The profit function of a certain firm is f(x) = -6x² + 1188x - 1200, where x denotes units of product produced, and f(x) is in Rands. PART A: a) If the firm produces 12 units of the product, its profit will be R b) If the firm produces 212 units of the product, it will suffer a loss c) If (x*,y*) is the highest point on the firm's profit curve, then x*= hs while y*=

Q: Show the complete solutions. Family of horizontal parabolas whose h to k ratio is 2 Ans: 2xy" - 4yy"…

A:

Q: Q6) (E.G.) If AABC~ A EFG, 2A 3EG and the perimeter of AABC is 12. Then the perimeter of A EFG is:…

A:

Q: 3. Using the following table, find the average rate of change from x = 2 to 11 X f(x) -1 -4 2 4 4 8…

A:

Q: Só 1 x²+7x+10 A. B. C. D. 3ln 2-ln 2 3 3ln 2+ln 2 3 3ln 2-ln 2 5 3ln 3-ln 2 3 dx

A: The given integral, ∫011x2+7x+10dx use the integral formula, ∫dxx+a=lnx+a+C

Q: During an 8-hour shift, the rate of change of productivity (in units per hour) of infant activity…

A:

Q: 3 Use the Squeeze Theorem to evaluate lim f(x), where f(x)=x²cos (-). x A B C D - 0 0 1 8 -0-x

A:

Q: (1) f dx x3-2x² (2) S dx x²√ √9-x² (3) fx² sin x dx

A:

Q: fcos (x) sin(x) dx

A: We need to find out the integration of the given integrand.

Q: Find the differential equations for each family of curves under the following conditions: a)…

A:

Q: Let the sample space be positive, real numbers and the events A and B as follows: A = {x | x 62.5},…

A: Note: We’ll answer the first question since the exact one wasn’t specified. Please submit a new…

Q: Suppose the quantity (in grams) of a radioactive substance present at time t is Q(t) = 38,416…

A:

Q: if f(x) = x + 5* . find the derivative of this function f'(x) A. f'(x) = 5* In 5 B. f'(x) = -1 + 5*…

A:

Q: Find a vector parametrization for the quarter-ellipse from (5, 0, 6) to (0, −2, 6) centered at (0,…

A:

Q: (a) lim f(x) (b) lim f(x) x-2+ (c) lim f(x) x-2 (d) f(2) (e) lim f(x) X-4 (F) (4) Need Help? Read It…

A:

Q: If f(x)=√x find limx-4 f(x)-f(4) x-4

A:

Q: Solve for the variable of the following quadratic equations. Kindly provide a COMPLETE and CLEAR…

A: We have to solve the given quadratic equations.

Q: (2) S dx x²√9-x²

A: Note:- Since you have asked multiple question As per our policy, we will solve the first question…

Q: A circle has the equation 4x² + 16x + 4y² = (a) Find the center (h,k) and radius r of the circle.…

A: Given Equation:- 4x2+16x+4y2=0

Q: if f(x) = x + 5*. find the derivative of this function f'( A. f'(x) = 5* In 5

A:

Q: 2. Eliminate the arbitrary constants of the equation below, where ß is a parameter. 4 x = C₁eßt + C₂…

A: To find- Eliminate the arbitrary constants of the equation below, where β is a parameter. x = c1eβt…

Q: Find the Differential Equation to the given Solution x sin y - xy² = c

A: To find the differential equation corresponding to given function.

Q: (1) lim,-0 √x+9-3 X (2) lim-0 1–c05x x sinx (3) limx-1 x²+3x-4 x-1

A:

Q: Problem 2. Determine if b 665 is a linear combination of a₁ = دا بن a2 11 a3 =

A: To find- Determine if b = 665 is a linear combination of a1 = 12-3, a2 = -3-41, a3 = 216.

