5. [a] Using the method of describing Quadrangles and Townships as dis distance, in miles between the geographic centers of these two Township (1) T1S, R2E and (2) T6N, R6W. Illustrate your response with a bri

Q: Show that the square of the length of subtangent at any point on the curve by2=(x+a)2 (b is not…

A: Here given curve  by2=x+a2

Q: 2. The midpoint of the line segment between Pi (x, y) and point P2 (-2, 4) is Pm (2, -1). Find the…

A:

Q: show that the square of the length of subtangent at any point on the curve by2=(x+a)3(b is not equal…

A:

Q: 4. The midpoint of the line segment with endpoints (x1, yı) and (x2, y2) is given by the formula

A: we know, the midpoint of the line segment with end points (x1,y1) and (x2,y2) is given by the…

Q: What is the horizontal distance of Lil's 1) landing zone from the plane? 2) What is the horizontal…

A:

Q: find the coordinate of point x such that the ratio of MX to XJ is 2:3

A: Let Position vector of point M and J be m→ and j→, respectively. Point X divides segment MJ into the…

Q: 2. Consider any five points P1, Ps in the interior of a square S of side length 1. Show that one can…

A: To solve this problem we use the Pigeonhole principle . Pigeonhole principle : If there are m holes…

Q: 2. Consider any five points P1, Ps in the interior of a square S of side length ... 1. Show that one…

A: Since you have asked multiple questions here, we will solve the first question for you. To get the…

Q: 4. What is the equation of a line parallel to the diameter of circle A, with a center at (-5,7) and…

A: Given query is to find the line which parallel to the given line.

Q: Find the shortest distance, d, from the point (4, 0, –4) to the plane x + y + z = 4.

A:

Q: / uousənd Solve for x and y in the parallelogram. (3x 4) (4y +'3) X =

A: Solution:- Given the parallelogram                            we need to find the value of x and…

Q: Sketch the solid described by the given inequalities: 0 <rs 2,s00szs

A:

Q: Where should the point P be chosen on line segment AB so as to maximize the angle θ? (Assume a = 3…

A: Given : a=3, b=4  and c=7 Let BP=x . So , PA= 4-x

Q: 23. The distance from a point (2, y) to the line 4x + 3y =0 is equal to 5. Find the value of y. O…

A: Given that the distance from a point 2,y to the line 4x+3y=0 isequal to 5. We need to find the value…

Q: For what values of a and b is the line 4x + y = b tangent to the parabola y = ax2 when x = 5? a = b…

A: Given: The line 4x+y=b is tangent to the parabola y=ax2 when x=5. To Find: Value of a and b.…

Q: 16)- Consider the quadrature formula 6 | f(x)dx = Af (-6) + Bf(6) -6 If the degree of precession is…

A:

Q: For what values of a  and b  is the line 2x  + y = b tangent to the parabola y = ax 2   when x = 2

A: Given line is 2x+y=b Given line can be written as y=-2x+b On comparing with equation of line y=mx+c,…

Q: Find the length of the curve from the entire hypocycloid 2 2 x3 + Y³ = a³.

A: Explained below

Q: Where should the point P be chosen on line segment AB so as to maximize the angle 0? (Assume a = 4…

A: Given that  The figure is

Q: The base of a three-dimensional figure is bound by the circle x² + y² = 9. Vertical cross sections…

A: Given circle x2+y2=9. The objective is to find the area of each triangle.

Q: 51. Show that the shortest distance from the point (x1, yı) to the straight line Ax + By + C=0 is Ax…

A:

Q: 5. In the standard (x, y) coordinate plane, the midpoint of LM is at (4, –4) and L is at (1,3). What…

A:

Q: Ue langrange multipliars to fined the Shortest distancé fam the to the pGine x+g+Z=1. point (7,0,)

A:

Q: Find the shortest distance, d, from the point (6, 0, -4) to the plane x + y + z = 4.

A: The shortest distance of a point from a plane is said to be along the line perpendicular to the…

Q: 1. Find the point on the line y = x nearest to the point (4, 1).

