Find the vertex, focus, and directrix of the parabola (10-x)2= 32 (1-y) Select one: O None O Vertex= ( 10, 1), Focus= ( 10,9), directrix: y = -7 O Vertex= (-10,-1), Focus= ( 2,1), directrix : x = 9 O Vertex= ( 10, 1), Focus= ( 10, -7) , directrix: y = 9 O Vertex= (-10,-1), Focus= ( 10,9), directrix : y= -7

Q: Is the distance between any two different real numbersalways positive?

A: State whether the distance between any two different real numbersalways positive or not

Q: Find the (a) component form and (b) length of the vector with initial point P(-3, 4, 1) and terminal...

A: the given initial and terminal point of the vector are: P(-3,4,1) and Q(-5,2,2) respectively. we hav...

Q: Verify the identity.

A: To verify the given identity

Q: Give the equation of the exponential function whose graph is shown.

A: Given

Q: 1 2 Calculate lim x→1 x – 1 x2 – -

A:

Q: In Exercises 13-16, find a vector normal to the plane with the given equation.15. 3(x - 4) - 8(y - 1...

A: Given: The equation of the plane is: 3 (x-4)-8 (y-1)+11 z=0 We have to find the vector normal to the...

Q: Finding LimitsIn Exercises 9–28, find the limit or explain why it does not exist.

A: “Since you have asked multiple questions, we will solve the first question for you. If you want any ...

Q: Sketch the graph of the function. y = −4 csc 3x

A: Given: y=-4csc 3x

Q: The figure below represents an informal way of showing that ∑ as given . Explain how the figure impl...

A: Prove ∑n=1∞1n2<2 by using the given figure.

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A:

Q: find the first and second derivatives r = 1/3s2 - 5/2s

A:

Q: A rectangular garden is 25 ft wide. If its area is 1125 ft 2 , what is the length of the garden?

A: It is given that the are of the rectangular garden is 1125 sq ft and its width is 25 ft. Thus, A=112...

Q: Let ƒ(x)

A:

Q: 2. The volume of a right circular cone is V =1/3nr²h, where r is the radius of the base and h is the...

A:

Q: Use the attached figure: List the y-intercepts b1 , b2 , b3 , and b4 in order of decreasing size.

A: Given Graph

Q: Solve absolute value inequality : 1 < l2 - 3xl

A: Given:2-3x>1

Q: Insert either <, >, or = in the blank to make a true statement l-2 l …...4/17 ÷ 4/17

A: Given: -2.........417417

Q: Convert the given coordinates (2, -2√3) to the indicated ordered pair (r, θ).

A: Consider the following coordinate: x=2y=-23 Consider the following formulae: r=x2+y2=22+-232=4+12=16...

Q: Find the dimensions of the rectangle of largest area that canbe inscribed in an equilateral triangle...

A: Solution:- We have to find the  dimensions of the rectangle of largest area that canbe inscribed in ...

Q: Find an equation of the form y = A sin Bx that produces the graph shown in the figure.

A: Given: The graph of the equation is: We have to write the given function of the form  y = A sin Bx ...

Q: Sketch the graph of each function, and state its domain, range, and asymptote. Show the x- and y-int...

A: Given function is fx=2-x+4. Graph of the given function is:

Q: Find the LCD of[(x + 2/2x - 3)and(4/(x + 3)].

A: Given that : The equation x + 22x - 3 and 4x + 3 .  

Q: tan(θ -  φ) =________.

A: Consider the following formula: tanθ-φ=tanθ-tanφ1+tanθtanφ

Q: Use the Intermediate Value Theorem and Rolle’s Theorem to prove that the equation has exactly one re...

A: The given equation is 3x+1-sinx=0. It can be seen that f0=1>0 and f-π=-3π+1<0.

Q: Use the three steps to graph the polar equation: r = 2/(1 - sin θ)

A: Given information: r=21-sinθ  

Q: prove the laws of sines a/sinA= b/sinB= c/sinC

A: Draw the figure and analyse the angle and apposite sides

Q: -6 and v2 Find the position of the 1 A particle moving in a planar force field has a position vector...

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Q: Use the figure to fill in the blank with the symbol <, >, or =. Explain your reasoning.

A:

Q: Trigonometric integrals Evaluate the following integrals.

A: To evaluate I=∫0π21-cos2xdx

Q: Integral

A:

Q: What is the result of integrating a population growth rate betweentimes t = a and t = b, where b &gt...

A: Integrating a population growth rate between a to b that is ∫abRatedt

Q: Evaluate the integral.

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Q: Find the area of the surface formed by revolving the polar equation over the given interval about th...

A: Consider the following polar equation: r=2sinθ Differentiate r with respect to θ: drdθ=ddθ2sinθ=2cos...

Q: Find parametric equations and a parameter interval for the motion oa a particle that starts at (a,0)...

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Q: If the demand equation is Q = 100 - 10P  find the consumer’s surplus when the consumer purchases 18 ...

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Q: A body builder consumed 4,400 calories yesterday. Today, he consumed 3,600 calories.What is the perc...

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Q: A spherical balloon is being inflated. Find the rate ofincrease of the surface area (S =4πr2)with re...

A: Given the surface area of the inflated S=4πr2 . We need to find the rate of increase of the surface ...

Q: Determine, without graphing, whether the quadratic function f(x) = -2x2 + 12x - 16 has a minimum val...

A:

Q: dollars dP =- 0.727 dt year

A: Given information: dPdtt=3=-0.727 dollarsyear

Coordinate Geometry

Coordinate geometry, also known as analytic geometry or Cartesian geometry in classical mathematics, is a type of geometry that is studied using a coordinate system. Coordinate geometry is a branch of mathematics that describes the position of points on a plane using an ordered pair of numbers called coordinates.