Suppose that the temperature at a point (x, y) on a metal plate is T(x, y) = 4x² – 4xy+ y². An ant, walking on the plate, traverses a circle of radius 4 centered at the origin. What are the highest and lowest temperatures encountered by the ant? NOTE: Enter exact answers.

Q: a circle is 24 cm and the distance is

A:

Q: What is csc a if sec a = -4/3 and tan a< 0? А. В. С. D. 4V7 V7 4V7 V7 - 7. 4. 7 4

A: We need to find cscα if secα=-4/3 and tanα&lt;0? A. -477 B. 74 C. 477 D. -74

Q: Points X and Y are respectively 12 m north and 5 m east of point Z. Calculate XY.

A: To solve this problem we use the Pythagorean theorem

Q: Find and write the "Y" coordinate of Point 1 illustrated in the figure below. • Write your answer to…

A: We have to find the y- coordinate of point 1.

Q: Graph the cardioid r = a(1+ sin®), a< 0?

A: We are given that r=a(1+sin∅), a&lt;0 Here as we know that sin∅ is always greater than equal to -1.…

Q: Calculate for w = xyz. By

A:

Q: Find Dxy. 6) y = tanh² 7x

A:

Q: H.W Y= Sin *る

A: Given, y=sinuu=x2ex Substituting u in y we get, y=sinuy=sinx2ex Differentiating equation (1) with…

Q: メ tan y.dx イ X" dう ニ ○ 2(ty')

A:

Q: then show that dz+z = % dy e te

A: Given:z=ex+yex+eyDifferentiation formula:ddxuv=v.dudx-u.dvdxv2

Q: B. Find y. 2. y = x tan- x – In vx² + 1

A: Given that     y = x tan-1x - ln√(x2+1) Here we have to find y(4) .

Q: dy 1. Solve the DE: + csc x(y+2 cscx+2csc xcot x)-ytanx= 0 dr

A:

Q: Find the area of the circle whose center is at (2, -5) and tangent to the line 4x+3y-8=D0

A: Area of the circle = 9π sq.units

Q: Find the angle of intersection between the curves y = x- +1 and y = x+x-

A: y = x2 + 1,y = x+ x-1Points of Intersection;x2 + 1 = x+1xx(x2+1) =(x2+1)x = 1y = 2point of…

Q: 32. In the diagram, VW= 3, WX= 4, and VX= 8. Is WX tangent to OV? W b. yes a. no

A: We will use the property that radius is perpendicular to tangent line.

Optimization

Optimization comes from the same root as "optimal". "Optimal" means the highest. When you do the optimization process, that is when you are "making it best" to maximize everything and to achieve optimal results, a set of parameters is the base for the selection of the best element for a given system.

Integration

Integration means to sum the things. In mathematics, it is the branch of Calculus which is used to find the area under the curve. The operation subtraction is the inverse of addition, division is the inverse of multiplication. In the same way, integration and differentiation are inverse operators. Differential equations give a relation between a function and its derivative.

Application of Integration

In mathematics, the process of integration is used to compute complex area related problems. With the application of integration, solving area related problems, whether they are a curve, or a curve between lines, can be done easily.

Volume

In mathematics, we describe the term volume as a quantity that can express the total space that an object occupies at any point in time. Usually, volumes can only be calculated for 3-dimensional objects. By 3-dimensional or 3D objects, we mean objects that have length, breadth, and height (or depth).

Area

Area refers to the amount of space a figure encloses and the number of square units that cover a shape. It is two-dimensional and is measured in square units.