Find the vertex, focus, and directrix of the parabola. (x+3)²=16(y-3)

Q: What is the result of the following limit? O lim 3x x→∞ √9x² 1 3 1 3 23 2|3 +∞ 4x + 4

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Q: Find the area of the region bounded by the curves y=2² and y= 2²+

A: Given :- The region bounded by the curves  and To Find :- The area of the region

Q: Explain why 4-4 using the relationship between radical expressions, rational exponents, and…

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Q: Example 0.4. A force of 40 N is required to hold a spring that has been stretched from its natural…

A: Using integration, we can find the required work.

Q: Suppose $4,000 is invested at 60% compounded monthly (i.e., 12 times a year). (a) What will the…

A: Invested amount is at interest rate compounded monthly.Formula to be used : Here we will use the…

Q: Find the angle between the vectors. (First find an exact expression and then approximate to the…

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Q: Find the critical points of the functions f (x, y) = x² + 2y² - 4y + 2x, g(x, y) = x² - 14xy + y Use…

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Q: A cardboard box with a square base and an open top has a volume of 2916 cm³. Find the dimensions of…

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Q: What is the average rate of change between x = 1 and x = 3 for the function g(x) = −3(x-1)² +11?

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Q: On what interval does the initial value provlem ty' = 3tsin(t) − y, y(1) = 2 have a unique solution.…

A: To determine the interval on which the initial value problem has a unique solution, we can use the…

Q: Find the interval of convergence of the power series. (Be sure to include a check for convergence at…

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Q: Find a polynomial function of least degree having only real coefficients, a leading coefficient of…

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Q: The position vector r describes the path of an object moving in the xy-plane. Position Vector Point…

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Q: g(x) = = X 2 2x² X-2 (a) Evaluate each of the following, if it exists. (If an answer does not exist,…

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Q: QUESTION 20 Find all real numbers that satisfy the equation. √3 sin x = {x1x = 7+2mm} X= (x1x - 72m…

A: Explanation of the answer is as follows

Q: The volume of the solid obtained by rotating the region enclosed by y = x², x = 1, x = 3, y=0 about…

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Q: Find the first and second derivatives of the function. f(u) = √10 - 5u f'(u) = -5 f"(u) = -5 du dx X

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Q: 9. y" - y' - 2y = 4x²; y(0) = 1, y'(0) = 4

A: The given differential equation is,Note that as per the rules, we are supposed to answer the first…

Q: 8. Suppose $2000 is invested in an account that earns 6.25% interest compounded continuously. The…

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Q: Find the formula for the function represented by the integral. (Use symbolic notation and fractions…

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Q: Find a set of parametric equations of the line with the given characteristics. (Use t for the…

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Q: Consider the equation 52x - 30-5x + 125 = 0. Enter the number of solutions of the given equation.…

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Q: Find the area of the region that lies inside both curves. r= 2 + cos(8), r= 2 - cos(0)

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Q: The graph of y=f(x) is given. Solve the inequalities. Write the solution set in interval notation if…

A: Graphical representation of f(x) indicates that, f(x) tends to 0 at x = inf, -inf.And, f(x) tends to…

Q: 1: 4 2 Graph of the function f(x) is given below. 3 2 1 6 5 4 1 y = f(x) Previous Page 1 1 lim…

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Q: Find the critical points, domain endpoints, and local extreme values for the function. y=3x√ √36-x2…

A: The solution is shown in step-2

Q: Write a polar equation of a conic with the focus at the origin and the given data. hyperbola,…

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Q: pose an arrow is shot upward on the moon with a velocity of 48 m/s, then its t in meters after t…

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Q: Using rectangles whose height is given by the value of the function at the midpoint of the…

A: Given,f(x) = x3 and , a= 2 ; b= 4

Q: Match the series with the graph of its sequence of partial sums. 27-1) Sn Sn Sn n .... 8 .... 8 ....…

A: The given series is:

Q: The diagram that has a limit at x = a is

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Q: Use the method of cylindrical shells to find the volume generated by rotating the region bounded by…

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Q: Find the exact value. (ore cos & - Oresin tan 2/3) =

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Q: Find a polynomial function f(x) of least degree having only real coefficients and zeros as given.…

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Q: Find the values of A and B such that the graph of the exponential function f(t) = Aeßt goes through…

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Q: Consider the equation 5x²+16x = 625X-8 Enter the number of solutions of the above equation.…

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Q: justify your answers to the following: (b) (a) Find intervals where fis increasing or decreasing.…

A: We have to find the monotone intervals, extrema points, concavity and inflection points.

Q: Determine £¹{F}. F(s) = 7s²-18s+7 s(s-7)(s-4) ***

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Q: The picture below shows an angle. Which of the answers is coterminal with that angle? (-1,0) 4 50.…

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Q: 1. Calculate the distance from the point to the line: (2,2,0); x = -t, y = t, z = -1 + t

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Q: Find the volume of the solid obtained by rotating the region bounded by the given curves about the…

A: To find the  volume of the solid obtained by rotating the region bounded by the given curves about…

Q: The US Postal Service will accept a box for domestic shipping only if the sum of its length and…

A: Let b be length of the box and a be the length of the side of the square.The volume V of the box…

Q: A kite 40 m above the ground moves horizontally at the rate of 3 m/s. At what rate is the angle…

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Q: 4. Given the function f and point P, find a unit vector in the direction in which f increases most…

A: The solution is shown in step-2

Q: 2 I 1 1 y=f(x) 2 lim {ƒ(x) – g(x)} x-1 A A/ 2 lim x⇒1 Use the functions f and g defined by the…

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Q: Consider the equation 22-15 = (1/4). Enter the number of solutions of the above equation. Determine…

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Q: Suppose the wholesale price of a certain brand of medium-sized eggs p (in dollars/carton) is related…

A: The equation  And 21000 cartoons of eggs available and the price is falling at the rate of…

Q: Find all solutions to 2 sin(0) = √3 on the interval 0 ≤ 0 < 2T 0 = Preview

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Q: Find the angle between (-1,-2) and (-6,3)

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Q: Consider the following. x=t², y=In(t) (a) Eliminate the parameter to find a Cartesian equation of…

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