Ex. 2: Find the length of the 2/3 curve

Q: Area of a regim enilosed is by Curves y= 12 and

A: To find the area enclosed by the given two equations

Q: Find the slope of the tangent line to the graph at the given point.

A: Slope of the tangent line is the derivative of the given curve at the given point. So…

Q: Find the slope of the tangent to the curve r=−6+5cosθ at the value θ=π/2

A: Given curve is

Q: Construct a smooth curve tangent to the line segments starting at point P. P

A: Given: a group of line segments joining to form a zig-zag figure. Aim to form a curve which is…

Q: 33. Find an cquation for the line that is tangent to the curve y = (1-r)/(1 +r) at r = 2.

A:

Q: Find the slope of the tangent line for the curve r=3+5cosθ when θ=π/6

A: Concept - If a function f(x) is given then slope of the line tangent to it at x=a is given by -slope…

Q: 2 Find the distance from the point B = [0 5 0 to the line 1 +t| 0 -3

A: Here we will find the distance between the given point and line,

Q: Consider the curve f(x) = x3 + ! for 3 < x < 4. Find the arc

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Q: 3. Find the slope m of the tangent lines to the parabola y = -x+ 5x+ 6t its point of intersection…

A:

Q: 98. Find the points on the graph of y = 2x6 – x* - 2 at which the tangent line is horizontal.

A: Find the points on the graph of  y=2x6-x4-2at which the tangent line is horizontal.

Q: 1. Find the set of points in the curve y = where the tangent lines are horizontal. r²+1

A: Hey, since there are multiple questions posted, we will answer the first question. If you want any…

Q: Plot the "astroid" y = (4 - x 2/3) 3/2 for 0 ≤ x ≤8. Show that the first-quadrant segment of each…

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Q: Find the equation of the tangent line to the curve y= (x-3)°(x+2) at the point (4,36).

A: Given,  The curve   y = x-38x+22   We have to find the equation of the tangent line to the curve at…

Q: 1. Find the equation of tangents to the circle x² + y² = 9 with slope 1.

A:

Q: Find the points on the curve y= 2x3 +3x2 -12x +1where the tangent is horizontal.

A:

Q: he line tangent to the graph of y=In(3x)+ 2x e at x =1 6

A: Equation of line is given as   y-y0 = dydxat x=1*(x-x0) Given,x0 = 1y = ln(3x) + e2x6y0 = ln(3x0)…

Q: Find the slope of the tangent line to the graph at the given point. 4xcosy+1=5 at the point…

A: To find the slope of the tangent line we need to find dydx.…

Q: Find an equation of the tangent Iine to the ollowing curve at the point (0, 5). xe' + ye* = 5

A:

Q: Find the exact length of the curve. y = ln (1 − x2),  0 ≤ x ≤ 1/3

A: We need to use the chain rule to find dy/dx.

Q: Find the point on the curve 4x

A:

Q: The tangent line to the graph of y 5x-x' when x 3 is y -22x +54 OB 8. y-12x +54 y=-9x+5 OD.

A: The equation of the curve is given by y = 5x-x3 To evaluate : The equation of the tangent line to…

Q: Q2/Find the length of the curve T = sino + cose between -s0s

A:

Q: Determine the tangent to the curve 3y2 = x3 at (3,3) and calculate the area of the triangle bounded…

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Q: Find the length of the following curve. y = 3x 2) fromx = 0 to x= 8

A:

Q: 42. Find k if the curve y = x2 tangent to the line y = + k is 2x.

A: The given line y = 2x, will be tangent to the y = x2 + k if and only if it touches the curve on a…

Q: If the line 3x - 4y = 0 is tangent in the first quadrant to the curve y = x^3 + k then what is the…

A:

Q: Use the guidelines of this section to sketch the curve   y = x e -1/x

A: The given function is y=xe-1x. Sketch the graph of the above function as shown below.

Q: 7. Find the length of the curve y= x'+ I from x = 1 to x . 12x Give your answer as a simplified…

A:

Q: 5x What is the slope of the tangent line to the curve y = at the point (2,2)? x2+1

A: Find the slope of the tangent line.

Q: Find an equation of the tangent line to the curve atthe given point.y =sqrt ( 1 + x 3 ),…

A: Given, y=1+x3 , (2,3)

Q: Sketch a curve with the following properties. 0, for x> 12

A:

Q: a) Calculate the length of the curve defined by x = -3 )on the interval 1 sys9.

A: (a) Given that, x = 13 y (y-3) on the interval 1 ≤ y ≤ 9   We have to calculate the length of the…

Q: 3 | co - 4. Find the length of the curve y = 7(6+ x)2 from x = 189 to x = 875.

A:

Q: Find the exact length of the curve. 1 x² -In(x), 1< x < 8 4

A:

Q: Find the exact length of the curve over the given interval. 4 3/2 X= 3 1sys4

A: Given curve is x=43y32, 1≤y≤4

Q: Find the slope of the tangents to the curve at the points (P1 and P2) where it crosses the x-axis.…

A: First find points P1 and P2 and than find the derivative at that points.

Q: Find the equation of the tangent line to the curve y = (1+2x)² at the point (3, 49).

A:

Q: The curve y = [In (x + 4)]² has horizontal tangent line at the point(s)

A:

Q: Find the length of the curve x2 1 In(1 – x) 2 4 1 between x = 0 and x 2

A: Recall: Length of the curve y=f(x) is given by on the interval a,b is…

Q: Q. Find the length of the arc of the curve f(x) =+3,

A:

Q: Find the exact length of the curve. y = ln(1-x^2), 0 ≤ x ≤ 1/9

A: Given curve is Length of curve is given by

Q: Find all the points of the graph of y = (x - 2)2 at which the tangent line is perpendicular to the…

A:

Q: Find the slope of the tangent to a parabola y=x^3 at a point on the curve where x=1/2

A:

Q: Find an equation of the tangent line to the graph of  y = x(x + 2)4  at the point (1, 81).

A:

Q: Find the area A of the largest rectangle that can be inscribed under the curve of the equation below…

A: Given that the rectangle inscribed under the curves of the equation in the first and second…

Q: 10. At what point on the parabola y = 3x² + 2x is the tangent line parallel to the line 10x – 2? y

A: Given,          The parabola y=3x2+2x is the tangent line parallel to the line y=10x-2.

Q: Find the length of the curve over the given interval.

A: Answer and explanation is given below

Q: Find the tangent to the curve a"-'y = x"

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

Q: Given the curve y=x2 and a point (5,17) Find the x intercept of the tangent line to the curve…

A:

Compound Probability

Compound probability can be defined as the probability of the two events which are independent. It can be defined as the multiplication of the probability of two events that are not dependent. 

Tree diagram

Probability theory is a branch of mathematics that deals with the subject of probability. Although there are many different concepts of probability, probability theory expresses the definition mathematically through a series of axioms. Usually, these axioms express probability in terms of a probability space, which assigns a measure with values ranging from 0 to 1 to a set of outcomes known as the sample space. An event is a subset of these outcomes that is described. 

Conditional Probability

By definition, the term probability is expressed as a part of mathematics where the chance of an event that may either occur or not is evaluated and expressed in numerical terms. The range of the value within which probability can be expressed is between 0 and 1. The higher the chance of an event occurring, the closer is its value to be 1. If the probability of an event is 1, it means that the event will happen under all considered circumstances. Similarly, if the probability is exactly 0, then no matter the situation, the event will never occur.