Find the vertex, focus, and directrix of the following parabola. Graph the equation. y +2y-x-D0 The vertex is (Type an ordered pair.)

Q: Use a graph below of f(x) = 3e¬5z° to estimate the x-values of any critical points and inflection po...

A: Given: f(x)=3e-5x2 Critical points are points where the function is defined and its derivative is ze...

Q: The function r(t) = 7i + 5 cos(t) j + 5 sin(t) k traces a circle. Determine the radius, center, and ...

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Q: or~r(t) =⟨3t−1,7t+ 2,t2⟩, t0= 1 find an equation o

A: Given: r(t)=(3t-1, 7t+2, t2)

Q: In x 1 <x < 4 5. у %3 4

A: We will solve the following 

Q: Consider three points P,QandRin space. If PQ×PR=then the area of the parallelogram spanned by PQ and...

A: In this question we will use basic of calculus i.e concept of vector calculus. We will use the conce...

Q: For the following exercises, points P (1,2) and Q (x, y) are on the graph of the function ƒ (x) = x²...

A: We have to  fill the table, estimate the slope of tangent at x=1, find the equation of tangent.

Q: Use a double integral to find the volume of the solid shown in the figure. -z = 4 – x² – y² 2 - 2 2 ...

A: We have to evaluate the volume of the given solid by using a double integral.

Q: Use the graphs, which show the functions f(x) and g(x), to find the following values. Note that you ...

A: Topic -composite functions

Q: Given the function f, defined by f(x) = 3x2+2x-4, find f(x+a)

A: Given f(x)=3x^2+2x-4

Q: A movie theater has a screen that is positioned 10 ft off the floor and is 25 ft high. The first row...

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Q: A conical paper cup is 20 cm tall with a radius of 10 cm. The bottom of the cup is punctured so that...

A: NOTE: Refresh your page if you can't see any equations. . height of the cone s h=20 and the radius o...

Q: 2. Show that the surface area of the solid of revolution obtained by revolving the curve y = 1/x, x ...

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Q: A piece of wire 29 m long is cut into two pieces. One piece is bent into a square and the other is b...

A: A piece of wire 29 m long is cut into two pieces. One piece is bent into a square and the other is b...

Q: A rectangle is inscribed in a circle with radius r. Find dimensions of such rectangle that will maxi...

A: This question is related to application of derivatives.

Q: (a) Find y' by implicit differentiation. (b) Solve the equation explicitly for y and differentiate t...

A: Given: To find  (a) Find y' by implicit differentiation. (b) Solve the equation explicitly for y and...

Q: Use the matrices to show that matrix multiplication is associative. [7 A= 1 -2 5 B= 2 4 3 1 and C = ...

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Q: Agrocery store estimates that the weekly profit (in dollars) from the production and sale of x cases...

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Q: f(x) = x' – 7x a) Find the critical numbers of f. (Separate multiple answers by commas.) --- b) Dete...

A: we have to find the critical value of the given function and also we have found the interval of incr...

Q: The rate (in liters per minute) at which water drains from a tank is recorded at half-minute interva...

A: We have to find total amount of water drained by using average of Left and Right Reimann Sum approxi...

Q: Find the function with derivative f'(x) = e7¤ that passes through the point P = (0, 6/7).

A: Given that f'(x) = e7x and we find function that passes through point (0,6/7). We know that f'(x) is...

Q: Use the Change of Variables Formula to evaluate the definite integral. 2 dx УЗх + 2 (Use symbolic no...

A: Given ∫0423x+2dx .............................(i) Put u=3x+2, du=3 dx ⇒dx=13du (i) become 23∫04duu.....

Q: The value of a timber forest after t years is V(t) = 444 t - 37t (for 0 sts 50). Find when its value...

A:

Q: Consider the part of the solid sphere x2 + y2 + z2 ≤ 4 contained in the first octant (the first octa...

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Q: 4. k=1 12k

A: Solving the problem by the process of geometric progression

Q: 5. Evaluate the integral: Jsin?x cos'x dx

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Q: te the triple integral x dV where E is the solid bounded by the paraboloid x = 9y + 9z? and x = 9. E...

A: Given query is to find value of the tripe integral.

