A trough has a trapezoidal cross section with a height of 5 m and horizontal sides of width 5/2 m and 5 m. Assume the length of the trough is 10 m. Complete parts? (a) and? (b) below.

a) How much work is required to pump the water out of the trough? (to the level of the top of the? trough) when it is? full? Use 1000 kg/m3 for the density of water and9.8 m/s2 for the acceleration due to gravity. Draw a? y-axis in the vertical direction? (parallel to? gravity) and use the midpoint of the bottom of one edge of the trough as the location of the origin. For 0?y?5?, find the? cross-sectional area? A(y) in terms of y.

b) Set Up the integral that gives the work required to pump the water out of the tank.

Step-by-step explanation:

Total mass of water = density X volume = 1000 kg/m3 x 187.5 m3

where H2 = initial position of centre of mass from ground

where H1 = final position of centre of mass from ground

company a

step-by-step explanation:

using the linear regression models , it is found that company a   pays about $14 more. but using the same regression (linear) company b pays about $10 more.

so company a pays more than b

the solution of the equation is 2.23 ⇒ answer b

step-by-step explanation:

* lets revise the meaning of exponential function

- the form of the exponential function is y = ab^x, where a ≠ 0, b > 0 ,  

  b ≠ 1, and x is any real number

- it has a constant base b

- it has a variable exponent x

- to solve an exponential equation, take the log or ln of both sides,  

  and solve for the variable

* lets solve the problem

∵

- the base is 7 and the exponent is x

- insert ㏑ in both sides

∴

- use the rule

∴ x ㏑(7) = ㏑(77)

- to find x divide both sides by ㏑(7)

∴

* the solution of the equation is 2.23 to the nearest 2 decimal places