Find two positive numbers with product 324 and whose sum is a minimum. Enter your answers in increasing order. First number: Number Second Number: Number Please explain, in your own words and in a few sentences, how you arrived at your answers. Answers with no relevant explanations may receive reduced or no credit. E E E = = = ΩΣ Equation Editor A- A- Ix BI US x, x" Styles Font Size

Q: A particle moves on a circle of radius 4 cm, centered at the origin, in the xyxy-plane (x and y…

A: Consider the following: The particle at t =0 at A (0, 4) rotates counter clock wise in 11 sec, Find…

Q: Draw the shear diagram for the beam. Follow the sign convention. (Figure 1) Click on "add vertical…

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Q: A particle is oscillating about a central point such that its displacement x (centimetres) at any…

A: Given that the displacement x at any time t is modeled by the equation x=sint+cost+cost-π3 for t≥0.…

Q: A model for the height h (in feet) of a Ferris wheel car is  h = 70 + 70 sin(4?t),  where t is the…

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Q: 2. (a) How do you trace a Regular point and a Singular poi Equation (DE). Determine the singular…

A: Introduction: If a differential equation has the form y"+p1(x)y'+p2(x)y=0, then the singular points…

Q: There is an ant on a circular heated plate. The plate temperature is given by f(x, y) = y² – x² + 12…

A: Consider the function fx,y=y2-x2+12, with equality constraint x2+y2=121 (since the radius is given…

Q: Find the minimum and maximum distances between the sphere x +y +z = 49 and the point (4,5,6). The…

A: We apply distance formula to calculate minimum distance and then find maximum distance

Q: Uraw the isoclines with their direction markers and sketch several solution curves, including the…

A: Given dy/dx= 3x        ,.       Y(0)=-1

Q: The design of boats is based on Archimedes' Principle, which states that the buoyant force on an…

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Q: Provide ONE first-order critical point of the curve f (x) = x4 - 8x² + 16 *Input the answer as…

A: Solve by derivative

Q: A planet P in the xy-plane orbits a star S counterclockwise in a circle with radius 10 units,…

A: Given, A planet P in the xy-plane orbits the star S  in a circle of radius 10 units, completing one…

Q: Equation of the tangent drawn from the point S(2,4) on the 8x = y^2 parabola ? 2y=2x+2 y=2x+2…

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Q: 2. Solve I = min (axu'+u+a u)dr – u°(1), u(0) = 0 where a is a parameter. (a) Find stationary…

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Q: (a) Find the minimum and maximum xcoordinates of points on the cardioid r =1−cosθ.(b) Find the…

A: given,       the cardioid r= 1-cosθ

Q: 3. Consider y= r+ y. Draw the isocline for the equation that corresponds to y = 1 and then draw ten…

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Q: Kepler's Third Law states that the ratio T/a³/2 is equal to a con- stant C for all planetary orbits…

A: Given :        Ta32 = C , where T is the period and a is the semimajor axis.

Q: Consider the surface S give by the equation z = f(x,y) = x²y+ax + 3. Here, in each part, a is a…

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Q: Suspension Bridge A cable for a suspension bridge has the shape of a parabola with equation y = kx²…

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Q: With a curve 56 3 17 x² + y = 6, y = x, y = -2 and x = -2. . Determine its area.

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Q: Find oveslapping Over of two equations also give ts alea geometoical representation. 2. (v-fr)-1…

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Q: Three points are given as follows to give the first digit x and the second digit y: (0, 0), (a, a,),…

A: Given:       Three points are given as:  (0,0), (ax,ay) and (bx,by)

Q: Determine the moment of inertia of the area about the y-axis of the curve y2 = 2x, x=2, and the…

A: We can calculate by integrating.

Q: A detector measures a positron moving through an electromagnetic field along a path given by r = \(x…

A: According to question given that r=x+22+y+32x and y correspond to the particle's location (x,y)And…

Q: Find a sinusoidal model for the situation, without a horizontal shift. The maximum value is 15 and…

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Q: (a) Draw a direction field and describe how solutions seem to behave. (b) Find the critical points.