Q: Find the area of the region specified in polar coordinates. the region enclosed by the curve r= 4 + ...

A: take r=0 the minimum value of cosine function is -1  so the above equation has no solution  so our...

Q: Find the area of the unbounded shaded region. y = 8xe- y 2.0 1.5 1.0

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Q: yA y = f(x) -2 2 8 Evaluate the following integrals by interpreting them in terms of areas: a) / s(x...

A: Recall: Slope intercept form of an straight line:         y-y1=y2-y1x2-x1x-x1

Q: All graphs should be drawn accurately on amiks a cup of coffe every morning at 7:00 am The amount of...

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Q: The speeds of vehicles on a highway with speed limit 100 km/h are normally distributed with mean 110...

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Q: Determine the largest open intervals of the domain over which each function is (a) (b) (c) increasin...

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Q: A function is given. h(t) = t² + 4t; t= -1, t = 1 (a) Determine the net change of the function betwe...

A: Topic:- Derivative 

Q: DETAILS LARAPCALC10 4.2.040.EP. 0/2 missions Used You wish to determine how much should be deposited...

A: NOTE: Refresh your page if you can't see any equations. . here we have t=5 years A=26000 r=7.4%=0.07...

Q: The point P(9, -3) lies on the curve y = . 8 - x 3 (a) If Q is the point (x, find the slope of the s...

A: take the derivative to find the slope

Q: The marginal cost for printing a paperback book at a small publishing company is c(p) = $0.013 per p...

A: Solution is given below:

Q: 9) The velocity of an object on the time interval [0, 5] is given in the graph below. Assuming veloc...

A: topic- graphs  9) speec can be directly  found from graph at t=4 .but we will eliminate negative sig...

Q: Use the given graph of f to state the value of each quantity, if it exists. (If an answer does not e...

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Q: Exercise 7. Show that the curvature of a circle of radius r is , and the curvature of the line is ze...

A: Show that the curvature of a circle of radius r is 1r and the curvature of the line is zero.

Q: X² + 5x + 6 / x + 2

A: Here we have to simplify x2+5x+6x+2

Q: Estimate the indicated derivative by any method. HINT [See Example 2.] (Round your answer to three d...

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Q: Evaluate the surface integral. ) ر م(ل 2) ds S is the part of the cylinder x² + y2 = 16 that lies be...

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Q: Find the absolute maximum and minimum values of the function, subject to the given constraints. g(x,...

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Q: (0) is the size of population Suppose maximum and minimum values of f(t) and the values of t where t...

A: Topic:- function

Q: The revenue R (in dollars) for a company selling x units is R = 700x - 0.1x2. dR (a) Find the margin...

A: Use differential

Q: A manufacturer has determined that the total cost C of operating a factory is C = 1.5x2 + 45x + 1500...

A: Given that the cost function is C = 1.5x2 + 45x + 15000. So the average cost function is A=Cx=1.5x2 ...

Q: A water trough 12 m long has ends shaped like inverted isosceles triangles, with base 6 m and height...

A: Given that a water trough 12 m longwhose ends shaped like inverted isosselestriangles, with base 6m ...

Q: ($4.7, Q16) Approximate the value specified to three decimal places using Newton's method. Use a plo...

A: Let's find. 

Q: An object's velocity after t seconds is v(t) = 26 – 2t feet per second. (a) How many seconds does it...

A:

Q: Consumer Credit The total amount of consumer credit has been increasing steadily in recent years. Th...

A:

Vertices Of An Ellipse

In the study of the conic section of the geometry, An ellipse is a plane curve surrounding two focal points, or foci where the set of all locus of points in the plane has their sum of the distances to the two foci is constant. On the ellipse curve, it is the intersection point of the main axis. In an ellipse graph, the center of the axis is the midpoint of the line segment connecting the foci. The major axis is the line section that runs through the ellipse's foci, while the minor axis runs through the middle and is perpendicular to the major axis.. The ellipse has two endpoints on the major axis which are known as the vertices (in plural), vertex in the singular. The equation of the major axis is 2a, the equation of the minor is 2b and the distance between the major axis and minor axis is 2c. The semi-major axis has a length of a and the semi-minor axis has a length of b. The ellipse's vertices are determined by the elliptical orbit's equation and graph.