30.) Show all steps to evaluate by hand: dA where R (rectangle) –1 < x < 1 and 0 < y < 3 y2+1

Q: Q3:- find the erea of the shap by the order 1- SS dydx 10

A: Please refer the attached image for complete solution.

Q: Express K#S^2#T#2P as a connected sum of projective planes or as a connected sum of tori.

A: To express the given connected sum (of surfaces) in the required form

Q: 7. P(0.5 < Z< 1.5)

A:

Q: Compute the discriminant D(x, y) of the function. S(x, y) = x' + y* - 6x – 2y² + 1 (Express numbers…

A: Given function f(x,y)=x3+y4-6x-2y2+1

Q: Use the following rule in mathematical morphology to fill the holes inside the image A to be black.…

A:

Q: f(x)=2sin(x)+4cos(x), then f'(x)=? f'(5)=?

A: Given  f(x)=2sin(x)+4cos(x)

Q: Find y" by imprcit differen fia fên. Simpliey unenoven Po Ssiole

A: Given:- x2 + 9y2 =9  To find:- y'' of given equation

Q: (a) Suppose X~ Uniform(0,2). Use the definitions to find E[X] and Var(X).

A: GivenSuppose X~Uniform 0,  2. Use the definitions to find       Ex  and   Var X

Q: consider this formula. z= y over x if z= 4.0 and y=6.0  express your answer to the tenths place

A:

Q: If X is uniform in the interval [-3,3] compute X(i.e. E{X}) and o² (i.e.E{(X-X)²}).

A: Given that X ~ U[-3,3] to find mean and variance

Q: We must have xo and x1 satisfying f(xo) f(x1) < 0 in order to apply the False Position method.…

A:

Q: Q2) Discus the existence and uniqueness of the following IVPS: y = x + ys y = x tan (i) (ii) y(1) =…

A: We Know that,

Q: Prove that in the pairs of positive numbers ¤, y for æ² + y° = r the sum a+y is greatest when z = y.…

A: Here we solve the given problem of calculus.

Q: 4. Given AGCH use the diagram below to prove ZA 2c. G A.

A: In△ABH and △CBGBH=BG             (given)BG=BH         (1)AG=CH        (2)add (1) and…

Q: 1on to ove tha (X +Y)(X + Y) =X

A: In this question, the concept of Boolean Algebra is applied. Boolean Algebra A boolean expression is…

Q: Find the Avorare valne of Hhe famdtiun en the interal [ 0,4J VI+ 2x

A: Average value of the function on a given interval is 1/(b-a) integration of a given funtion…

Q: For what value(s) of tt does the equality ⟨t3−6t,0.333333t2+3⟩=⟨0,5⟩⟨t3−6t,0.333333t2+3⟩=⟨0,5⟩ hold…

A:

Q: O Find the by the ainves : y=x", enelured area y= x 16, x o and x-5 EO and x-5

A: To Find : the area enclosed by the following curves      y = x2 and y = x + 6  and x varies from 0…

Q: Since X~N(0,1) and Y = e^x , E [Y] = ?, Var

A: Given that X~N(0,1) Y=ex Consider, E(Y)=E(ex)        =∫exf(x)dx       =∫01ex12πe-12x-012dx…

Q: x is the distance 1:- Show that the from morm Il x|l o7 2 to

A: We have to show that x of x is the distance from x to 0 Hence, x can e written as x−0 x=x−0 The…

Q: The domain and the range of z=cosh x+y are represented respectively by O A. D = { (x,y) ER X R: y 2…

A:

Q: Compute the length of the curve r(t) = (21, In(t), r?) over the interval 1 <t < 9. (Use symbolic…

A:

Q: If the inequality 1 - <1- sin [æ³y³[ < P ) |z*y*| for all æ and y. Then, find the lìm(z,9)→(0,0) 2…

A: We will use Squeeze theorem in the given problem.

Q: Given that X~N (2,25) , find pr (0 < ? < 10)

A:

Q: ome 9/ for Find The domain Dp and Rag Re De fallowing fandinse,

A:

Q: Given: 5x+4y= 24, x + 7y= 11; Prove: y = 1

A:

Q: 4. Find Rable With respect ho X and X is also iable nith respect b . a ssuming fhat Y is diffrent…

A:

Q: Find a, b > 0 such that the following equality holds: {r €R : -a < br – 3 < v2} = [-3, 3).

