A semicircular plate with radius 8 m is submerged vertically in water so that the top is 3 m above the surface. Express the hydrostatic force against one side of the plate as an integral and evaluate it. (Round your answer to the nearest whole number. Use 9.8 m/s2 for the acceleration due to gravity. Recall that the weight density of water is 1000 kg/m3.)

If the square end is under water: 312271.92  N

If the round end is under water:   262976.67 N

Step-by-step explanation:

We have to:

P = ρ·g·d

where:

P is hydrostatic pressure, g is gravitational acceleration, d is depth, ρ is fluid density

Force = hydrostatic pressure x submerged area

F = PA

You didn't specify the orientation

If the square end is under water:

F = (1000 kg/m³) (9.81 m/s²) (2) ∫ (2-y)√(64 - y²) dy from 0 to 2

F = 19620 ∫ (2-y)√(64 - y²) dy from 0 to 2

The result of the solution of the integral is 15.916

Thus:

F = 15.916*19620 = 312271.92  N

If the round end is under water:

F = (1000 kg/m³) (9.81 m/s²) (2) ∫ (y - 3) √(64- y²) dy from 3 to 5

F = 19620 ∫ (y - 3) √(25 - y²) dy from 3 to 5

The result of the solution of the integral is 13.403

Thus:

= 13.403*19620 = 262976.67 N

answer: yes youre right.

step-by-step explanation:

b: |12 – x| ≤ 0.25

step-by-step explanation:      

let x be the possible lengths in inches, of the ribbons jaime cut.

we have been given that jaime is cutting strips of ribbon for a project. he tries to cut each piece to be 12 inches long, but sometimes he cuts it too long or too short by as much as 0.25 inch.  

we can represent this information in an inequality as:

by the definition of absolute value function we will get,

upon combining our inequalities we will get,

therefore, the inequality   describes all the possible lengths (x), in inches, of the ribbons jaime cut.

step-by-step explanation: