Use cylindrical coordinates. Find the volume of the solid that lies within both the cylinder x² + y² = 25 and the sphere x² + y² + z² = 100.

Q: Determine the Cartesian equation of a plane that passes through a point (2,1,-5) and perpendicular…

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Q: 2 IF □ is defined by ▼ ах functions and A&B are differentiable Show that • (A+B) = √•A + V•B. = it 2…

A: Please see the below picture for detailed solution.

Q: Part 2. Find the Standard Equation 4. parabola with vertex at (5,4) and focus at (-3,4)

A: If the focus and the vertex has same y-coordinate then the equation of a parabola can be given as…

Q: 23 In the graph below, determine whether the given walk is a trail, a path, or a circuit. VI V5 V2…

A: We have to determine the path of given walk.

Q: The interest on an account increases exponentially. If an initial investment of $4000 earns $1300 in…

A: Given the interest increases exponentially. The investment is $4000 and the interest in 3 years is…

Q: 03: Evaluate the following integrals: dx (4) √√√²+4x+4

A: Solve the integration

Q: ᴛʜᴇ ᴅɪᴀɢʀᴀᴍ ʙᴇʟᴏᴡ ʀᴇᴘʀᴇꜱᴇɴᴛ ᴛʜᴇ ʀᴏᴏꜰ ᴏꜰ ᴛʜᴇ ʙʀᴏᴡɴ'ꜱ ꜰᴀᴍɪʟʏ'ꜱ ꜰᴀᴍʜᴏᴜꜱᴇ. ᴀʟʟ ʀᴀɪɴ ᴡᴀᴛᴇʀꜰʟᴏᴡꜱ ꜰʀᴏᴍ ᴛʜᴇ…

A: We have to find the total area.

Q: 10. Let w = f(z) = Find f(1 - i) 1+z 1-z A. 1 - 2i B. −1+2i C. -1-2i D. none of the above

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Q: 5) a) Find the eccentricity, b) identify the conic, c) give an equation of the directrix & d) Sketch…

A: Concept: We know that a conic section is defined as the locus of a point that moves in such a way…

Q: 1. Given a. b. C. [(5x + + + + 1) dx Evaluate the indefinite integral above Evaluate the integral…

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Q: 04: Find dy/dx for the following function:: (5) y = x³ log₂ (3 - 2x)

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Q: ■ Find equation of plane which is containing Points A(2,1,1) and B(7,5,2) and normal to 2 x - 3y -…

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Q: 4) Find the value of a for which the limit lim x-0 evaluate the limit. sin(ax)-sinx-x. x3 is finite…

A: find limit

Q: sec ( =) af Given f = e - yt+y, find dy sec 21 ____=_=(4) tam(3) ²(3) __g²¹3-¹ (z+y+yn (y)] xe sec…

A: see below the answer and calculation

Q: Write the logarithmic equation y = log5x² in exponential form.

A: We are authorised to solve only one question please repost remaining questions Logarithm

Q: 5. y = log(7x + 3). 4²x¹+8

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Q: 12. The modulus of elasticity of the spring is given as 270,000 N/m. find the work done in…

A: k=270000 N/ma = 0b = 1 mm = 0.001 m

Q: coplanar.

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Q: Find each function value and limit. Use - ∞o or ∞o where appropriate. 7x+2 f(x) = 2x-2 (A) f(10) (B)…

A: Solve the following

Q: Evaluate the following integrals C. [x√x + 1dx

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Q: Sir Lancelot 40 TO 54° X = Sir Robin 1000 4x-12 X= 26° Sir Galahad C X= Sir Bedivere 16 16 9 2x + 34…

A: Concept: Secant and tangent: A secant line connects two or more curve points.A tangent line only…

Q: Q2/A/ Prove cot² @ csc 0+1 + 1 = csc0 B/Find the value of c if f(x) is a continuous function at x =…

A: To prove the given trigonometric equation and  To find value of c for which function is continuous…

Q: 3 Find the area between the curve of X = and the y-axis on the interval [2, 5]. 2.749 3.296 4.159…

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Q: -if y=x² the dy dx

A: Finding dy/dx

Q: 2x² +9 x4 + 10x² + 25 dx

A: given

Q: A conical vessel 12m across the top and 15m deep. If it contains water to a depth of 10m, find the…

A: Concept: Similar triangles are those which are of the same shape but need not be of the same size…

Q: Calculates the JR f(x,y)dA bounded by the given region I Loyan dA where the region S is given by the…

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Q: Find 2 2 [²³²³ (5x + 2y) dxdy

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Q: Find the first derivative of sin x y = In 1+2 In x x cot x-2(In x) cot x-2 x(1+2 In x) x cotx+2(In…

A: Since you have asked multiple questions in a single request we would be answering only the first…

Q: O cos y (cos x + 1)

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Q: Homework) read the following mathematical steps of finding sum of series. Σ 2n = 1+2+4+8+16+ ....…

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Q: Find a, b, c, and d such that the cubic function f(x) = ax3 + bx2 + cx + d satisfies the given…

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Q: Find the critical points of the function f(x) = 2x3 + 3x2 − 12x + 5.

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Q: For the curve f(x) = 2-5x +4x², the slope of the tangent is -5 + 8a at the general point where x =…

A: This question is related to tangent to the curve, we will solve it using given information.

Q: Q2-Solve the differential equation dy = - y xcos² (-) dx

A: I am attaching image so that you understand each and every step.

Q: 14 Approximate (x²-6) dx using 4 rectangles. 2 It is approximatley (If necessary, round to two…

A: Please follow the next step.

Q: 11. A plate in the form of a parabolic segment of base 12 m and height of 4 m is submerged in water…

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Q: Find the general solutions of the system. 601 x' = 08 8 -4 x 01 4 x(t)=

A: The given system,x'=60108-4014x

Q: where does the function 1/sin(x) not exist? what happens if we try to calculate any of these values?

A: We have to find the values where function values doesn't exist.

Q: )

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Q: Give the domain and range of the graph shown to the right. Then, use the graph to answer parts (a)…

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Q: .suppose that the virus was accidentally released on the open fields.it was found out that there are…

A: Given:  there are thirty persons gets infected by the virus every two second.           i.e. 2…

Q: 3. fsin (3x) cos(x + 1)dx

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Q: A loan, amortized over 10 years, is repaid by making payments of $1,000 at the end of every month.…

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Q: (I) Find the critical points of the function f(x) = x + x² + 1

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Q: The demand function for a product is given by P(x) = 80 -0.018x, where x is the number of units of…

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Q: Find dy/dx for the following function: (3) y = √tan x

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Q: Find the area of the region bounded to the right by x = y + 3 and to the left by x = y² + 2y + 1. K…

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Q: dx 6) Stanh-¹ (in √x) x (1 - in ² √ x

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Q: Evaluate the integral. 5 0 √ x² + 25 dx

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