State the formula for the distance between (x1, y1) and (x2, y2).

Q: Find the shortest distance, d, from the point (11, 0, –6) to the plane x + y + z = 6. = p

A:

Q: Find the exact length of the curve. x- 2, y=? - 2, Osts 6

A:

Q: Find a formula for the distance from the point P(x, y, z) to the y-axis.

A: Given : The point is P ( x , y , z ) to the y - axis .

Q: Use the above formula to find the distance from the point to the given line. (0, 2, 1); x = 3t, y =…

A:

Q: find the distance from the point P (2,1,1) to the lins x+1 y-1 Z-3 L: 6 -2 -3 = =

A: To find the distance from the point to the line.

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

A: y=ax2y'=2axy'(4)=2a(4)y'(4)=8a Now we have 5x+y=b ⇒y=-5x+b Compare with the equation y=mx+b From…

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: Find the coordinates of the midpoint of HX 1 ,-3 2' X 2

A:

Q: Use the above formula to find the distance from the point to the given line. (5, 3, -3); x = 1 + t,…

A:

Q: Find the value of x,if the distance between the points (x,1) and (3,2) is 5

A: Use the distance formula and solve for unknown.

Q: Find a formula for the distance from the point P(x, y, z) to the a. x-axis.    b. y-axis    c.…

A: The formula for distance between two points (x, y, z) and (a, b, c) is

Q: Find the length of the curve r=θ^2 from θ=0 to θ=6

A: Given: -

Q: Use the Midpoint Formula three times to find the three points that divide the line segment joining…

A:

Q: The tangent of the acute angle between the lines y = 4x – 3 and y =x-5 is 4. IA 2 D

A: Two lines are given as : y = 4x - 3 and y = x - 5

Q: Find the distance between the lines: ri = +! r2 = + s

A: We have to find the distance between given 2 lines.

Q: Use the side-splitter theorem to solve for x in the triangle below.

A: Given,

Q: 2. Find the distance between and

A:

Q: Find all values of y such that the distance between (4, y) and (-2, 6) is 10 units

A: Given that the distance between (4, y) and (-2, 6) is 10 units.

Q: find the distance between

A: We have to find the distance between two points.

Q: Find the point that is 2/5 of the distance from C to D.

A:

Q: Find the acute angle between the planes x = 7 and x + y + sqrt(2)z =-3.

A: We know that cosine of angle between plane a1x+b1y+c1z=d1 and a2x+b2y+c2z=d2 is given by

Q: Find the distance between points P, and P2. Pi(0,5, - 1), Р2(3, - 4,5)

A:

Q: Find the distance between the lines: r = + t r; = + s

A: Given: r1→=1,1,0+t1,6,2 and r2→=1,5,-2+s2,15,6 where a1=1,1,0 , a2=1,5,-2,b1=1,6,2, and b2=2,15,6 To…

Q: f d(x, y) denotes the distance between two points

A: answer is in next step

Q: 3. The distance between two distinct points (x1, y1) and (x2, y2) is given by the formula

A: Given: Points x1, y1 and x2, y2

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: Find the midpoint between the two points A

A: To calculate the mid point,   X coordinate of the mid point is the half of sum of x coordinates of…

Q: The formula for the distance between two points is: O True O False

A: Please see the explanation below

Q: Find the distance between the points: (3, 7) and (2, 12) ww.. A

A:

Q: Find the distance from the point (4, 3, 0) to thea. x-axis b. y-axis c. z-axis

A: It is given that, the point 4,3,0.We have to find the distance from the given  point to the a…

Q: Find the distance between the following two points: (0, -1) and (2, 0) O 2 O V5 O V13

A:

Q: Use the distance formula to find the distance between the two points: (7,3) and (15,3)

A:

Q: use the distance Formula tO Find the distance between e) and(3,2)

A:

Q: Find the distance between the two given points. S (-1, 6) and T (-1, 14)

A: We know that distance between two point (x1,y1) and (x2,y2) is  (x2-x1)2+(y2-y1)2 Therefore distance…

Q: Find the distance from the origin to the point (x, y).

A: Distance between Ax1, y1 and Bx2, y2 is, AB=x2-x12+y2-y12

Q: The formula for the distance between two points is:

A:

Q: I. Find I = ždz where C is the line segment from 3 +i to 3 - 2i.

A:

Q: Which of the following mathematical models is used to determine the distance between two points…

A:

Q: (a) What is the formula for finding the distance between the points (x, yı) and (x2, y2)? (b) What…

A: Given: (a) Points (x1, y1) and (x2, y2) (b) Points (x1, y1) and (x2, y2)

Q: Find the exac length of the curve 3/2 , 0dxE y=2+2x

A:

Q: Find the distance between the following two points: (0, -5) and (5, 1)

A:

Q: Find a formula for the shortest distance from a point (a,b,c) to the y-axis.

A: We will find the formula as following.

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

A:

Q: Prove that the equation ax² + 2hxy+by² + 2gx+2 fy+c=0 wi h²2 = ab and bg2 = af?. Also find the…

A:

Q: which sketch is a cross-section in the x-direction (L to the y-axis)? Why?

A: Given are three graphs. We need to find out which one is a cross section in x-direction. The…

Q: which sketch is a cross-section in the y-direction (L to the x-axis)? Why?

A: Given: Let us determine the cross-section in the y-direction perpendicular to the x-axis.…

Q: Find the tangent plane to the equation z = 5a° + æy? + 2 at the point (2, – 4, - 6)

A:

Q: Determine the exact distance from the point P (1,2) to the line (-1,3) + t(2,9), t e R . Show your…

A: Given

Q: d. (1,1/2), (1/2,-2) e. (2, -4), (0,7) f. (-2.5, -3.5), (6.5, -5.5)

A: We can find the distance using the distance formula as below.

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.