Determine the a) vertex, b) focus, c) directrix, d) axis of symmetry, and e) opening of the parabola in each item.

Q: A tank contains 60 kg of salt and 1000 L of water. A solution of concentration .03 kg of salt per l...

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Q: Approximate V(2.03)² + (0.8)² + (2.1)² using a linear approximation.?

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Q: The base of a solid is the region in the first quadrant bounded by the curves below. 4y = 4 – x? x-a...

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Q: 8. In triangle ABC, the point D is the midpoint of BC and E the midpoint of AC Vectors are marked as...

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Q: Find the abscissa of the points of inflection f(x) = -x* - 2x3 + 3x2 + 4x – 4

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Q: 12) A right circular cone has a fixed height of 7 units. Find the rate of change of its volume V wit...

A: NOTE: Refresh your page if you can't see any equations. . the volume of the right circular cone is g...

Q: 1. Find the equations of the normal and osculating planes of the curve x Int, y 2t, z = t2 at the po...

A: Equation of the plane :  r→.n^ =a→.n^ ; where 'r→' is the position vector and 'a→' is the given poin...

Q: 7. There is a removable discontinuity at x = 1 and f(1) = 4 %3D

A: 7.  There is a removable discontinuity at x=1 and f(1)=4

Q: For problems # 16 £17 to Find the requested derivative Use implicit differentiation ln (x y) x +9 fi...

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Q: y tan x dx + In* ydy=0

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Q: O Convert the following integral to polar coordinates. Do not evaluate the integral. 1 V1-x² (x + y)...

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Q: 6x° + 8x² + 45x +36 Consider the indefinite integral 2' + 9x2 Then the integrand has partial fractio...

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Q: In a lab experiment, the decay of a radioactive isotope is being observed. At the beginning of the f...

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Q: 33. lim arctan(e*)

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Q: Evaluate the following triple integral: 3 x x 6z dzdydx 0 0 y

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Q: B. Determine the standard form of equation of the hyperbola whose general form is given. 4. 4x - 3y ...

A: Note:- Since you have asked multiple question As per our policy, we will solve the first question fo...

Q: If T is the point at a distance T from P(1, 0) on the unit circle with its center at (0, 0), in what...

A: T is the point at the distance of 5π4 in the unit circle.To find the point.

Q: 3 e3/x - dp- x2 83.

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Q: x²-x-12 b. f(x) = x²-2x-8 Write f(x) as factored form: Vertical Asymptote(s), if any: Horizontal Asy...

A: The given function f(x)=x2-x-12x2-2x-8

Q: F(x) = (x – 2)3 f(x), g(x))

A: Given the query is rewrite the function in the form fog .

Q: Differentiate the following functions. Use any applicable method unless otherwise specified. 5. m =...

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Q: Find the slope of the tangent lines on the curve y = 6x^3 +24x^2 -39x -43 at poins (-5, 2) and (1/3,...

A: We know that, The slope of the tangent line to the curve at a given point Px1,y1 is equal to the der...

Q: Use the graph to find the following limits. a. lim f(x) b. lim f(x) x+1 x3 a. Find lim f(x) or state...

A: From graphlimx→1-f(x) =0limx→1+f(x) =0Thus limx→1f(x) =0

Q: One diagonal of a parallelogram is 80.5 m. It makes an ' respectively, with the sides. Find the leng...

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Q: The total costs for a company are given by C(x) = 5400 + 20x + x2 and the total revenues are given ...

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Q: x² 1. dx X=3 cos 0 /9—х2

A: Given that: ∫x29-x2dx

Q: Using the definition of the derivative, find f'(x). Then find f'(-4), f'(0), and f'(4) whenm f(x) = ...

A: We can find the derivative as below.

Q: Given g(æ)+ x/g(x) + 8 = x² + 1, g'(0)=

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Q: List the points in the graph in the interval -1<x<7 at which the function is not differentiable.

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Q: Consider the integral sin-'(5x) dæ: Applying the integration by parts technique, let U = and dv dx %...

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Q: Find the maximum and minimum points of f(x) = x(12 – x)?

A: topic - application of derivatives

Q: Using the definition of the derivative, find f'(x). Then find f'(1), f'(2), and f'(3) when the deriv...

A: f'(x)=limh→0f(x+h)-f(x)hf'(x)=limh→0-(x+h)2+4(x+h)-2-(-x2+4x-2)hf'(x)=limh→0-(x2+h2+2xh)+4(x+h)-2-(-...

Q: 3. The vectors i and y are each vectors of length 3 units, i.e., = | = 3. If + = V17, determine – j....

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Q: Consider a hemispherical tank that is completely filled with water. The water exits the tank from th...

A: Given that, There is a hemisphere, Radius (R) = 5 m Length (L) = 2 m density of water (d) = 1000 kg/...

Q: In this activity, you are going to supply what is being asked in each item. Use the given figure of ...

A: Given that: Graph of an ellipse.

Q: Use Table the limit of values to defermine tim.

A: The limit is given by limx→0x1-x To evaluate: The value of the limit using table values.

Q: 5 ex dx e2x

A: Given: ∫5-exe2xdx

Q: Find the solution to the differential equation dy/dx= (11xy)/((lny)^2) which passes through the poin...

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Q: S S( 3x² +x³y)dxdy

A: Evaluate ∫13∫023x2+x3ydxdy=?

Q: Use the product rule to find the derivative of (102° – 72*) (6e" – 7) Use e^x for e". You do not nee...

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Q: #37

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Q: Dur heroine is trapped in a rectangular room that is 10 feet by 16 feet, with a ceiling that is 9 ee...

A: Given query is to find the rate of change of height of water in the room.

Q: 2. 4x +2x lim X00 4x -x+1

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Q: Solve the following problem on separate paper being sure to show all supporting work. Answer any "in...

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Q: The half-life of caffeine is 5.5 hours. You drink a double espresso, which contains 128 mg of caffei...

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Q: The period of y = cos x is units. 4 7I

A: We can find the period as below

Q: Use the properties of limits to help decide whether the limit exists. If the limit exists, find its ...

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Q: Find the x-value(s) where the graph does not have a derivative. The x-value(s) where the function do...

A: NOTE: Refresh your page if you can't see any equations. .

Q: sinxtanx/cosx+1

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Q: Each of the following definite integrals are improper. Determine which converge and which diverge. F...

A: We have to evaluate the improper integrals ∫0∞ 11+x2 dx ∫02 x4-x2 dx ∫1∞ ln(x)x dx