The relationship shown in the figure is: Y 'C line Y.c = mxounts + b 10 VDC 1000 High 500 Alarm Detection Range 'C Low 100 O VDC 4095 Alarm Count Detection Range Differential second order. Differential third order. Differential first order. Linear.

Q: 6. Parallel to the line Y = = -}(x – 100) – 99, 3 4 passing through (1, 3)

A: Given query is to find the equation of the line passing through (1,3) and parallel to the line…

Q: Find the slope of the line tagent to the curve of y = In x/x at point (1,0)

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Q: If z=(X+Y) e and X-u * find the tollawing partial derivatives using Chain ruleo Express answers as…

A: Given, z=x+yeyx=u2+v2y=u2-v2 To find : ∂z∂u , ∂z∂v

Q: A function has a tangential gradient of 2sin3x. If the curve cuts the x-axis at, determine the…

A: A function has a tangential gradient  of 2 sin 3x.If the curve cuts the  x-axis at π3.To determine…

Q: Question 1 Find the total differential of the function z = 7x³y8 Odz = 7x¹y³dx + 7x³y+dy dz =…

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Q: az QI. Find the az and ax partial derivative ду x² sin (y*) + xe³ – cos (z) = 3y – 6z + 8

A:

Q: Find the first and second partial derivatives (there should be five in total) of the wo-variable…

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Q: 25. Find equations of all lines having slope −1 that are tangent to the curve y 1/(x − 1). = 1/4…

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Q: Show that the point (2, 4) lies on the curve x3 + y3 - 9xy = 0. Then find the tangent line and…

A: Given: f(x, y) = x3 + y3 - 9xy = 0 To find:  Equation of tangent and normal to the curve at point…

Q: dz at the point (1,1,1) if the equation 4xy +z°x-2yz = 3 defines z as a function of the two…

A:

Q: Find both first partial derivatives. z = tan(2x − y)

A: Z=tan2x-yZx=sec22x-y∂∂x2x-yZx=sec22x-y2Zx=2 sec2 2x-y

Q: 2b. Explain the difference between a partial derivative and a directional derivative.

A: Dear learner, as per our guidelines we can provide the solution for one part only. Kindly post other…

Q: Explain how a directional derivative is formed from the two partial derivatives ƒx and ƒy.

A:

Q: The curve y = ax² + bx + c passes through the point (2, 28) and is tangent to the line y = 4x at the…

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Q: Perpendicular to y + x = 0; (2, 0) on line

A: To find equation of a line ,which is perpendicular to line y+x=0,and point (2,0) lies on line.…

Q: Find both first partial derivatives. 6y* az ду.

A:

Q: Find equations for two lines through the origin that are tang net to the curve x²-4x+y²+3=0 .

A: We have given equation of curve x2-4x+y2+3=0. We also know that the slope of the line will be the…

Q: 12. The line y = 8x + b is tangent to the curve y = 2x². Determine the point of tangency and the…

A:

Q: Find the line tangent to the curve x 3 + y 3 4 at the point (-3/3, –1). V3 y = 3 x – 4 V3 4 - 3 -V3…

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Q: The curve y = a x 2 + b x + c passes through the point ( 1 , 2 ) . The line y = 2 x + 1 is tangent…

A: Given that the curve passes through a point.

Q: Calculate First order Partial Derivatives Find df dy

A:

Q: Continuity equation is derived using the conservation

A: Equation of Continuity: The continuity equation states that in the case of steady…

Q: ) Find the equation of the line normal to the curve x'y+ y'x = 10 at point (1,2).

A: Slope of a normal to the function y=f(x) at point m,n is given by the value of -dxdy at m,n Equation…

Q: Find the equation of a that has a y" = 4 if it has a slope of of 3 Curve Second derivative %3D at…

A: equation of the curve  is given below...

Q: b) Find equation of line passing the point ( 4, -1) and normal to 3y+ x=1. ||

A:

Q: 20. Does the line that is normal to the curve y = x² + 2x - 3 at the point (1, 0) intersect the…

A:

Q: 9. If f(x, y) = +, then find the first and second order partial derivatives.

