7. A 200-litre tank initially contains 100 litres of water with a salt concentration of 0.1 grams per litre. Water with a salt concentration of 1/3 grams per litre flows into the tank at a rate of 30 litres per minute, and the well-mixed solution is pumped out of the tank at a rate of 20 litres per minute. Let C(t) grams per litre be the concentration of salt in the tank at time t minutes. We can model C(t) with the differential equation, C'(t) = 10 - 20C(t) 10t + 100 Solve this differential equation for C(t).

Q: |4 -7 9 6 2 7 3 6 -3 0 7 4 1 0 3 -1

A: The given matrix  A= 4 -7 9 1      6 2 7 0      3 6 -3 3      0 7 4 -1.

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A: In the Given Right angle Triangle we have   Base = 7  Hypotenuse = 25

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A:

Q: 1. Provided the following matrices, solve for the following: -2 2 -67 12 -7 7 9 A 1=[1²/77³1 B = -5…

A: Solution is given below:

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A:

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A: Topic:- Algebra

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A:

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A: Given trigonometric functions.

Q: Solve numerically the following equation X3 + 5x = 20, give answer to three decimal places, start…

A: Given, x3 + 5x = 20, We know that xn+1=xn+f(x)f'(x)Here f(x)=x3+5x-20f'(x)=3x2+5

Q: Solve the following differential equation Select one: a. None O b. Ye.s=C₁te¹ +c₂t²e² O C.…

A: To find the general solution of the given differential equation.

Q: 1 1(2) + 1 + 2 (3) 1 1 + 3(4) 4(5) +...+ 1 n(n+1) = 1-¹ if n E N. n+1

A: Explanation of the answer is as follows

Q: A) |2x² + 5x + 1 = 1 B) 12/1 x-1 x+1 C) 5x + | ≥ 1

A:

Q: 9p5q9

A:

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A:

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A:

Q: Electrical power = 1²R [I= 4.0 x 10-8 A, F

A: On solving this we will get

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A:

Q: Given transformation T: R³ → M2x2 which is defined as T(x, y, z)=(x + y ) M2x2 is a vector space…

A: We can solve this as follows:

Q: L(e³t cos 2t)

A:

Q: Solve using the following system by determinants following Cramer's rule. x+y+z = 5 x - 2y - 3y = −1…

A: We have to slove determinants by use camer's rule

Q: 6. Discuss the nature of the solutions of the given equation without solving. A) 7x² + 5x - 1 = 0 B)…

A:

Q: 1. L{t²sinwt}

A: As we know from the property of the Laplace transform. Ltnft=-1ndndsnLft And Lsinat=as2+a2 Given:…

Q: The coordinate B (2, 30°, 3) is _____ in RCS. B (1.7321, 1, 3) B (1,1.7321, 3) B (0.3085,-1.9761, 3)

A: Topic:- co-ordinate system

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A: We use Lagrange multipliers method for optimization to solve the given question.

Q: Consider a triangle ABC like the one below. Suppose that c=51, a=59, and C=30°. (The figure is not…

A:

Q: Simplify (3x³ + 5z − 1) ÷ (x + 1) O 3z² + 3z +8+- O 32³-32² +8z-9 3x³ +3z² +8z+7 O 32²- 3z +8-7271

A:

Q: Use the functions f and g in C[-1, 1] to find (f, g), ||f||, ||g||, and d(f, g) for the inner…

A:

Q: Find two consecutive whole numbers that √39 lies between. and 10 x 5 ?

A: Given 39 We have to find two consecutive whole numbers that 39 lies between

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A:

Q: 6. √2+ i over R over O

A:

Q: Let S be the following relation on ℂ: S = {(x, y) ∈ ℂ2 : y − x is real}. Prove that S is an…

A:

Q: 3. The calories per serving of 11 fruit juices are shown in the following table. Find the mean,…

A: A detailed solution is given below.

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A:

Q: Prove the following Theorem. Let A and B be sets and f a function from A to B. Then the following…

A: We will prove it by using basic definition.

Q: en cos 0 = 2, find the other five trigonometric functions. Draw a picture to support your answers 20…

A:

Q: Given: 12 HI 9 12--9 12 9 can be simplified to i, find a + b. 12+√9

A: Solution given below

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Q: Find the norm of and the unit vector u in the direction of if 3 4 1-2) 18 |||| 13 = - 18 ||

A:

Q: 4. In a women's professional tennis tournament, the money a player wins depends on her finishing…

A: To write a rule which calculates the actual prize money won by nth player.

Q: 5. Design an algorithm that asks the user for the name of a text file containing a grid of numbers…

A: answer is in next step

Q: Help please I don't understand

A:

Q: Rafael launches a rocket straight up into the air. The table below gives the height  Ht  of the…

A:

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A: Answer is order of permutation

Q: Sketch the graph of on the axes below, indicating the value of the y-intercept. O y = 15 x 7x X

A:

Q: In which function does t vary jointly with q and r and inversely with s? Answer choices: t = kq/rs t…

A:

Q: x + 2y +32 = -1 - 2 + 5y +7z=5 +3₂ = 5 32 4y 2. X+Y-2=3 Sx - 2y + 2 = 8 x + 3y + 4z = 5 1.

A: To find the solution of the linear equations (1) x+2y+3z=−1   ...(a) −z+5y+7z=5 ⇒5y+6z =5…

Q: Determine the Wo fourth root of 16+ 16i in exponential form. COMPLETE THE MISSING THE BLANKS FOR THE…

A: To determine the w0 fourth root of 16+16i in exponential form.

Q: 11. f(x) = 10x³-15x²+12x+14, g(9) 12. f(x) = -10x+14, g(x) = 15x+13; find f(g(5)) 13. f(x) =…

A:

Q: If the perimeter of a rectangle is 38 cm and the area is 84 square cm, then what are the dimensions…

A:

Q: xx9 (6abc)(5a²c2) (6a)-3 NI m 을 (6¹x6) ²2/ 14⁰ 30 - 12

A: 1. x7.x92. x9x73. 6abc5a3c24. 64x6125. 6a-36. 14030-127. 2233