Find the equation of the parabola described below. Find the two points that define the latus rectum, and graph the equation. Focus at (-3,-1); directrix the line x=5 *** The equation of the parabola is (Type an equation. Use integers or fractions for any numbers in the equation.) C

Q: Evaluate 0-3 2 1 • S₁ (2² - 2)² - 0 3 2 da. The improper integral diverges.

A: Given problem:- ∫141x-22dx

Q: Example: find the complex Fourier expansion of the periodic function shown below f(x) = cosx…

A: Basic definite integration is done

Q: If ƒ(x) = 2x² - 6x + 7, find ƒ'(2). Use this to find the linear approximation to f(x) at x = 2. The…

A:

Q: Inflection points Local Extrema points с B

A: Given function is: y=xe-x

Q: A. Show that f(x, y) = (x-1)(y-2) (x-1)²+(y-2)² 7 (x, y) = (1,2) (x, y) = (1,2) at (1,2). 1 is…

A:

Q: Jonathan enjoys gardening. The east side of his house is 45 units in length. He can put 30 flowers…

A:

Q: Plot the point LO T given in polar coordinates, and find other polar coordinates (r.0) of the point…

A:

Q: Write an equation for the parabola shown to the right. The equation of the parabola is (Use integers…

A:

Q: [₁₁ ) If nd f*. f(x) dx = 4 and g(x) dx = 1, what is the value of ولاء f(x)g(y) dA where D is the…

A:

Q: Find the solution to the boundary value problem: Y dt2 dy dt +18y = 0, y(0) = 1, y(1) = 9

A: Given equation is the linear equation with constant coefficients.  So first assume the solution and…

Q: Evaluate the iterated integral 4x²y³ dxdy

A:

Q: Two sides and an angle are given below. Determine whether the given information results in one…

A: Two sides and an angle are given below. To determine whether the given information results in one…

Q: or =40x4 8. Determine the constant a, b, c and d so the curve defined by X-ax+bx+c+d has a local…

A:

Q: Answer the following True or False: If p(x) and g(x) are polynomials such that p(4): O True O False…

A:

Q: Analyze and sketch a graph of the function. Find any intercepts, relative extrema, points of…

A: For x-intercept , set y=0 For y-intercept , set x=0 . For inflection point , f''(x) =0 . Second…

Q: A baseball team plays in a stadium that holds 50000 spectators. With the ticket price at $8 the…

A: Topic- Application of Derivatives

Q: [x = t - 1 Q.1 Verify that the lines L₁ y=1-t lz=1-t and find the distance between them. and [x = 2t…

A:

Q: K Find an equation for the hyperbola described. Graph the equation Center at (1,-2) focus at (6,-2):…

A: Let's find equation of hyperbola.

Q: Find an equation for the ellipse. Graph the equation. center at (3,-2); vertex at (8,-2); focus at…

A: We need to find equation of ellipse.

Q: Evaluate [F·dr if F(x, y)=(x²y)ī +(xy²)ƒ and the curve C is given by r(t) = (t²)i + (t)j, 0≤t≤1.

A:

Q: Let f(x) = (x−³+4)5 – 1.

A: Assume that y=f(x) and use the description of f(x) and then express x in terms of y, that formula in…

Q: Calculate the double integral of f(x, y) over the triangle indicated in the following figure: 4 3 1…

A:

Q: Write an equation for the hyperbola shown in the graph. 747 7-112

A: We know Standard Equation of vertical hyperbola y-k2a2-x-h2b2=1 Here Center h,k  Equation of…

Q: 2. f sin √tdt

A: To evaluate the given integral.

Q: 7. Сучу+9 93)dx хоч до з 3 - и х 'dyto

A: Let's solve given differential equations.

Q: Find an antiderivative F(x) with F'(x) = ƒ (x) = 11+ 15x² +14x6 and F (1) = 0. Remember to include a…

A:

Q: 12 The function f is defined by (a) Write down the value of x that must be excluded from any domain…

A: Since you have posted a question with multiple sub-parts, we will solve first three sub parts for…

Q: price

A: At Equilibrium, Demand = Supply,

Q: Express the given quantity as a function f(x) of one variable x. The product of two numbers x and y…

A:

Q: Write an exponential mathematical equation to justify the statement log, (54) = 2.87744. Answer:

A: given, log454≈2.87744

Q: Consider the following region R and the vector field F. a. Compute the two-dimensional divergence of…

A: Solution: F=<8xy,x2 -4y2 >; R : y= x(3-x) and y=0

Q: 10. y' + y cotx = 5e cos x, when x ANSWER KEY: 10. y sin x + 5e cos x TT ‚ y = −4 = 1

A:

Q: Consider the following. f(x) = tan(x), (3,-1) (a) Find an equation of the tangent line to the graph…

A:

Q: ver (++)

A:

Q: Find the area of the region enclosed by the graphs of the functions f(x) = 14e*, g(x) = -x + 14 and…

A:

Q: 18. Find each indefinite integral by using appropriate substitution. cosx − xsinxdx XCOSX fco

A: Topic = Integration

Q: Evaluate the double integral J[₂x² x³ dA, where D = {(x, y) : 1 ≤ x ≤ e, 0 ≤ y ≤ ln x}.

A:

Q: Find the slope of the line tangent to the following polar curve at the given point. 3π r= 5-5 sin 0;…

A:

Q: Solve for x using the image as a reference. The perimeter of the triangle is 36 units. x = 12 x = 2…

A:

Q: A function is given below. Determine the average rate of change of the function between t = 6 and t…

A: The objective is to determine the average rate of change for the function.

Q: Problem 4. A point P is often identified in mathematics using the notation P(x, y) to reference a…

A:

Q: How do you find a bata ratio? What is the formula?

A:

Q: 11. Sketch the graph of the following function. f(x)= x³ - 6x² - 9x [1]x- and y-intercepts

A:

Q: The traffic flow rate (cars per hour) across an intersection is r(t) = 500 + 1000t - 180t², where t…

A:

Q: Using the Runge-Kutta method of order 4, find y for x = 0.1, 0.2, 0.3 given that dy/dx = xy + y²,…

A:

Q: Find the function represented by the following series and find the interval of convergence of the…

A: We have to interval of convergence

Q: 6. Sketch y = xe-*. First derivative A

A:

Q: Given f''(x) = - 16 sin(4x) and f'(0) Find f ¹ƒ(3/3) = = 6 and f(0) = - 5.

A: SOLUTION-

Q: 13. Show that there are no tangents to the curve y = can be concluded about the graph? 2x+1 4x +3…

A: We have to find the nature of curve.

Q: The graph of g' is given below: N

A: solution:-(A)g is increasing when g'>0 x∈-6, -4∪-4, 3∪7, ∞(B)g is decreasing when g'<0…