find the mass of lamina in the given region and density function: d[(x,y)],0

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Find the mass of lamina in the given region and density function: D[(x,y)],0 <= x <= pi//2,0 <= y <= cos x and rho=7x A. 2 C. 4* B. 3 D. 5 Find the area of the region bounded by the curves y=x^2-4x and x+y=0 . A. 4.5 * C. 6 B. 5.5 D. 4 A conic section whose eccentricity is less than one is known as: A. Circle C. hyperbola B. Parabola D. ellipse* The plate number of a vehicle consists of 5 -alphanumeric sequence is arranged such that the first 2 characters are alphabet and the remaining 3 are digits. How many arrangements are possible if the first character is a vowel and repetitions are not allowed? A. 90 C. 9,000 B. 900 D. 90,000 * The axis of the hyperbola, which is parallel to its directrices, is known as: A. Conjugate axis* C. Transverse axis B. Major axis D. Minor axis The minute hand of a clock is 8 units long. What is the distance traveled by the tip of the minute hand in 75 minutes? A. 10pi C. 25pi B. 20pi * D. 40pi Find k so that A=(3,-2) and B=(1,k) are perpendicular. A. 2 C. 1//2 B. 3 D. 3//2** The probability of a defect of a collection of bolts is 5%. If a man picks 2 bolts, what is the probability that he does not pick 2 defective bolts? A. 0.950 C. 0.0025 B. 0.9975 * D. 0.9025 If f(x)=(1)/(x-2) , if (f◻g)^(')(1)=6 and g^(')(1)=-1 , then g(1)= A. -7 C. 5 B. -5 * D. 7 Three randomly chosen senior high school students were administered with a drug test. Each student was evaluated as positive to the drug test (P) or negative to the drug test (N). Assume the possible combinations of the 3 students' drug test evaluation as PPP, PPN, PNP, NPP, PNN, NPN, NNP, NNN. Assuming each possible combination is equally likely, what is the probability that at least 1 student gets a negative result? A. 1//8 C. 7//8** B. 1//2 D. 1//4 The tangent line to the function h(x) at (6,-1) intercepts the y -axis at y=4 . Find h^(')(6) . A. -1//6 C. -4//5 B. -2//3 D. -5//6 * The cable of a suspension bridge hangs in the form of a parabola when the load is uniformly distributed horizontally. The distance between two towers is 150m , the points of the cable on the towers are 22m above the roadway, and the lowest point on the cable is 7m above the roadway. Find the vertical distance to the cable from a point in the roadway 15m from the foot of a tower. A. 16.6m** C. 12.8m B. 9.6m D. 18.8m In how many different orders may 5 persons be seated in a row? A. 80 C. 120 * B. 100 D. 160 The symbol "/" used in division is called A. Modulus C. solidus* B. Minus D. obelus Find the area of one loop r^2=16 sin (2theta).

Question

115

Answer

43: A 44: C 45: D 46: D 47: A 48: B 49: A 50: B 51: B 52: C 53: A 54: A 55: C 56: C 57:

