2. A company has contracted to manufacture 10,000 closed wooden crates having dimensions 3 m, 4 m, and 5 m. The cost of the wood to be used is P120 per square meter. If the machines that are used to cut the pieces of wood have a possible error of 0.5 cm in each dimension, find approximately, by using the differential, the greatest possible error in the estimate of the cost of the wood.

Q: 9) Suppose that the total cost of manufacturing x units of a certain commodity is C (x) = 2x? + 6x +…

A: Given function is as below : C(x)=2x2+6x+12 Marginal cost can be given by Derivative of C(x) .…

Q: 12)Estimate rio by using a linear approximation at aこ 9. timi

A:

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A: Query- How can we minimise the error of an approximation in a linear approximation at the point…

Q: of two observat

A: Let the Geometric mean of two observations is  1n. GM=1nHM To prove that  (1+1-n²) :(1-1- n²)

Q: 2. the rate at which the total average number of COVID cases is increasing at x = 10 tents and= 1…

A: The solution for question no 2 is given below:

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A:

Q: The measurement of the edge of a cube is found to be 15 inches, with a possible error of 0.03 inch.…

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A: Given Rx=6x3-αx2 To find the value of α when average value is $20 for x=10

Q: One side of a right triangle is known to be 20 cm long and the opposite angle is measured as 17°,…

A: We have to estimate the error in computing the length of the hypotenuse.

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A: We have to Find the number of units x that produces the minimum average cost per unit C (with a line…

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A:

Q: Use Euler's Method with an appropriate h value of your choosing to estimate y(4) with y = 0.5, y (1)…

A: Topic- Differential Equation

Q: The volume V of a cylinder is computed using the values 3.9m for the diameter and 6.7m for the…

A: When a physical measurement is made, there is always some uncertainty about it accuracy. For…

Q: 2. The rate at which the total average of COVID cases is dz increasing at r = 10 tents and than if…

A: If 30 tents are built, the average number of COVID cases per tent will be 7 cases while the average…

Q: Suppose that the total cost (in dollars) of producing a product is C(x, y) = 50 + 7x2 + 8y2, where x…

A: Differentiate wrt x and y

Q: 1. A lifeguard is at point A on a straight shore AB, where point B is 100 ft from point A. He wishes…

A: This question is related to distance and speed we will solve it using given information.

Q: 2. A firm uses capital, K, and labor, L, to produce output P according to P = KaL, a, ß are positive…

A:

Q: The volume V of a cylinder is computed using the values 4.5m for the diameter and 8.6m for the…

A: Given : height of cylinder is 8.6 cm and diameter of cylinder is 4.5m error in diameter is given by…

Q: Suppose that the total cost of manufacturing x units of a certain commodity is C (x) = 2?2 + 6? +…

A: Given, Total cost of manufacturing x units of a certain commodity =  C(x) =  2x2 + 6x + 12 We need…

Q: The rate at which the total average of COVID cases is dr increasing atr= 10 tents and = 1 tent per…

A: If 30 tents are built, the average number of COVID cases will increase by 7  while the average…

Q: 5. Use differentials to approximate V4 + In(1.2) correct to two (2) decimal places.

A: Let us take the function f(x)= √x f'(x)=1/(2√x) f(x+Δx)=f(x) + f'(x) . Δx   ___i) Here let us…

Q: How can we minimize the error of an approximation in a linear approximation at the point (a. ƒ (a))?…

A:

Q: A manufacturer incurs the following costs in producing x water ski vests in one day, for 0<x< 175:…

A: Given : The manufacturing cost of x vest in one day is given by  C (x) = 0.05 x2 + 25 x + 500 ,…

Q: Use the method of variation of parameters to find a particular solution of the DE…

A:

Q: Jesaki Inc will sell N units of product after spending $x thousand in advertising, as given by  N=…

A:

Q: 2. Suppose that 2 J of work is needed to stretch a spring from its natural length of 30 cm to a…

A: Given data: The work done is 2 J. The change in length is (42-30)=12 cm=0.12 m The expression for…

Q: 2. Assume Barry Bonds's head is a perfect sphere. If Dr. Beeresgood measures Barry's head's radius…

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Q: 9. The surface area of a cylinder is A = 2h+2². If the radius is measured to be 6 inches with a max…

A: Given, Surface area of cylinder, A=2πrh+2πr2 Given radius r=6in with maximum possible error dr =…

Q: 1. Find the orthogonal trajectories of the given family of curves: Circles through the origin with…

A: note : As per our company guidelines we are supposed to answer ?️only the first question. Kindly…

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A: It is provided that the length and width of a rectangle are l=29 cm, w=17 cm, respectively. The…

Q: 7. The raidus of a circle is equal to 4m and is measured with an error of ±0.5m. Use differentials…

A: Given: The radius of the circle is 4m and with an error ±0.5m To find the relative error ∆AA≈dAA "As…

Q: Two large tanks, each holding 24 liters of a brine solution, are interconnected by pipes as shown in…

A: Let x(t) and y(t) be the mass of salt in tanks T1 and T2 respectively. Fresh water follows into tank…

Q: In an effort to make the distribution of income more nearly equal, the government of a country…

A:

Q: 5. Find the orthogonal trajectories for a family of circles tangent to the at y-axis.

A: Here we have to find the orthogonal trajectories for a family of a circle tangent to the x-axis and…

Q: A manufacturer incurs the following costs in producing x water ski vests in one​ day, for 0<x<200​:…

A: =&gt;c(x)=0.05x^2+15x+245 =&gt;c(x)=0.05x+15+245/x

Q: Suppose that the total cost (in dollars) of producing a product is C(x, y) = 15 + 3x2 + 5y2, where…

A: C(x, y) = 15 + 3x2 + 5y2, x is the cost per pound for material and  y is the cost per hour for…

Q: Question 5 The length of the side of a square floe area of the tile. O +1.5025 cm2

A:

Q: 9) Suppose that the total cost of manufacturing x units of a certain commodity is C (x) = 2x2 + 6x +…

A: Given function is as below : c(x) = 2x2+6x+12marginal cost c'(x) =ddx2x2+6x+12…

Q: 6. The radius of a sphere is measured to be 7 cm, with a possible error of + (1/10) cm. Estimate the…

A: Volume of sphere   V=3π​r3/4 Percentage error in volume    ΔV​×100/V=3×Δr​×100/r =3*1*100/10*7= 4.3…

Q: according to the following differential piece rate of scale  1-25 chairs in a week, $10 each ;…

A:

Q: Consider the Cobb-Douglas production function f(x, y) = 100x1/3y2/3 where x is the number of units…

A:

Q: 5. Find the orthogonal trajectories for a family of circles tangent to the y - axis and centers at x…

A:

Q: Find the general solution to the DE using the method of Variation of Parameters: у" — Зу" + Зу' — у…

A: The solution is given as

Q: 4. Consider a lake of constant volume 12200 km³, which at time t contains an amount y(t) tons of…

A:

Q: If a current I passes through a resistor with resistance R ,Ohm’s Law states that the voltage drop…

A: Given the ohm's law relationship that is V=IR , where V is the voltage , R is the resistance and  I…

Q: Jesaki Inc will sell N units of product after spending $a thousand in advertising, as given by N=71…

A: Take the derivative both sides and substitute the values then simplify.

Q: 2. The rate at which the total average of COVID cases is dx = 1 tent per day, given dt increasing at…

A: Given,  number of tents= 20 and average number of cases will be 5

Q: If 0 = KHLV-, where k is a constant, and there are possible errors of ±1 per cent in measuring H, L…

A: We will find out the required value.