Answer:
The work will be "1909212.015 J". The further explanation is given below.
Step-by-step explanation:
The given values are:
Liquid's density
= 760 kg/m³
Height
= 3 meters
Gravity
g = 3.8 m/s²
Value of y is:
y = 5 log (x-2)
y = 0
y = 4
As we know,
⇒ ![\Delta V=\pi r^2 \Delta y](https://tex.z-dn.net/?f=%5CDelta%20V%3D%5Cpi%20r%5E2%20%5CDelta%20y)
⇒ ![y =5log(x-2)](https://tex.z-dn.net/?f=y%20%3D5log%28x-2%29)
⇒ ![\frac{y}{5} =log (x-2)](https://tex.z-dn.net/?f=%5Cfrac%7By%7D%7B5%7D%20%3Dlog%20%28x-2%29)
⇒ ![e^{\frac{y}{5}}=(x-2)](https://tex.z-dn.net/?f=e%5E%7B%5Cfrac%7By%7D%7B5%7D%7D%3D%28x-2%29)
⇒ ![x=e^{\frac{y}{5}}+2](https://tex.z-dn.net/?f=x%3De%5E%7B%5Cfrac%7By%7D%7B5%7D%7D%2B2)
Now,
![\Delta F=ma](https://tex.z-dn.net/?f=%5CDelta%20F%3Dma)
![=760 \pi (e^{\frac{y}{5}}+2)^2(9.8)\Delta y](https://tex.z-dn.net/?f=%3D760%20%5Cpi%20%28e%5E%7B%5Cfrac%7By%7D%7B5%7D%7D%2B2%29%5E2%289.8%29%5CDelta%20y)
So that,
⇒ ![\Delta W = \Delta F.distance](https://tex.z-dn.net/?f=%5CDelta%20W%20%3D%20%5CDelta%20F.distance)
![=\Delta F(4-y)](https://tex.z-dn.net/?f=%3D%5CDelta%20F%284-y%29)
The required work will be:
⇒ ![W=760\times 9.8 \pi \int_{3}^{0}(e^{\frac{y}{5}}+2)^2 (\Delta-y)dy](https://tex.z-dn.net/?f=W%3D760%5Ctimes%209.8%20%5Cpi%20%5Cint_%7B3%7D%5E%7B0%7D%28e%5E%7B%5Cfrac%7By%7D%7B5%7D%7D%2B2%29%5E2%20%28%5CDelta-y%29dy)
![=760\times 9.8 \pi[{-20(y-9)^{e^{\frac{y}{5}}}-2(y-8)y}]](https://tex.z-dn.net/?f=%3D760%5Ctimes%209.8%20%5Cpi%5B%7B-20%28y-9%29%5E%7Be%5E%7B%5Cfrac%7By%7D%7B5%7D%7D%7D-2%28y-8%29y%7D%5D)
![=760\times 9.8 \pi[81.455]](https://tex.z-dn.net/?f=%3D760%5Ctimes%209.8%20%5Cpi%5B81.455%5D)
![=1909212.015 \ J](https://tex.z-dn.net/?f=%3D1909212.015%20%5C%20J)
<u>Your answer is 28x^2-37x+12</u>
<u>1) Use the FOIL method: (a+b)(c+d)=ac+ad+bc+bd</u>
28x^2-21x-16x+12
<u>2) Collect like terms</u>
28x^2+(-21-16x)+12
<u>3) Simplify</u>
28x^2-37x+12
Answer:
A: 180° B: 360° C: 540°
Step-by-step explanation:
A: The measures of interior angles of a triangle sum to 180°. Since figure ABC is a triangle, the interior angles of figure ABC sum to 180°.
B: We can see the quadrilateral ACDE is a trapezoid. If you can see, the trapezoid can be split into two triangles if you connect points C and E. As U mentioned before, the measures of interior angles of a triangle sum to 180°. Since we know figure ACDE can be split into <u>two triangles</u> we have to do: 180x2 which is 360°.
C: Now that we know the Pentagon ABCDE can be split into 3 triangles(1 from figure ABC and 2 from figure ACDE), we have to multiply 180 by 3 because like I mentioned before, the measures of interior angles of a triangle sum to 180°. So, 180x3=540°.
For this case, the first thing we must do is define a variable.
We have then:
t: number of years
P (t): number of people since 2010
We know that:
1) There were 30,700 people in the city
2) The population is growing at a rate of 850 people per year.
The equation modeling the problem is given by:
![P (t) = 850t + 30700](https://tex.z-dn.net/?f=%20P%20%28t%29%20%3D%20850t%20%2B%2030700%20)
Answer:
a formula for the city's population is:
![P (t) = 850t + 30700](https://tex.z-dn.net/?f=%20P%20%28t%29%20%3D%20850t%20%2B%2030700%20)