A: “Since you have asked multiple questions, we will solve the first 2 questions for you. If you want…

Q: b. Differentiate both sides of the equation in part (a) with re- 86. The hyperbolic in hyperbolic…

A: (a) We can draw the graph of the sector AOP as shown below. Now,  We observe that the area A(u) of…

Q: Compute each of the following line integrals. (a) a ds, where C is the portion of the parabola from…

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Q: 6.6.7 Find the area of the surface generated when the given curve is revolved about the given axis.…

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: 25. The diagram below shows a box for packing chocolates. The box is a right prism of height h cm.…

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Q: A particle moves on a circle of radius 6 cm, centered at the origin, in the ry-plane (x and y…

A: Given,  A particle moves on  a circle of radius 6 cm, centered at the origin in the xy-plane.  It…

Q: Find an equation of the tangent plane at P = ( 2, 3, to the given surface. 8x? + z?e"-* = 41…

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Q: 5) A spherical storage tank has a radius of 3 feet, and half of it is underground: The equation of…

A: From the given data,  the radius of the tank is 3 feet. Consider the horizontal slices of ∆y…

Q: Find the Area of the Surface obtained by rotating the curve about the x - axis X= (²+2),

A: The objective is to find the surface area.

Q: A very high end paint company wants to construct a paint can in the shape of a cylinder to hold 1000…

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Q: H.W: Find the center of mass- a thin Plate af deusity S=3 bouuded the by lines X- o, y=x iad the…

A: we have to find the center of the mass of a thin plate of density δ =3 bounded by the line x=0, y =…

Q: Find a sinusoidal model for the situation, without a horizontal shift. The maximum value is 6 and…

A: sinusoidal modal is given below

Q: Find the maximum and minimum values of f(x, y) maximum value = = xy on the ellipse 2r2 + y? = 2.…

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Q: Find the point P where the function f(x, y, z) = x¹y¹z7 reaches the maximum value for x, y, z ≥ 0 on…

A: Given the function fx,y,z=x4y4z7 reaches the maximum value for x,y,z≥0 on the unit sphere x2+y2+z2=1

Q: A detector measures a positron moving through an electromagnetic field along a path given by V(x +…

A: Step:-1 Given that   distance  r=x+32 +y+12 subject to  y-2x=0 Take  gx, y=y-2x Let L=r -λ gx, y…

Q: 1. The response around the stationary point can be described by the estimated equation in the…

A: The given function in canonical form : y^=30.0-2.0w12+3.0w22+1.5w32 For stationary points,…

Q: The cross-section of a long conducting duct is shown in the following figure. Three of the sides are…

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Q: 4. A uniform cable is suspended between two poles of equal height. Assume that the equation of the…

A: Given: y=acosh(x/a), a >0.

Q: Taw the isočlines with their direction markers and sketch several solution curves, including the…

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Q: as engineer design a cooling tower in the shape of hyperboloid of one sheet. The horizontal cross…

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Q: A particle moves on a circle of radius 6 cm, centered at the origin, in the ry-plane (x and y…

A: As the particle started at the point (0,6), hence the circle must have its x-coordinate equal to 0…

Q: Find a sinusoidal model for the situation, without a horizontal shift. The maximum value is 6 and…

A:

Q: determine a cubic spline approximation that fits through data pts: P1(1; 1); P2(2; 2); P3(3; 1:5);…

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Q: A planet P in the xy-plane orbits a star S counterclockwise in a circle with radius 10 units,…

A: Given, A planet P in the xy-plane orbits the star S  in a circle of radius 10 units, completing one…

Maximization

Have you ever seen a bridge in the shape of a parabola? Where is its maximum on the bridge? The maximum of that bridge is the highest point on that bridge. The process of finding the maximum of the bridge here is called the maximization.