A: Since you are asking multiple questions. As per our guidelines, we are supposed to answer only one…

Q: Find both first partial derivatives. az

A:

Q: Find the partial derivative. z = sin (6

A: We have to find

Q: The equation of the line tangent to the curve at (−1,4)is x+y=3. What is the slope of the normal…

A: Product of slopes of two perpendicular lines is -1.

Q: ху x, y) = x² + y2

A: Given function is fx,y=xyx2+y2. We have to find partial derivatives of given function with respect…

Q: The curve has a gradient function 2x - 3 and passes through (1,-6). Find the value of x when y = 0

A: Clear solution is given.

Q: Find the point on the line y = 3x + 4 that is closest to the origin. (x,y)=

A:

Q: The line that is normal to the curve x + 3xy - 4y² = 0 at (3,3) intersects the curve at what other…

A: Given: x2+3xy-4y2=0 at (3,3)

Q: Find both first partial derivatives. : = 6y²/x az ? Əx az ? ду II II

A: We have to find the partial derivative

Q: 6,3 + 4x°y +5. 5. 2 Find the first partial derivatives of f(x, y) = 5x°y° + 4x°y +5. af dx II

A: Given: fx, y=5x6y3+4x5y2+5 To  Find: ∂f∂x=?

Q: Early in the twentieth century, an intelligence test called the Stanford-Binet Test (more commonly…

A: Given: I.Q=MC×100 Find the derivative with respect to M I.QM=1C×100=100C At point (12,10)…

Q: Find the linear velocity of a point moving with uniform circular motion, if the point covers a…

A: From the data: s=45 cm t=5 sec

Q: What is the equation of the curve that passes through the point (0, 3) and has a slope at any point…

A: We have to find

Q: slope of the tangent to the curve y2x+ y2x2 =6at (2,1) is

A:

Q: dg Use the Chain Rule to evaluate the partial derivative at the point (r, 0) = (2/2, 7 where g(x, y)…

A:

Q: A heat-seeking particle is located at the point (2,3) on a flat metal plate whose temperature at a…

A:

Q: Find the orthogonal trajectory of the curve x^2 + y^2 = 2 ln x

A: See the details solution in below

Q: Find the first partial derivative wx, wy, and wz of (x + yw )2 –  ez  – 2 = 0  Make the solution…

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Q: Find the equation of a Tangent line to y = 2x2 – 5x – 1 that is parallel to line x + y –

A:

Q: Make the curve y = ax4 + bx3 + cx2 + dx + e pass through the points (0,3) and (-2,7) and at (1,4)…

A: The curve y=ax4+bx3+cx2+dx+e

Q: The y-axis and the line x = c are the banks of a river whose current has uniform speed a in the…

A:

Q: The curve y = ax² + bx+c passes through the point (3,6). The line y = 4x + 1 is tangent to the curve…

A:

Q: 2. Find the curve that passes through the point (1, 3) and whose tangent line at (x, y) has slope

A: Solve for the curve

Q: Let f(x,y) = x^2 y + e^xy sin y.   At Point (1,0) State the direction where the function…

A: Given: fx,y=x2y+exysiny

Optimization

Optimization comes from the same root as "optimal". "Optimal" means the highest. When you do the optimization process, that is when you are "making it best" to maximize everything and to achieve optimal results, a set of parameters is the base for the selection of the best element for a given system.

Integration

Integration means to sum the things. In mathematics, it is the branch of Calculus which is used to find the area under the curve. The operation subtraction is the inverse of addition, division is the inverse of multiplication. In the same way, integration and differentiation are inverse operators. Differential equations give a relation between a function and its derivative.

Application of Integration

In mathematics, the process of integration is used to compute complex area related problems. With the application of integration, solving area related problems, whether they are a curve, or a curve between lines, can be done easily.

Volume

In mathematics, we describe the term volume as a quantity that can express the total space that an object occupies at any point in time. Usually, volumes can only be calculated for 3-dimensional objects. By 3-dimensional or 3D objects, we mean objects that have length, breadth, and height (or depth).

Area

Area refers to the amount of space a figure encloses and the number of square units that cover a shape. It is two-dimensional and is measured in square units.