A: Since, we have been asked to solve part(i) which aims to findthe point on the line y=x nearest to…

Q: What is the distance between points F(2, 9) and G(4, 14)? Round to the nearest whole number.…

A: F(2,9) and G(4,14) Distance between the points /-(14-9) 2+(4-2)2 /-52+22 /-25+4 =/-29

Q: A man in a rowboat at P.5 miles from the nearest point A on a straight shore. wishes to reach to a…

A: This problem is based on maxima minima function. After getting minima function we got the value of x…

Q: The area bounded by the curve y= 4x and the lines r = 7,1 = 10 and x - aris is O 4900 square units O…

A: From the given curve bounded region is shown below:       So,   I=∫x=7x=10∫y=0y=4xdydx

Q: The Cardovo Drive-In Movie Complex is a pop-up movie theater in a large field, allowing up to 5 cars…

A: Given : screen is 20 m across            The perpendicular edge of the field is another 10 m To find…

Q: Where should the point P be chosen on line segment AB so as to maximize the angle 0? (Assume a = 3…

A: Given query is to find the position of P to maximize the angle theta.

Q: 1 x = + 6 2y What is the length br of the portion of the graph of the between the points with y = 1,…

A:

Q: 2- The distance d from the point R=(1,4,-3) to the line L: x=2+t,y%3-1-t Z- 3t is 4.43 False True

A:

Q: 3. The distance between city A and city B is 38 miles; city A's population is 100,000, city B's is…

A: According to Reilly's law of retail gravitation, point of indifference is given by:

Q: Find the per pendicualar olistace from the P (5,6) to the line -2xr+3Y+4=0.

A: Formula for perpendicular distance is as below : Given :-2x+3y+4=0Ax+By+C=0A=-2B=3C=4 Point  (m , n…

Q: Find the points on the cone 2 = r² + y? that are closest to the point (4, 2, 0). (Hint: You can…

A: Here we use the distance formula  D=(x2-x1)2+(y2-y1)2+(z2-z1)2 where D is the distance between the…

Q: The area bounded by the curve y = 4x and the lines r = 6 ,x = 12 and a – axis is 144 square units O…

A:

Q: 2. Find the distance between the parallel lines: L: 2x- 5 y + 3 = 0 ; (Hint: It suffices to compute…

A: Consider the given equations of the lines, L1: 2x-5y+3=0 and L2: 2x-5y+7=0 The formula of the…

Q: What is the sum of the abscissas of the points where the tangents of the y=(1/3) x^3-(3/2) x^2 – 2x…

A:

Q: For what values of a and b is the line 4x + y = b tangent to the parabola y = ax2 when x = 4?

A: Consider the equation of the parabola, y=ax2 differentiate the equation with respect to x to find…

Q: In a plane, l lm and t 1 m. l and t related? By appearance, how are

A: We know that in a plane if l⊥m and t⊥m then l will be parallel to t So, l and t are related as l∥t

Q: B is the midpoint of line segment AC. Find x C 5X-6 3X +4 Ox = -5 O x 2 Ox = 5 Ox = 10

A: A line segment is a finite section of a straight line. A mid-point of a line segment is a point…

Q: 2 14 - For what value of K is the line 2x+ky = 3 Perpen odicular to the line 4x+y=12 For what the…

A: We will find to the value of k when  the line ,2x+ky = 3 perpendicular to the line 4x+y=1 . And olso…

Q: 2 (720). 8 If the length of the curve y = 3 x, from the point (0, 0) to the point (xo, f(xo)) is L=…

A:

Q: 17) - Consider the quadrature formula ²₁ f(x) dx = f(-²) + ‡ƒ (²) If the degree of precession is 1,…

A: Consider the given quadrature formula, ∫-11fxdx≅45f-12+65f13 Here it is given that degree of…

Q: Sketch the solid described by the given inequalities. Oses n/2, r szs4

A: We have given that 0≤θ≤π2 &amp; r≤z≤4

Q: What is y = _ + x3 1 curve x = 1 and x = 2 the length of the part 12 х between the abscissa points?

A: We find dy/dx using the power rule

Q: The figure shows a semicircle with radius 1, horizontal diameter PQ, and tangent lines at P and Q.…

A: As per the question we are given a circle of radius 1 and a horizontal line above the x-axis. Now we…

Transformation of Graphs

The word ‘transformation’ means modification. Transformation of the graph of a function is a process by which we modify or change the original graph and make a new graph.

Exponential Functions

The exponential function is a type of mathematical function which is used in real-world contexts. It helps to find out the exponential decay model or exponential growth model, in mathematical models. In this topic, we will understand descriptive rules, concepts, structures, graphs, interpreter series, work formulas, and examples of functions involving exponents.