For what values of z and y is orthogonal to both (-1 and

Q: Find f, and f, and evaluate each at the given point. y' f(x, y) = e*y2, (In 4, 2) %3D

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Q: Find fx and fy, and evaluate at the given point.

A: The given function is: fx, y=xyx-y and the point is 2, -2. To find the fx and fy, first…

Q: For what values of the constants k and c does the line x- 3 ** =- lie in the plane x - y + 2z = c? O…

A: Given equation of   line  ;   x-32=y-2k=z+14plane;  x-y+2z=c key points 1)  given line lies in the…

Q: Express ∂w/∂r and ∂w/∂s in terms of r and s if w = x2 + y2, x = r - s, y = r + s.

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Q: if was T!R R? Linearidentifir grandfather OkerT ImiT

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Q: Given, f(x, y, z) = xln(x?y)+ x*y – e a2. Compute fa, f, fry, fayz-

A: If f(x,y,z) is a multivariable function, then the variables x,y, and z are called the input of the…

Q: where C is rE by the lines X

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Q: If X and Y are independent RVs, then E(YIX) - F(Y) nd F(Y10

A: X and Y are independent then joint distribution of X and Y is  f(x,y)=f(x)f(y)

Q: For what values of the constants k and c does the line x- 3 _ y-2 z+1 * = = 2 lie in the plane x - y…

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Q: 4 - If w = x + 2y + z? , x =, y= r2 + In(s) , and z = 2r aw find at the point (r, s) = (-8,4). as…

A: See the attachment

Q: 30. Let f(x, y) (x - y) (x + y) for which Find the directions u and the values c

A: Note: we, as company policy, solve the first question only and first three sub-parts. Please…

Q: ؟ - ؟ - A = If A is orthogonal, what must x equal? Answer: √2 ال است - اة - أي اه اه الله √√x √3

A: We state the definition of an orthogonal matrix and then try to solve this problem.

Q: Let f(x, y) = x2 – xy + y² – y. Find the directions u and the values of Duf(1, –1) for which Duf(1,…

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Q: Given points J(1, 4), A(3, 5), and G(2, 1), what are the coordinates of AJ'A'G' when reflected over…

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Q: If A and B are independent and the P(A|B) = 0.4 and P(B) = 0.7. %3D %3D Find the P(A u B).

A: Given data,P(A|B)=0.4P(Bc)=0.7IF A & B are independent eventsP(A∪B)=?

Q: 2 W = Span- - 1 1 .Then, the distance and y = 1 -3 -21 3 11 ny to W is

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Q: Suppose L, is the line through the origin in the direction of u and L2 is the line through the point…

A: For first line L1, the line passes via origin, i.e., 000 and the line is parallel to u=110, so, the…

Q: If the distance from P(1, 0) to the point T(12) is x, determine the coordinates P(1,0) of the point…

A: Find coordinates

Q: Determine if the following two lines are parallel, coincident or distinct: h:ri= (-5,-3, 1] + t (-3,…

A: The given lines are                          l1 : r1→=-5, -3, 1+t-3, 1, 0 ; t∈ℝ…

Q: Find the value of X and Y in given that; 1 - 2y 4 7 2 2 - 2x 4 - 5 I3D 3. 2.

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Q: If Fu,y, z) = xzi + xyzj =ý k, find v.È %3D ........

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Q: Find b∈R so that ∫C4x^2dy − 2xydx = 53, where C is the segment from (1, −5) to (−2, −3), followed…

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Q: Let z = e*y, where x = Vuv and y = . Find in terms of u and v.

A: Change the z in the terms of u and v and the differentiate.

Q: If u = x²zî + yz?j – xyk and 0 = x²yz then find the value of u. (To)

A: Consider a function fx,y,z. The gradient of the function can be defined as, ∇→f=∂f∂xi^+∂f∂yj^+∂f∂zk^…

Q: We are given w = 2yln(y+2z)x2, where x=b√c, y=c-a2, and z=ab+1. Find the following ∂w/∂a at the…

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Q: If VW is not parallel to UX, what is VW?

A: Clearly from the figure we can see that the base angles are same. So this figure is an isoceles…

Q: Which of the following equation is symmetric with respect to a- axis and y- aris. O z6 - y = 50 O z8…

A: here 5th option is correct. Graph of x4-y6=25 is symmetric both about X- axis and Y axis. Graph of…

Q: If = 2 z-x'y and A = 2x'î-3 yzj +x z'k, find A.V and A xV4 at the point ( 1,-1,1).

A: given ϕ=2z-x3y and A=2xi^-3yzj^+z2 k^ find at the point 1,-1,1 1) A·∇ϕ 2) A×∇ϕ

Q: 1 4 1. 3x 8 3x

A: Hello! thank you for the question but as per our honor code, we'll able to solve only the first…

Q: Find the DC’s of the line that is perpendicular to each of the two lines whose directions are and

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Q: (0,1) R h5 15 30 (1,0)

A: Simple coordinate finding problem.....

Q: If C is a closed contour , , and n+1, then z" dz = ? О а. 2л O b.0 O C. 2ni O d. None of the above

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Q: R and r are defined by E(r, – 5)(y – T) Sry VS., Syy SSR R2 r = SST' (1) Show R? = r².

A: If y = a+bx is the linear equation  Correlation attempts to measure the strength of the relationship…

Q: Find a and b such that v = au + bw, where where u = (1, 2) and w = (1, -1). v = (0, 24) V = a = b =

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Q: The exact value of x and y is

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Q: (Ex) : Find the Dir (direction ) between - 21-2j +k & B =i+j+k

A: Direction between A→ and B→is the unit vector along  A→ - B→.

Q: Which of the following points does NOT lie on the line x + 3y = 10? %3D O (-4, 14/3) O (-2, 4) O (2,…

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Q: If f(x, y) 3D х'у? — 2x'y + 3х, find (а) f.(x, у) and f,(х, у), (b) f:(2 , –1) and f;(2 , –1)

A: To find partial derivatives of f(x,y) = x3y2 - 2x2y + 3x To find :- (a)fx(x,y) and fy(x,y)…

Q: Which of the following lines is perpendicular to the equa y=-2x + 8 Ox+2y = 8 O x- 2y = 6 O 2x-y = 1…

A: Perpendicular line

Q: y = f(x) ナ

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Q: We are given w = 2yln(y+2z)+x2, where x=b√c, y=c-a2, and z=ab+1. Find the following ∂w/∂a at the…

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Q: Which of the following lines bisects the line segment between (0,3) and (4,5) 5 x = -2y Dy = -2x 5 x…

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Q: 4 - If w = x+ 2y + z? , x= , y =r2 + In(s) , and y = r2 + In(s) , and z = 2r aw find at the point…

A: Using chain rule the given question has been solved in step 2.

Q: 9. Determine the indices for the directions shown in tl D 112

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Q: 5. Find fx, fy, and fz given x®y? f(x, у, 2) z4 %3D

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Q: P to the line L is equal P that is orthogonal to t

A: Given as, The distance is given as, d=AP→sinθ

Q: Which of the following is not linear in the variable x and y? O 2x-3y =4 %3D O a? + y? = 4 %3D +2…

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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.