r(x) = 5 log4 (3x + 10)

Q: Find the angle that maximizes the area of an isosceles triangle with legs of length / = 10. 1 (Use…

A: The given isosceles triangle with legs of length l=10

Q: 1. I. Evaluate each determinant. -5 -3 3 -4

A: Given,            -5-33-4

Q: Calculate the gradient of f(x, y) = sin(x² - y) Vf=

A: Finding the partial derivative of the function.

Q: The integral of sin x³ dx is cos x + Option 1 cos³ x 3 + C cos x + Option 2 cos² x 2 + C

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Q: √ √(x²-1)dx

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Q: y = In (cot 8x)

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Q: Suppose that f(x, y) = 6, and D = {(x, y) | x² + y² ≤ 4}. I Then the double integral of f(x, y) over…

A: Explanation of the answer is as follows

Q: SET-UP a triple integral that will solve for volume of the solid S bounded by the sphere x² + y² +…

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Q: Let F be the vector field defined on the plane by F(x, y) = (x¹+3y, 6x - siny). Let C be the unit…

A:

Q: Find the present value of a continuous stream of income over 5 years when the rate of income is…

A: On solving this we will get

Q: 2) fff (x² + y² + z²)ž dv D is the unit ball. Integrate using spherical coordinates.

A:

Q: Convert the rectangular coordinates (5,-5√3) to polar form. Letr> 0and 0 <0<2TT.

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Q: 6.) I. Simplify. Write "undefined" for expressions that are undefined. -3 -6 -2 +69 4 -4 6

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Q: Which of the following graphs is the correct plot of y = 5+ 5 4 4 -3 3 2 2 -1 + 5 6 2 4 -1 -2 --3-…

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Q: A rocket is fired vertically upward from the ground. The distance in feet that the rocket travels…

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Q: cos 3t dt 5 + 3 sin 3t Ocos 3t

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Q: Find the average value of the function on the given interval. f(x)=x²-7: [0, 1] Set up the integral…

A: Average value of a function f(x) on [a,b] is given by, V=1b-a∫abf(x)dx

Q: If Vf = F, then F is called a potential vector field, and f is called a conservative function. True…

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Q: The area bounded by the parabola x²- 2x+y=3, the y axis and the line y=4 revolves about line y=4.…

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Q: Simplify csc(t) sin(t) - cot(t) to a single trig function with no fractions.

A: csct-sintcott=1-sin2tsintcot(t)=costcottcott=cost

Q: √ √tan tan x dx

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Q: The ellipse + 1 can be drawn with parametric equations where (t) is written in the form 4²2 r(t) = r…

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Q: Find the critical point of the function f(x, y) = x² + y² + xy +7.5x C=

A: To find the critical point of the function fx, y=x2+y2+xy+7.5x.

Q: Verify that Rolle's Theorem can be applied to the function f(x) = x³ - 6x² + 11x − 6 on the interval…

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Q: Use the graph below to fill in each entry of the grid with positive, negative or zero. y = f(x) f''…

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Q: Use a double integral to find the volume of the solid region under the paraboloid z = x² + y² and…

A: Use double integral concept

Q: Q1: A- Write the following algebraic expression in its simplest form: 5x+3x²+5x+6 X *+3 25x²-9

A: Please refer to the image below

Q: Find the volume of the region enclosed by z = 1 - y² and z = y² - 1 for 0 < x < 42. V =

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Q: p(x,y,z)=xz²+sin(y) ex e*

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Q: E = 5 -2 -4 3 2 2 -4 -4 -4 0 -3 2 3 2 4 4 -2

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Q: 2. A cyclist applies a force F with magnitude F = 50N in the same direction as the vector b = 4 j.…

A: We have to find the vectors.

Q: 16+19+22+25+...Which one of the following is the sum of the first 90 terms of this series? a)16,701…

A: Concept: Arithmetic Progression: Arithmetic Progression (AP) is a numerical series in which the…

Q: क्ने Find the curl of F(x, y, 2) = (2x,3y, 52). depends on the point (x, y, z) ● 10 O

A: Let's find curl.

Q: estion 9 s triple integral represents the volume of a cylinder. True False V = f²" f²f³ r dz dr do

A: To evaluate the triple integral.

Q: USING CYLINDRICAL METHOD Find the volume of the solid obtained by rotating about the y-axis the…

A: Given that, Solid obtained by rotating about the y-axis the region bounded by y=2x2 - x3 and y = 0

Q: 1. Find of ахду OF f(x,y) = xy (x+y-1) -x2

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Q: Find the volume of the solid obtained by rotating about the axis the regi and bounded by y=2x²) Y=o…

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Q: 1. y ecos(-2x) =

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Q: Question 16 This equation represents what? O a sphere an ellipsoid O a paraboloid O a double cone x²…

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Q: What is the 6th term of (x - 1)¹0?

A: Given problem:- what is the 6th term of (x-1)10

Q: Convert the Cartesian coordinate (-4,-2) to polar coordinates, 0≤ 0 < 2π r= 2√5 Enter exact value. 0…

A: We need to find polar coordinates.

Q: For the function f(x) = 2x², make a table of slopes of secant lines and make a conjecture about the…

A: Slope= df/dx

Q: Find the equation of the tangent line to right branch of the hyperbola π π x = sect, y = tant, ≤t≤at…

A: Given :x=secty=tant

Q: 1.) a function f f (x,y, 2) = 2-eªsing is given. of this function p= ((n 3, 31,-3) at the point what…

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Q: C. Find the average rate of change of the given functions at the indicated interval. 1. f(x) = x² at…

A: We know that average value of function f(x) on given interval [a,b] is f(b)-f(a)b-a

Q: nd the reference angle, the quadrant of the terminal side, and the sine and cosine of 225°   Enter…

A: Find the reference angle, the quadrant of the terminal side, and the sine and cosine of 225°

Q: Find the volume of the solid of revolution formed by rotating about the x-axis the region bounded by…

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Q: If s(t) 813 122-48t6, where t2 0 represent the position of a particle traveling along a horizontal…

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Q: Use integration by parts to evaluate the integral. [2xe™x dx dx = [2xetx

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Q: Use DeMoivre's theorem to compute (1+i)¹²

A: