Solve. Be sure to show and explain your work. log₁(x + 3) + log(x − 3) = 2

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A: given ball radius is 12 cylindrical hole radius is 7 ball is the shape of sphere volume of sphere…

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A: y=f(x)=x2+xat x=1 , x=4 (a)  equation of secant line is y=mx+c,  where m is slope

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Q: Suppose that 9x² +9x+7 < g(x) < 7x² − 8 x+7 for all x 0. Compute the exact value of lim g(x) x→0

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Q: (a) In order to express the function y=(2t^4−8)^5 as a composition of two functions the outer of…

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Q: the Cartesian equation xy = 21 with an equivalent polar equation. ivalent polar equation is…

A: Topic:- calculus

Q: Find the cross product a × b. a = (t₁3, 1), b = (12², 1², 1) 8, Verify that it is orthogonal to both…

A: Given  data :  a=t, 8, 1t, b=t2, t2, 1.

Q: Solve x³ + 3x² - 4x=0. Enter the values below. Smallest value: x= 0 x Middlex value: x= 0 Largest x…

A: Given :x3+3x2-4x=0

Q: by a factor of 5 not 1/5?

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Q: Use the given graph of the function f to find the following limits: 1. lim f(x) = 5 x 17 2. lim…

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Q: Find the sum of the series below. Σ n=1 48n (2n-1)² (2n + 1)² The sum of the series is.

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Q: A graphing calculator is recommended. If a rock is thrown upward on the planet Mars with a velocity…

A: As given height of the particle is y=14t-1.86t2 after time t of throwing.

Q: The graph of a function is given. Determine the average rate of change of the function between the…

A: Given query is to find average rate of change.

Q: Find the scalar and vector projections of b onto a. a =(4, 7,-4) b = (4, -1, 1) scalar projection of…

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Q: The graph of the quadratic function y = f(x) is shown. Determine the interval where f(x) > x. 6 5 3…

A: Consider the figure,

Q: 98 x = 62° 29° NOTE: The triangle is NOT drawn to scale. Answer the following: Round your answer to…

A: We are required to find the value of x

Q: Find an equation for a circle with center at (5, 12) and a radius of 4. Make a sketch of the graph.

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Q: Given the function find the following. (a) the average rate of change of ƒ on [−3,3]: (b) the…

A: The given function fx=3x2-3x+5. We have to find the average rate of change of f on the given…

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Q: 5 ၊ ၀ 9-

A: Given query is to find the correct graph of the function.

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Q: A tank contains 50 kg of salt and 2000 L of water. Pure water enters a tank at the rate 6 L/min. The…

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Q: Step 1 of 4: Find lim f(x). x-4 10 -5 10 5 ✔ -10 Enable Zoom/Pan 10 X

A: Given:

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A: red one represents x+4y ≤12   whereas violet one represents 4x+5y≥20   region is UNBOUNDED

Q: $19,000 is invested for 3 years at an annual simple interest rate of 19%. (a) How much interest will…

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Q: Let f(x) 3x2+6. Evaluate lim h→0 f(4+h)-f(4) h

A: Solution ⇒     f(x)=3x2+6    and we have to perform  limh→0f(4+h)−f(4)h    Now put…

Q: Use the graph of F to find the given limit. When necessary, state that the limit does not exist. lim…

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Q: A radio tower is located 350 feet from a building. From a window in the building, a person…

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Q: The region bounded by the given curves is rotated about the specified axis. Find the volume V of the…

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Q: Determine the center and radius of the circle. (x+1)²+(y-2)² = 81

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Q: Suppose f(x)=√x + 2. Evaluate the limit below by using algebra to simplify the difference quotient…

A: NOTE: Refresh your page if you can't see any equations. . here we have x=8 . substitute x=8+h

Q: Determine the value of k for which the system i has no solutions. k- 34 Т +y +4z = 0 P +2y-4z = 3 3x…

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Q: Given that f(x) = x² - 14x and g(x) = x + 10, find (a) f(x) + g(x)= (b) f(x) = g(x)= (c) f(x)g(x)=…

A: Given that fx=x2-14x and gx=x+10, to find a fx+gxb fx-gxc fxgxd fxgx

Q: 5. Given that the particular solution of y" - y' = cosx + sinx has the form = Acosx + Bsinx.…

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Q: 3. Evaluate the limit lim 0 20 –sin r x² The limit does not exist

A: To find the limit of the given function.

Q: An aircraft (at Z) is spotted by two observers (at X and Y) who are L=1150 feet apart. As the…

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

Q: 8. Which of the following statement is true? ○If h(x) = f(x)g(x), then h'(x) = f'(x)g'(x) f(x) =…

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Q: The distance of a particle from some fixed point is given by the following function. s(t)=t² +5t-4…

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Q: Use properties of limits and algebraic methods to find the limit, if it exists. (If the limit is…

A: Here we have to find the limit.

Q: Find the domain of Domain: ·∞, 3 Write your answer in interval notation. interval notation. - 28 1)…

A: Find the domain of function

Q: he area of the triangle in the first quadrant formed by the line ax + by = c, the x-axis, and the…

A: Given query is to find the area.

Q: 3. In this question, we consider y = f(x) = = 3x - 2 4x² +1 (a) Calculate the derivative y'(x). Find…

A: A detailed solution is given below.

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Q: A circular oil slick is expanding with radius, r in feet, at time t in hours given by r = 6t -…

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Q: f(x)= = J 5x - 3 9x² − 12 if x < 3 if x ≥ 3 Enter the exact value of the one-sided limit lim f(x)…

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