Let

denote the amount of salt in the tank at time

. We're given that the tank initially holds

lbs of salt.
The rate at which salt flows in and out of the tank is given by the relation


Find the integrating factor:

Distribute

along both sides of the ODE:




Since

, we get

so that the particular solution for

is

The tank becomes full when the volume of solution in the tank at time

is the same as the total volume of the tank:

at which point the amount of salt in the solution would be
lets take the number 555<u>5</u>
the bold 5 is the one with the greater value since its worth in 5,000
the underlined has less value since its single worth is 5
Answer:
15+5 and 5(3 + 1)
Step-by-step explanation:
I did the test :3
Answer:
-5
Step-by-step explanation:
you plug in zero for x and then just solve.
h(0)=-0-5
=-5
Volume of the cake= volume of right pyramid + volume of cube below the pyramid = 1/3 (b)(h) + b^3 where b = 19.5 and h = 13 plug these value into the formula, you get 7502.875, the volume is less than 10, 000. remember that the batter can supply 10, 000 in^3 of cake and the cake that you are making is only 7499 in ^ 3 so she has enough. now let's move on with the frosting. Surface area. we need the formula of a triangle and a square. formula of triangle is bh/2 and square area is b^2. let's do the pyramid first. how many triangles are there for the pyramid? 4 so we have to multiply the number of triangles to the area of one triangle to get the s.a. for each. Area = 4 x 1/2 bh base = 19.5 height= 13 plug your given values in the formula and you'll get? 507 now let's move on with the surface area of the cube. how many squares(sides) are there in a cube? 5 since she does not frost the cake at the bottom, we will only find the area of 5 squares. area of a square is b^2 So 5 x b^2 b=19.5 what will you get? 1901.25 now add the area of the triangles to the area of the squares, 2408.25 is it less than or greater than 3000 in^2 ? less the frosting that she has can cover 3000 in^2 of a cake. you have 2408.2 in^2 cake, so does that frosting enough or nah? remember 2408 is LESS than 3000, so it means she has more so the frosting is enough to cover your cake :) therefore, both the frosting and the batter are enough to make your house cake !