Discrete Mathematics: Introduction to Mathematical Reasoning
1st Edition
ISBN: 9780495826170
Author: Susanna S. Epp
Publisher: Cengage Learning
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A tank contains 60 kg of salt and 2000 L of water. Pure water enters a tank at the rate 8 L/min. The
solution is mixed and drains from the tank at the rate 11 L/min.
Let y be the number of kg of salt in the tank after t minutes.
The differential equation for this situation would be:
dy
dt
y(0) =
Simplify the below expression.
3 - (-7)
Solve the initial value problem:
y= 0.05y + 5
y(0) = 100
y(t) =
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- I need expert solution to this question s pleasearrow_forward(6) ≤ a) Determine the following groups: Homz(Q, Z), Homz(Q, Q), Homz(Q/Z, Z) for n E N. Homz(Z/nZ, Q) b) Show for ME MR: HomR (R, M) = M.arrow_forwardAlready got wrong chatgpt answer Plz don't use chatgpt answer will upvote otherwise leave it .arrow_forward
- y=f'(x) 1 8 The function f is defined on the closed interval [0,8]. The graph of its derivative f' is shown above. How many relative minima are there for f(x)? O 2 6 4 00arrow_forward60! 5!.7!.15!.33!arrow_forwardUse Euler's summation formula to prove that, for x > 2, Σ log n n3 = A log x 2x2 n≤x where A is a constant. - 1 +0 4x2 log x x3 "arrow_forward
- • • Let > be a potential for the vector field F = (−2 y³, −6 xy² − 4 z³, −12 yz² + 4 2). Then the value of sin((-1.63, 2.06, 0.57) – (0,0,0)) is - 0.336 -0.931 -0.587 0.440 0.902 0.607 -0.609 0.146arrow_forward1. If f(x² + 1) = x + 5x² + 3, what is f(x² - 1)?arrow_forward2. What is the total length of the shortest path that goes from (0,4) to a point on the x-axis, then to a point on the line y = 6, then to (18.4)?arrow_forward
- The value of cos(4M) where M is the magnitude of the vector field with potential ƒ = e² sin(лy) cos(π²) at x = 1, y = 1/4, z = 1/3 is 0.602 -0.323 0.712 -0.816 0.781 0.102 0.075 0.013arrow_forwardThere is exactly number a and one number b such that the vector field F = conservative. For those values of a and b, the value of cos(a) + sin(b) is (3ay + z, 3ayz + 3x, −by² + x) is -0.961 -0.772 -1.645 0.057 -0.961 1.764 -0.457 0.201arrow_forwardWhat is the volume of a sphere with a radius of pie cm?arrow_forward
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