Which of the figures below shows a direction field for dy dr 10 (Please answer carefully. After you move on to the second question, you will not be able to change your answer to this question.) ty t tt 1 - t 1 4 11 t t tt ↑ 21 -4 -2

Q: What is the coordinate of P? of R?

A: Explanation: Given x-axis

Q: S-6. You have a sailboat and a motorboat. The sailboat can sail at S miles per hour, and the…

A:

Q: 3. Consider the figure below. Write the equation of the line of reflection. 4 -2 4. -2 了

A: In the given figure the x-coordinate of image of each vertex of the triangle remain same but the…

Q: Determine the point (x, y) on the unit circle associated with the following real number s. Write the…

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Q: What are the coordinates of point D? O2,-3

A: Given cartesian plane is :

Q: The dependent variable is the second value in an ordered pair. O True O False

A: The dependent variable is the second value in an ordered pair  A.TRUE  B.FALSE

Q: Which of the points below correctly plots the point (-3,)?

A:

Q: A

A:

Q: For which independent value do the equations generate the same dependent value? Y- 6x + 10 Ya 4x+4…

A: Given;  Y1 = 6x +10 Y2 = yx + 4

Q: 3元 Which point represents (3,)? 12 F 13元 12 D. 112 12 C.

A: Given the point is 3,3π4

Q: Which equation represents OB? ty 2 B -2 2 -2 O A. (x - 2)2 + (y – 1)² = 9 O B. (x+ 2)2 + (y + 1)2 =…

A:

Q: Find the stationary point(s) of ?(?1, ?2) = 6?1 − ?12 + 16?2 − 4?22.

A: We have to find the stationary points of given function

Q: The table shows the variation between a, b, c, and d. Complete the table. a with b b with c c with d…

A: a with b has inverse variation. ∴a.b=k, where k is any constant⇒b=ka b with c has inverse variation.…

Q: 50 R. 12r-7 57 53 Sy-33 32+ 14 W

A: Given triangles, The objective is to find the values of x,y,z.

Q: Which angle number represents the linear pair of ZSXT? X\1 R 3 2 S W Y|4 65 U

A: Please see the below explanation.

Q: Question 6 For the line 3x - y = 12, complete the following ordered pair so that it is a point on…

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Q: In the figure below, XY=4 and YZ=7. Find XZ. Y XZ = \| %3D

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Q: Directions: Find the values of x in the following. Show your complete solutions. E H H. M Y E 1.…

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Q: Which table matches with the linear equation y =-2x 3? X-2 03 5 y -1 -3 0-8 X-2 -1 1 -1 -5 -11 4 -1…

A: In  the question it is asked to find the table which matches the equation y=-2x-3.

Q: Consider the diagram below. 10 V.V 6 4 Figure A 2 10-8 -6 -4 -2 0 2 4 6 8 10 -2 -4 -8 Figure B-10,…

A: Given: Figures is given .

Q: Which of the following equations is symmetrical about the origin? O x = -6y² +6 0 x=бу2 Oy=6|x|-6…

A: This is a problem related to symmetry of the curve. Please follow the procedure given below.

Q: R-R 14. Find between 0 and 360 degrees so that

A: Given, is radian then we have, So, the angle in degree =angle in radian The radian measure of an…

Q: Name the intersection of CX and AB.

A: According to given figure CX and AB are not intersecting which means there is no intersection point…

Q: 8, E 12, A с a. DAED - ДАСВ. Х D √6 B

A: This is a problem related to geometry of triangle. Based on the general formula and concept we will…

Q: Identify the line of reflection. Select the TWO choices that apply.

A: Follow the procedure given below.

Q: Which equation is an equation of a line perpendicular to y = 3x + 9? O A. y = -3x + 4 = -11 O C. y =…

A: We have given equation of a line  y = 3x + 9  So comparing this line with  y = mx + C We get slope…

Q: Find the value of Line WY. W 43 – 2x 12x + 1 Y O 43 O 29 O 37 032

A: We know that,  Two tangent line on circle from an external point is of same length.  So, Length of…

Q: Which of the points below correctly plots the point (-2,-²)? B A DE 3

A:

Q: Transpose the equation to make Q₂ the subject of the equation Select one: ○ Q₂ = 9-91 O Q2 = Q1Q O…

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Arc Length

Arc length can be thought of as the distance you would travel if you walked along the path of a curve. Arc length is used in a wide range of real applications. We might be interested in knowing how far a rocket travels if it is launched along a parabolic path. Alternatively, if a curve on a map represents a road, we might want to know how far we need to drive to get to our destination. The distance between two points along a curve is known as arc length. 

Line Integral

A line integral is one of the important topics that are discussed in the calculus syllabus. When we have a function that we want to integrate, and we evaluate the function alongside a curve, we define it as a line integral. Evaluation of a function along a curve is very important in mathematics. Usually, by a line integral, we compute the area of the function along the curve. This integral is also known as curvilinear, curve, or path integral in short. If line integrals are to be calculated in the complex plane, then the term contour integral can be used as well.     

Triple Integral

Examples: