. Write a description of the rule (x, y)→(x+10,y+8). (a) translation 10 units to the right and 8 units up (b) translation 10 units to the left and 8 units down (c) translation 10 units to the right and 8 units down (d) translation 10 units to the left and 8 units up

Q: 1. Explain why (b x c) must be a linear comnbination of b and c. a X

A: We will use properties of cross product of two vectors

Q: (b) Let R = {(x, y) E R × R : 1 < ¤ < 4 or x = 6}, and S = {(x, y) E R × R : -1 < y < 1}. i. Find…

A: Solution: The given relations are R=x,y∈ℝ×ℝ : 1≤x≤4 or x=6 and S=x,y∈ℝ×ℝ : -1&lt;y&lt;1

Q: What is the need of y=mx+b

A: The need of y = mx +b is given in the next step.

Q: Verify whether yı = 3t4 and y2 = 4 t-2 form a fundamental set of solutions for f y" +7t y' + 8 y =…

A: We will verify the given statement.

Q: Determine whether the following are linear trans- formations from R³ into R²: (а) L(x) 3 (х2, хз)"…

A:

Q: For Va. Vy evaluate y' when y = 4.

A:

Q: Explain why it is not necessary to use the Quotient Rule to compute

A: Because in the first expression x is in the numerator and we are doing partial derivative with…

Q: 49y = t ²e-7t as the independent varie and c₂ as C₂ as arbitrary con

A:

Q: For Vx 3 evaluate y when y = 4. 2

A:

Q: (a) Find x, y el such that x+y || x || .. = 1 = || y || = || ** ||**y. ∞o 2

A:

Q: Evaluate f (xz + yz²) dV for the box B: 0 ≤ x ≤ 2, 2 ≤ y ≤ 4, 0 ≤ z ≤ 2. (Use symbolic notation and…

A:

Q: (b) Let R= {(x,y) E R × R : 1 < x < 4 or x = 6}, %3D and S = {(x, y) E R × R: –1< y < 1}. i. Find…

A:

Q: Use reduction of order process to find y.: x²y"-2xy'+2y = 0; Y = x? %3D %3D

A:

Q: ди Use the Chain Rule to find for x + Y и — y + z when x = p+ 5r + 9t, y = p– 5r + 9t , and z = p+…

A:

Q: 3. Using the definition find y' y = x* +x+1

A: Given function: y=x4+x+1

Q: The domain of f (1, y) = (a) {(z, y) E R| r +y? > 1, z #0} (c) {(z, y) € R| + y? > 1,z # 3} 1. is D=…

A: Given that: f(x, y)=x2+y2-1x-3

Q: Let f(x, y) = 5x + 9y, r(t) = (r³,1²). Use the Chain Rule to calculate f (r(t)) at the value t = -4.…

A:

Q: Q1. Find the Jordan nomal form of T-2 A =|0 -2 -2

A: A Jordan normal form is an upper triangular matrix of a particular form called a Jordan matrix. Such…

Q: 1. xdy + ( 4y y when x = 1, y = 1

A:

Q: Find y" of y=- y" = y" = O y" = y" = X-1 2 (x-1)² 2 (x - 1)³ 1 (x - 1)³ -2 (x - 1)³

A: Topic = Derivative

Q: Suppose that a = xdy is a 1 form and Y(v1, v2, v3) = ((v1 – v3)² (v2 – v3)²) ædy what is "a ?

A: Given α=xdy-----(i)γ(v1,v2,v3)=((v1-v3)2,(v2-v3)2)---(ii) To find γ*α------(iii) from (ii) we…

Q: For 16 - 19 consider the translation defined by the coordinate notation T(x,y) (x+4,y-6)

A: Explanation of the answer is as follows

Q: y dy Find using the substitution +5= √√y+2. √x+2 A²/(√y+2-5)(-5√/y+2+y+21) +C 3 ® ²/(√y+2-5)…

A: ∫ydyy+2 Substitute, u+5=y+2 Then , du=12y+2dy ⇒2y+2 du =dy ⇒2u+5 du =dy and y=u+52-2=u2+10u+23

Q: Find the real numbers x,y,z,t if -3x +y+ zt = 0 3x + y(t – 1) – z(t+ 1) = 0 3x +y+ zt =t+2 - 3x +…

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Q: 5. By Chain Rule , evaluate b. y' for y = u² + 2u and u = x² + 2 %3D

A:

Q: 3x²y if (x, y) = (0, 0) + y? if (x, y) = (0, 0) f(x, y) = { x +

A: In this question, we have to check the continuity of a function of two variables.

