Use a graphing calculator to generate the curve over the interval for the parameter t. Then find the equivalent rectangular equation. x- 2t, y=t+1 for t in [ - 2,3] Select the correct graph from those shown on the right.

Q: Write the equations of the lines tangent to the curve y x- 4x at both a 0 and a 2. Then, determine…

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Q: If the random variable Y has the pdf pictured below: 2 a) Find pdf of X? b) Find CDF of X? c) Find…

A: From the figure we can see, P.d.f of X  is given by, f(x)= 1/2 ,.        0<X<t

Q: Determine the parameter equation of the following curve x2 + y2= 5

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Q: The slope of the tangent line to the parabola y = 2x² + 7x + 7 at the point (4, 67) is: The equation…

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Q: Find the tangent plane to the equation z = − 2x² + y² - 5y at the point (4,5,-32) z = Question Help:…

A: Given z = -2x2 + y2 - 5ypoint → ( 4 , 5 , -32 )

Q: Graph and calculate the relation of the equation x2/4+y2/16 = 1 using the points calculated in the…

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Q: Find an equation for the line that is tangent to the curve y = 5x - 5x at the point (1,0). The…

A: Our Aim is to find an equation for the line that is tangent to the curve y=5x3-5xat the point (1,0).…

Q: A curve is generated by the equation x² + 4y² = 16. Determine 2. whose corresponding tangent lines…

A: Given data:- The given equation of curve is, x2+4y2=16 Curve corresponding tangent line are…

Q: Eliminate the parameter t to find a Cartesian equation of a curve. x = 1 + 3t,  y = 2-t^2

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Q: For the cruciform in the figure below, the equation is x²y2 - 9x2 – 4y2 = 0, find the equation of…

A: To find the equation of the tangent line for the given curve.

Q: Find the standard form of the equation of the circle tangent to both axes at (-3,0) and (0,3).

A: Given that: The circle is tangent to both axes at (-3, 0) and (0, 3)

Q: The slope of the tangent line to a plane curve y=f(x) at the point (x,y) is given by 3 - 2 m=- + 16x…

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Vector Arithmetic

Vectors are those objects which have a magnitude along with the direction. In vector arithmetic, we will see how arithmetic operators like addition and multiplication are used on any two vectors. Arithmetic in basic means dealing with numbers. Here, magnitude means the length or the size of an object. The notation used is the arrow over the head of the vector indicating its direction.

Vector Calculus

Vector calculus is an important branch of mathematics and it relates two important branches of mathematics namely vector and calculus.