Find a formula that expresses the fact that P(x, y) is a dis- tance 5 from the origin. Describe the set of all such points.

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 Picard's theorem, find the largest interval for which the IVP y y(0) = 1, %3D %3D x² +x – 6' has…

A: Given that, y''=yx2+x-6,y(0)=1 Let F(x,y,y')=yx2+x-6 Then, ∂f∂y=1x2+x-6 Since,…

Q: A________ is the set of points P in the plane such that the ratio of the distance from a fixed point…

A: The conic section is known as the set of points, in which the curve of any of the conic, that are,…

Q: Evaluate the integral. Please refer to image.

A: Obtain curl F as follows.

Q: Determine the coterminal angle of 0 that is in the interval [0, 27) -29T 0 = 4

A:

Q: Use Picard's theorem, find the largest interval for which the IVP y y(0) = 1, %3D x² +x – 6' has a…

A: Given that, y''=yx2+x-6,y(0)=1 Let F(x,y,y')=yx2+x-6 Then, ∂f∂y=1x2+x-6 Since,∂f∂y=0,…

Q: Find the length of arc AB in terms of x.

A: Arc length is given by s=r.θwhere r = radius of the circle and  θ = central angle in radian

Q: :If the tangent at (a, b) to the curve x³ + y° = c° meet the curve again in (a,,b,). b, Prove that…

A:

Q: sketch the interval (a, b) on the x-axis with the point c inside. Then find a value of delta>0…

A: Given: a=49, b=47, c=12.

Q: ) Given the set set of e trii equatins param x= 2t -1 and y = 3t + 4 eliminate the parame er t and…

A: Given parametric equation is x=2t2 -1   and   y=3t+4

Q: Find the length of the cardioid r = 1 - cos θ.

A: Arc length in polar coordinate is given by:

Q: The graph of g consists of two straight lines and a semicircle. Use it to evaluate each integral. y=…

A: A) 4 B) 6.28 C) -35/2  ( mark limit is given from 0 to 7)

Q: Let θ be the angle between the line y = mx +b and the x-axis. Prove that         m = tan θ.

A: The slope of a line is the rate of change of the y-axis with respect to x. Formula for slope=riserun…

Q: The perimeter of a circumscribed polygon was used to find an approximation for pi by the ancient…

A:

Q: 2. If B is the midpoint of AC, which of the, following must be true? I. АВ + ВС 3D АС II. 2ВС - АС…

A:

Q: PROVE THE FOLLOWING THEOREMS USING ANALYTIC PROVING. 3. If point P(x, y) is a point on the…

A:

Q: If the distance from P(1, 0) to the point T(1 ) is x, determine the coordinates P(1,0) of the point…

A:

Q: 2. Find the angle of intersection between the following pairs of curve. Express your answers in…

A: We know that; The expression for the angle of the intersection between the two curves is:…

Q: A- Using Simpson s Rule to estimate the area of the circle (r-4), c (1, 0) with (n=4). B- Prove…

A: The equation of a circle having center C(1,0) and radius r=4 is given by: x-12+(y-0)2=42…

Q: Find the length of are リ-Jx-2+ Sa'z) + Sin

A:

Q: Find all angles between 0 and 2T satisfying the condition -1 Cs x = Separate your answers with…

A:

Q: Show that the curves r = a sin θ and r =  a cos θ intersectat right angles.

A:

Q: Find the exact length af te of the curve, 2. x-

A:

Q: Determine the measure of the interior angle at vertex F. 4x 4x 4x 4x 2х 2x F A OA. 54 Ов. 36 Ос. 108…

A: Interior angles polygon is given

Q: Ex: Let tanh u = – determine the values of the remaining five hyperbolic functions.

A:

Q: The distance from a point P1(x1, Y1) to the line ax + by +c = 0 is laxi + by, + c] Va? + b2 Use this…

A:

Q: In the figure below, PQ RQ and PS RS. Based only on the given information, which theorem could be…

A: in the △QPS &△QSR we know that PQ=RQ and PS=RS

Q: Let (a, b) be an arbitrary point on the graph of y = 1/x, x > 0. Prove that the area of the…

A: The given function for the curve is, y=1x The slope (m) of the tangent at the curve is,…

Q: Find the path of the sloping path y = x² + c such that θ = π / 4 is the angle between the tangents…

A: Slope = 1  Point are (a,b) So equation of tangent      Y-b = 1.(x-a)

Q: at.p.(I,.0)..and. the directiun. in. whichit.occurs

A:

Q: Find the tirst B secend dericatices %3D

A: y=7x55-x+8ex Differentiating with respect to x, we get dydx=ddx7x55-x+8ex=75·5x4-1+8ex…

Q: Find the length of the arc formed by x^2=12y^3 from point A to point B where A=(0,0) and B=(144,12)

A: This question is based on application of Integration.

Q: Find the exact length of the curve. y = In(1 - x²), o s x s

A: Solve the problem using definite integral

Q: Evaluate the intergral attached as an image with the question.

A: The given integral is,

Q: In a pole zero plot, there are only two poles in the origin. Hence the Type & Order number is O a. 0…

A:

Q: Determine the exact soluticn of the for -TTLOLTI (restrictions) equation sect©-2=0,

A:

Q: Find PR, given that SQ 4 and PS = 3. %3D %3D Q

A: Consider the provided graph, And given that SQ=4 and PS=3 Find the value of PR.

Q: The ________ ________ is derived from the Pythagorean Theorem.

A: We know that, The distance formula is derived from the Pythagorean theorem.

Q: This diagram shows a tangent TA with chord AB parallel to chord PQ.«

A: (a) To prove : ∆PAT is similar to ∆BAQWe can see that ABQP is a cyclic…

Q: The notation y = arccos x means that y is the _________ between ____ and ____,inclusive, whose…

A: The notation which is given here :                                                 y=arccos(x)…

Q: The DE for the family of circles of radius 9 is:

A:

Q: The figure belows shows two larger circles of radius 1 inscribed in a square in such a way that they…

A: To find: the value of r

Q: O, Solve the foluing differanital equehins -1 Ĉ (-o + g(t)), with ☺ (to) - 0, ? %3D dt

A: In this question we have to find the solution of the ODE.

Q: Is it true that if ƒ(x) > 0 at a point, then ƒ′(x) > 0 atthat point? Is it true that if ƒ′(x)…

A: a) Let f(x) = sin(x) f ' (x) = cos(x). Let x=2π3 Find the function's value at a point x=2π3.…

Q: Prove that if 0 < x < 2r, then a circle of radius r has a chord of length x. (You can do this using…

A: According to given ,only 1st solved....Radius of circle = r

Q: y = In(1 – a²) ; 0 < æs

A: Solution:-

Q: Find the exact length of the curve. y = In(1 - x²), o sxs

A: Find dy/dx, then put it in the arc length formula.