Explanation

43. This question demands the mass of a given laminar region defined by the mentioned limits of x and y, with a provided constant density function. It becomes a double integration problem, however, to solve it requires familiarity with calculus concepts, especially those closely tied to the theory of mass and centers of mass. 44. The question deals with finding the area between two given curves y=x^2-4x and x+y=0. This requires understanding of concepts related to the finding the areas between curves by using definite integration method and treating some part of each as a kind of symmetry form to simplify the task. 45. This is a problem based on basic understanding of the conic sections: circle, parabola, hyperbola and ellipse each with defined eccentricities values accordingly it's found unusual in circular state. 46. We have a combination question on finding total arrangements for given conditions of a random license plate where elements can't replicate themselves. The problem becomes a calculations issue primarily based on Permutations. 47. Various definitions grant names to the axes (or lines) in respect to a hyperbola. The options offers four possibilities, so the respondent is being tested on theoretical hyperbola knowledge and how it’s functionally held relative to its focus points. 48. This a circular motion related practical question where requires simple math; demonstrate the understanding of distance covered by minute hand round trips all around minute circle. 49. Asks to find the mathematical value depends comparing orthogonal force of vectors having point A(3, -2), and B(1, k) based on a right triangle values property. 50. The concept of probability. This question requires knowledge of understanding combinations & statistics principle on calculation of probability when you draw two random bolts. 51. For a composite function, it asks to obtain the values that adhere to set rules with how it confers correctness based on our comprehension of derivative relationships. 52. Need understanding of the combinations and permutations principle, it talks about the statistics where randomness and chance are intrinsically compounded by statistics, thereby needing a procedural method to attain possible solutions. 53. This problem delves fairly advanced as the concepts explored lean closer on graps concepts of limits, derivatives(dereivative for the function provides the slope of tangent line), and real world application of ascensions in mathematics like rate and variation. 54. This is a real-world applications problem that draws elements from varies small mathematical divisions like piecewise functions/ parabolic activities mathematic values respectively upside/down direction. 55. More numerical combinatorics applying the problem of familiar with permutations-resolution: which counts arrangements while considering order. 56. Here this problem is an exploration of just straightforward mathematic interspersing fun maybe for choosing better algebra and it does spark practitioners and newcomers alike to dive lust language symbols and conventions to inspire expressive showings & topic flashpoints hinges that apples dynamism here. 57. This math question relates to polar coordinates domain with its integration maneuvers where waits the difference tuning in radians inherently both comparative array conceptual angle and regularly procedural numerical solve steps inside.

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FAQs

How do you find the mass of lamina? ›

For the total mass of the lamina, we add up the boxes and take a limit to get M = ∬Dρ(x,y)dA. This integral can be done in rectangular coordinates, polar coordinates, or by whatever method you prefer.

How do you find the mass of the thin bar with the given density function? ›

To find the mass of the thin bar, we have to integrate the density function over the interval. The formula for the mass is m = ∫ a b ρ ( x ) d x . For evaluating this definite integral, we use the integration power rule, sum and difference rule, and constant multiples.

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What is the mass in terms of density? ›

Density offers a convenient means of obtaining the mass of a body from its volume or vice versa; the mass is equal to the volume multiplied by the density (M = Vd), while the volume is equal to the mass divided by the density (V = M/d).

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How to find the mass of lamina? ›

The total mass M of the lamina is approximately the sum of approximate masses of subregions: M≈n∑i=1Δmi=n∑i=1δ(xi,yi)ΔAi. Taking the limit as the size of the subregions shrinks to 0 gives us the actual mass; that is, integrating δ(x,y) over R gives the mass of the lamina. mass M=∬R dm=∬Rδ(x,y)dA.

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How to find mass from a density function? ›

We can calculate the mass of a thin rod oriented along the x-axis by integrating its density function. If the rod has constant density ρ, given in terms of mass per unit length, then the mass of the rod is just the product of the density and the length of the rod: (b−a)ρ.

How do you find the volume of lamina? ›

An irregular lamina is a two-dimensional object that doesn't conform to any standard geometrical shape, and its thickness is so small compared to its length and breadth, it can be considered negligible. However, we can still calculate its volume using a simple formula: Volume = Area x Thickness.

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How do you find the center of mass of a rectangular lamina? ›

For a rectangular lamina, the centre of gravity lies at the point of intersection of its diagonals.

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How the student could find the centre of mass of the lamina? ›

If a geometrical axis of symmetry of a uniform lamina exists, then the center of mass lies along that line of symmetry. Similarly, if a uniform lamina has more than one geometrical line of symmetry, then the center of mass will lie at the intersection of these lines of symmetry.

find the mass of lamina in the given region and density function: d[(x,y)],0 <= x <= pi//2,0 <= y <= cos x and rho=7x a. 2 c. 4* b. 3 | Question AI (2024)