4. Consider all possible rectangular solids defined by 0 ≤ x ≤ a, 0 ≤ y ≤ b, 0 ≤ z ≤ 1 and the vector field given by F = (−x 2 − 4xy)i − 6yzj + 12zk. (a) Calculate the total outwards flux through the 6 sides of the solid. (b) Find value(s) for a and b that yield the maximum flux. (c) Calculate the maximum total flux.

Write the fraction 9/50 as a decimal if needed round to the nearest hundredth

Submarines control how much they float or sink in the ocean by changing the volume of air and water contained in large ballast tanks. when the tanks are completely full of water, the submarine increases its overall mass and sinks down to the bottom. when the tanks are completely full of air, the submarine reduces its overall mass and floats to the surface. depending on the density of the seawater surrounding the submarine, it will pump seawater in or out of the tanks in order to achieve the same overall density as the sea water and float neutrally in the water. the volume of the submarine never changes. when the tanks are completely full of water, a submarine with a volume of 7.8\times10^3\text{ m}^37.8×10 3 m 3 7, point, 8, times, 10, start superscript, 3, end superscript, space, m, start superscript, 3, end superscript has a total mass of 8\times10^6\text{ kg}8×10 6 kg8, times, 10, start superscript, 6, end superscript, space, k, g. the density of the seawater is 10^3\text{ kg/m}^310 3 kg/m 3 10, start superscript, 3, end superscript, space, k, g, slash, m, start superscript, 3, end superscript. to make that submarine float neutrally, and neither float nor sink in the ocean, what volume of water does that submarine need to subtract from its tanks?

Question 1 (3 points) saved what is the solution for the following system of equations? use any method to solve. y = -x +4 y = x - 2 question 1 options: ( 4 , -2) (2, 1) (3, 1) (3, -2) question 2 (3 points) saved the solution to a system of equations is where the lines intersect. question 2 options: true false question 3 (3 points) which ordered pair is the best estimate for the solution of the system of equations? the graph of the system of equations : y = 3/2x +6 and y=1/4x - 2 question 3 options: (-6, -3) (-6.5, -3.5) (-7, -4) (-7, -3.5) question 4 (3 points) what is the solution for the following system of equations? use any method to solve. 2x + 8y = 4 x = -3y + 5 question 4 options: x = 14, y= -3 x = 2, y = -3 x = -3, y = -3 x = 12, y = 5 question 5 (3 points) solve the following system using any method. 8a - 4b = 20 5a - 8b = 62 question 5 options: a = 5, b = -4 a = 8, b = 4 a = -5, b = -8 a = -2, b = -9 question 6 (3 points) breana is selling tickets to a choral performance. on the first day of ticket sales, she sold 3 senior citizen tickets and 1 child ticket for a total of $38. breana took in $52 on the second day by selling 3 senior citizen tickets and 2 child tickets. what is the price of a senior citizen ticket? question 6 options: question 7 (3 points) a farmer has 5 times as many cows as pigs. the farmer only has cows and pigs, and he has 168 animals. how many cows does he have? question 7 options: 140 cows 120 cows 50 cows 28 cows question 8 (3 points) how many solutions does the system have? question 8 options: zero one infinitely many question 9 (3 points) what is the solution to the system of equations? graph of x+2y = 6 and y = x question 9 options: (1 , -2) (2, 2) (3, 5) (-2, 2)