Q: Calculate 127 y [1/10 ds where C is the parabola r(t) = (t, t², 0). Let 1 ≤ t ≤ 4. X

A:

Q: lim x→2 f(x), where f(x) =    10  −  2x    if x < 2 x2  −  x    if x ≥ 2

A:

Q: A research lab grows a type of bacterium in culture in a circular region. The radius of the circle,…

A:

Q: Show the complete solutions. Family of circles centered at the line y = 2x. Ans: y" (y-2x) + 2(y')³…

A: Given problem:- Differential equation of family of circles centerd at the line y=2x

Q: Find the domain and sketch the graph of the function

A:

Q: 28. Se cost sin 2t dt

A: ∫0πecostsin2tdtSolution :∫0πecostsin2tdt2∫0πecostsintcostdtlet, cost=x-sintdx=dxsintdx=-dxat…

Q: Find the parametric equations for the tangent line to the curve x =t* _ 1,y=t* +1,z=t* - at the…

A:

Q: Show the complete solutions. Family of circles centered at the line y = 2x. Ans: y" (y-2x) + 2(y')³…

A: To find out the differential equation for the family of circles having centre on the line y=2x.

Q: A. Complete the table below Given 1. 2x - 3x² = 5 2. 4 – x2 = 5x 3. (2x + 5)(x-4) = 0 4. 2x(x - 1) =…

A: Standard form of the quadratic equation : ax2+bx+c =0 . Note : As per our Guidelines we can solve…

Q: 2. 1 is equivalent to which of the following? - (A) 0.2 2 (B) 10 (C) 20% (D) all of the above (E)…

A: To convert a number to its equivalent percentage we have to multiply the number by 100 and add the…

Q: The equation y² = cx is the general solution of

A: We have to find the differential equation.

Q: The functions f(x) and g(x) are graphed below. 5+ 4. } -5 -4 -3 -2 -2 -1 Determine proma -2 -3 -4…

A:

Q: Find the general term of the sequence, starting with n = 1. Determine whether the sequence…

A: Here, the given sequence is: 2-8, 3-9,4-10,...

Q: Find the area of the parallelogram whose diagonals are represented by the vectors a =(3,-3,1) and b…

A: See this solution in below

Q: Consider the triangle shown in the figure. y (cm) 11 10 8 7 6 5 4 3 2 1 0 012 3 4 5 6 7 89 10 11 x…

A:

Q: 4 3 1 -1 -2 -3. -5 п/2 25 3п/2 2п

A:

Q: Write the first five terms of the sequence: {√n²+ n-n} Determine whether the sequence converges, and…

A: We can solve this as follows:

Q: 3. Evaluate the integrals √tanh x sech² xdx

A:

Q: The height y (in feet) of a ball thrown by a child is 1 y = 142² where x is the horizontal distance…

A:

Q: dy dt = e¹+y +}

A: We can answer the question as below.

Q: Prob 2 Use the Direct substitution rule and justify why you can use it to evaluate Лет 2-2 ln x + ex…

A:

Q: Match the properties of a circle in Column A to the Equation of the circle in Column B. Then pick…

A: Let's analyze the column A first. (1) Center at (3,-3) , radius of 4 Now we know that the equation…

Q: 3. A function f(x) satisfies the inequality 1-<f(x) < 1 + tan²x, when x →0. Using the Sandwich…

A:

Q: Evaluate the limits given the following information: lim f(x) = 6 lim g(x) = -9 24-6 x--6 a) lim x 6…

A:

Q: Find the General Solution Choices: 1.x4=c2(4x2+y2) 2. X2=c2(4x+y) 3. X2=c2(4x2+y) 4. X4=c2(4x2+y)

A: Since this a homogeneous differential equation of degree 2 thats why we replace y=vx and solve it to…

Q: Verify if the given equation is a solution of the given differential equation. Show full solution.

A:

Q: Q6. Let O(0,0), A(1,0), B(1,4) be points in the plane R². Then the following point lies in the…

A: I am attaching image so that you understand each and every step.