh}{dt}\\\\-9\pi =\dfrac{dh}{dt}\\\\-28.28=\dfrac{dh}{dt}](https://tex.z-dn.net/?f=-4%3D%5Cdfrac%7B1%7D%7B9%7D%5Ctimes%20%5Cpi%5Ctimes%20%282%29%5E2%5Cdfrac%7Bdh%7D%7Bdt%7D%5C%5C%5C%5C-9%5Cpi%20%3D%5Cdfrac%7Bdh%7D%7Bdt%7D%5C%5C%5C%5C-28.28%3D%5Cdfrac%7Bdh%7D%7Bdt%7D)
Hence, level of the liquid dropping at 28.28 inch/second when the liquid is 2 inches deep.
Unit rate means one. So the best way to solve this is using a proportion over one. If there are 258 pencils in 3 purses 258/3 then how many are in one purses x/1. Cross multiply next.
258/3 * x/1. You get 3x and 258. To get the x alone, divide both sides by three. Your answer is 86 pencils in one purse.
Purple flowers: black flowers = 4:8 = 108
4 + 8 = 12
108 / 12 = 9.
9 x 4 = 36.
36 of the flowers are purple.