A: Note the result : The set can be represented in interval form as .

Q: 5. Use the Mean Value Theorem to establish the following inequality |cos r- cos y < |r – yl, for 1,…

A: According to the guideline we should have been able to solve only first one question at a time

Q: Compute the length of the curve traced by r(t) = (4t, 7 – 4t, 5) over the interval 2 < t < 10. (Use…

A: Use formula of length of curve in parametric form

Q: ppose it is kr ta that X, th intersection 11 terized by th

A: 3.35) Let x denote the number of cars that arrive at a specific intersection during a 20-second time…

Q: x[n] x₁ [n] = festas O Î X,(z) ? X(Z) x₁₂[n] = x [2n] nieven niodd x[n]→→→x(z)

A: Introduction: Signal processing is broadly speaking a department of sign evaluation wherein…

Q: sec²(3vt) dt (4) VE

A: According to the bartleby guidelines I have to solve only first question in order to get the…

Q: Which of the following would represent an approximation of R(51) using information from R'(x)? O…

A: In the question it is asked to write the approximation of R(51) using information from R'(x).

Q: 20. Provc the incquality using the mcan valuc thcorcm (or dcrivatives). tan x < 2x, 0 <x < T/4

A:

Q: - Given y= ela's -x²-In'r, what is y'?

A:

Q: Prove using INDIRECT PROOF: 1) P → Q 2) R → S 3) ﬢQ ۷ ﬢS ﬢP ۷ ﬢR

A: The statements given are as follows: P→QR→S~Q∨~S For the first statement, we will apply the…

Q: Solve the following inequality graphically in two-dimensional plane:y + 8 ≥ 2x

A: Given:

Q: Compute the length of the curve r(t) = (21, In(?), r²) over the interval 1 < t < 7. (Use symbolic…

A:

Q: 8) So for x and y. Bound to the nearcast tenth. 12 メニ 50

A:

Q: Given f(x,y)=x-exy, evaluate fy(3,0). 06 O 27 O 9 O 13

A: topic- partial differentiation

Q: 4) Fund the interval of x-value on which the Carve is Con Cave up and Con Cave dawn 3 fex) = +x-3X

A:

Q: a?u, a?u (c) = 0;0< x5 5,0 sys 10 əx² ду? subiect to

A: Given,     ∂2u∂x2+∂2u∂x2=0;      0≤x≤5,   0≤y≤10    ...(1)subject to      u(0, y)=u(5, y)=0; 0≤y≤10…

Q: 4. Use the algebraic description to find the image of AMNO). (x, y) → (x + 2, y - 3) M y

A: From the given figure, the vertices of the triangle are O-1,0,N-3,1 and M-2,4. The given algebraic…

Q: 6., Given that= 1' + sy = ) and that y = 1 dr (a) show that for values of r close to 0, 1 when = 0,…

A: Let y(x) is a function. Then the expansion of Taylor series of the function y(x) at the point x=a…

Q: Solve for x in the figure * AJKL is isosceles with KJ = LJ. K x+3 X-1 J 2х- 5

A: Since, triangle JKL is isosceles, so, we have, KJ = LJ

Q: II. Let U = R, { x € R | 26x + 25x = 0}, J = { x €R | |4x + 2| > 10 } and K = { x € R | x? – 3x – 4…

A:

Angles in Circles

Angles within a circle are feasible to create with the help of different properties of the circle such as radii, tangents, and chords. The radius is the distance from the center of the circle to the circumference of the circle. A tangent is a line made perpendicular to the radius through its endpoint placed on the circle as well as the line drawn at right angles to a tangent across the point of contact when the circle passes through the center of the circle. The chord is a line segment with its endpoints on the circle. A secant line or secant is the infinite extension of the chord.

Arcs in Circles

A circular arc is the arc of a circle formed by two distinct points. It is a section or segment of the circumference of a circle. A straight line passing through the center connecting the two distinct ends of the arc is termed a semi-circular arc.