Q: or the DE y' = xy2, y(0) = -1. Then, y(2)=

A:

Q: a. R1 is defined on R by x R1 y if x² + y? = 1. b. R2 is defined on R by x R2 y if 4x² + 3y² = 1. c.…

A: (a) Given relation is xRy⇔x2+y2=1 The relation is not a function because Take x=1/2,…

Q: If (x. y)- (x+ 3, y-7) maps TUVW to 7'Uvw, what is the algebraic description that will map T'UV'W to…

A: Given if (x,y) →(x+3, y-7) maps TUVW to T'U'V'W', we need to find the algebraic expression that will…

Q: sWhat are the points of discontinuity? (x+1Xx-5) y3D *+4x+3 Ox-3, x--1 Ox--3, x=-1 Ox=5 Ox=5,x=-1

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Q: Compute the discriminant D(x, y) of the function. f(x, y) = x³ + y4 - 6x-2y² + 2 (Express numbers in…

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Q: HW.3 Find y (2.1),y(2.4), y(2.6) For the follomsing table 1 2 3 4 3 -1 10 15

A: We can solve this by using lagrange interpolation formula

Q: Write the translation rule from EF to E'F,

A: In the given graph-coordinates of E=(-7,-4)F=(-1,-3)E'=(1,3)F'=(7,4)

Q: Use Runga-Kutta 4 to determine y(1.3) for f(r, y) = with y(1)%3D 1

A: Here we have to use Runga Kutta 4 method

Q: 12. Which equation represents the image of y Oy= 1 x-4 Oy+4=1 1 Oy=274 x+4 Oy-4-1- 1 after a…

A: The objective of the question is determine the new function (equation) after translation upward.

Q: Using a suitable variable change find

A: Refer to the question we need to solve the provided integration of region using a suitable variable…

Q: In(r – y) 9-r2 - y?. Vr + y? – 4 Find and sketch the domain of f(r, y)

A:

Q: O Let f(x, y) = (5æ – y)°. Then -

A: We can find the required partial derivatives as below

Q: (b) Let R= {(x, y) E R × R : 1 < x < 4 or x = 6}, and S = {(x,y) E R × R : –1< y < 1}. i. Find the…

A: Solution: The given relations are R=x,y∈ℝ×ℝ : 1≤x≤4 or x=6 and S=x,y∈ℝ×ℝ : -1&lt;y&lt;1

Q: æ' = -a(4 – y), y = 4y(1 – 2?) %3D Find the critical points (x, y) entered as a comma separated list…

A: The critical points of the system is given by x' = 0 and y' = 0 simultaneously.

Q: Express.  y=√(3x²-9)  as a composition of u(x)=√x , v(x)= (x)² , j(x)=3x-9

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Q: Find W for the set W y e R : 2x – y – 5z = 0

A: We will find out the required solution.

Q: For Vx - 3 evaluate y when y = 4. O 2 O 2 O 4

A:

Q: A. Compute for Coefficient of r Let x ΣΥ Ξ [x² = Y n= [x = [xy = £y = r= Analysis & Interpretation…

A: Solution-: Let, X=Weight (lbs) and Y=Chest size (cm) We have following data: X Y 5.64 29.5…

Q: Ехample 14. 3 Differentiate w.r.t'x' y = 4\x + 2+ 4e*

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Q: Eliminate* the arbitrary constants c1 and c2 from the relation y = cje-2* + cze³* у" -у — бу %3D 0 O…

A:

Q: I need help with this problem Please. Thanks!

A: To convert the word problem into inequalities and represent them graphically

Q: Given z1= j3 and z2 =(4+j2), perform the multiplication for z= z1 · 2. Then, draw the Argand diagram…

A: Since you have asked multiple questions in a single request we will be answering only first question…

Q: Solve for x, y, z and w. (Enter your answers as a comma-separated list.) х- у х-z y - w (х, у, z, w)…

A:

Unitary Method

The word “unitary” comes from the word “unit”, which means a single and complete entity. In this method, we find the value of a unit product from the given number of products, and then we solve for the other number of products. 

Speed, Time, and Distance

Imagine you and 3 of your friends are planning to go to the playground at 6 in the evening. Your house is one mile away from the playground and one of your friends named Jim must start at 5 pm to reach the playground by walk. The other two friends are 3 miles away.

Profit and Loss

The amount earned or lost on the sale of one or more items is referred to as the profit or loss on that item.

Units and Measurements

Measurements and comparisons are the foundation of science and engineering. We, therefore, need rules that tell us how things are measured and compared. For these measurements and comparisons, we perform certain experiments, and we will need the experiments to set up the devices.