Use polar coordinates to find the volume of the given solid. Above the cone z = (x2+y2)1/2 and below the sphere x2 + y2 + z2 = 25

Q: A common inhabitant of human intestines is the bacterium Escherichia coli. A cell of this bacterium ...

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Q: Find dy/dx if x^3y^2+2xy=x^3

A: Solving the problem by finding the dy/dx of the given expression.

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Q: Use vectors to find the lengths of the diagonals of the parallelogram that has i + j and i – 10j as ...

A: Here we will find the magnitudes of both diagonals,

Q: A solution composed of 50% ethanol (EŁOH), 10% methanol (MEOH), and 40% water (H2O) is fed at the ra...

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Q: G(t), of the function g(t) = (2n?t? - t)V2n2 – t?. %3D

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Q: Vx – x The lim x→1 In x

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Q: Find the vector component of v = (4, - 1, 7) along b = (3, 6, -6) and the vector component of v orth...

A: This question is based on Use of Dot product and cross product.

Q: Find the volume generated by revolving bout the line x -1 the area bounded by (y + 2) = 4(x + 2) and...

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Q: xy' + y = 0, y(4) = 6 %3D

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Q: 1. From the graph, determine the function f (x) is continuous at x = -1. f(x) 3 %3D %3D -5 -4 -3 1 -...

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Q: Evaluate the integral using the following values. 8. x³ dx = 960, 8. 8. x dx = 24, = xp — Зх dx 14

A: ∫48-3x dx=-3∫48x dx Using the given data,  ∫48x dx=24 ∫48-3x dx=-324

Q: d²y y = f(x) and x = e', prove that = xf'(x) +x²f"(x). %3D %3D dx2

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Q: Find the volume of the solid generated by revolving the area bounded by x2 – 2kx – 4ky + k² = 0 and ...

A: Given curves are:  x2-2kx-4ky+k2=0 4x-4y+k=0 The area bounded by them is revolving about the line x=...

Q: A police car is located 30 feet to the side of a straight road. A red car is driving along the road ...

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Q: A rock is thrown into a still pond. The circular ripples move outward from the point of impact of th...

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Q: Find the vectors that satisfy the stated conditions. NOTE: Enter the exact answers using the provide...

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Q: Evaluate f(cos* x – sin“ x)dx

A: To evaluate the given integral.

Q: 11. A gate in an irrigation canal is constructed in the form of a trapezoid 3 ft wide at the bottom,...

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Q: A cookie jar contains 10 cookies - 4 are chocolate chip, 3 are almond, 2 are oatmeal and 1 is a high...

A: Answer -  Total cookies = 10  Chocolate chips = 4 almond = 3 oatmeal = 2  high fibre cookie = 1

Q: Find the vector component of v = (4, – 1, 7) along b = (2, 3, –6) and the vector component of v orth...

A: This is a problem related to vector. Based on the general formula vector we will solve the question.

Q: f) {1,0,–1,1,0, –1,1,0,...}

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Q: A solution composed of 50% ethanol (EtOH), 10% methanol (MEOH), and 40% water (H2O) is fed at the ra...

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Q: 1. Fill in the following blanks for this function: y = - 4 cos 2x - 5 a)amplitude b) reflection c) p...

A: Given query is to find the Indicated points of the function.

Q: (y- 2xy +6x ) dx-(x – 2xy + 2) dy = 0

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Q: Consider the fünction: f(x) = 5x + 15x² - 5x- 3 %3D Step 1 of 2: Determine the intervals on which th...

A: Concave up if f"(x)>0 Concave down if f"(x)<0

Q: 3 cos xy? O f(x,y)= Zsinxy Find fx fy and

A: On solving this we will get:-

Q: Hew-2 Verify that Wxy Wyx fer the functions's T- R(Xsy) = Lu (2X +34) f cxッy) é^+x Luy +y Lnx 2-

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Q: Find the area of the region bounded by the curves, y = -6, y = 6, the y - axis and the parabola y – ...

A: Find your answer below 

Q: Cami plays softball. The table to the right shows the frequency of the number of hits she has per ga...

A: a)  D. Divide the frequency of two hits by the total. Probability = 1153 b) A. P(at most two hits) =...

Q: x² + ax + 2bx + 2ab + 2x² – ax² + 6bx² dx x* + ax² + 2bx² + 2abx²

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Q: Evaluate the following limits. 1. lim(1+ Vw)(2–- w² + 3w*) w+1 12 - 1

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

Q: The base of a solid is the region in the first quadrant bounded by the graph of y = sin xand the x-a...

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Q: Use the given graph of f over the interval (0, 6) to find the following. y -1 1 (a) The open interva...

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Q: Plot each of the given complex numbers in an Argand diagram and label all the necessary parts. Also,...

A: Since there are multiple questions the first question is answered as per our guidelines. Kindly repo...

Q: Question 3. The parametrized curve x = cos(t) – 5sin(t), %3D 101 y = -10cos(t)+ sin(t) is an ellipse...

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Q: 12 TT CoS + i sin + i sin 6.

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

Q: If L is a line in 2-space or 3-space that passes through the points A and B, then the distance from ...

A: This question can be solved as per the instruction given.

Q: since dv=adt the v-t graph is determined by differentiating the straight line segment of the a-t gra...

A: Explanation of the answer is as follows

Q: arbitrary

A: We have to eliminate the arbitrary constants from the given  function

Q: In considering normal and tangential components, the t axis is tangent to the curve at the point tha...

A: True. When a particle moves along a curved path, it is sometimes convenient to describe its motion u...

Q: tind the deatNe of 2メー3 うメース the definition - ensing

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Q: 3. a) Find polar coordinates (r, 0) of the point (1, -/3), where r> 0 and 0 <0 < 2 p2 = x² + y?, tan...

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Q: Find the vectors that satisfy the stated conditions. NOTE: Enter the exact answers using the provide...

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Q: Find the area of the triangle with vertices P(1, 4, –4), Q(0,0,0) and R(4,6, 1). NOTE: Enter the exa...

A: We know that; The expression for the area of the triangle △PQR is; A=12PQ→×PR→   The given vertices ...

Q: Find the derivative of the function. 6z 12 - 5 u² – u?+5du g(r) = 32

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Q: a man who is standing 5 meters above a shoreline is pulling up a boat that is 12 meters away from th...

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Q: 2. Find the derivative of y = (5x³ + 2 x)tanx. %3D

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Q: ( a) Σ-1"+1, 2η+2 Vn3 + n2 + n n=1 ,2η n2n (b) en3 n=1

A: Given

Q: (8. e Sin y Ausi Sin 2

A: Solution is written in below steps.