Consider the following planes. 3x + 4y – z - 56 x - 8y + 2z = 0 (a) Find the angle between the two planes. (Round your answer to two decimal places.)

Q: r=1+ 3sino

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Q: For neN simplty 2-글 + 4-1 +8-금+16-습+. + +2"-그 2n

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A: Aec length of the given curveL=∫131+dxdy2dy    Considerx=16y3+12y-1thendxdy=(16×3y2)+-12y2…

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Q: Use the Babylonian's formula to calculate the circumference of a circle with diameter of 30 units.

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A: Given; y=x^2 between x=1 to x=2

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Q: 27. | (u + 2)(u - 3) du 2+x 29.

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Q: Determine the area of the region enclosed by y=x^2 and y=x^1/2

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Q: Evaluate the limit using L'Hospital's rule: Lim0+1 In(x+1) 2xe"

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Q: Use Theorem 13.9 to find the directional derivative of the function at P in the direction to PQ

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Q: |r'(t) × r"(t)|| ||r(t)||° Use the formula k(t) = to find k(t). r(t) = 7 cos(4t)i+7 sin(4t)j + 5tk

A: Given problem:-

Q: Use a triple integral to find the volume of the solid. The solid bounded by the surface y = x' and…

A: Solution:

Q: A tank originally contains 100 gal of fresh water. Then water containing - Ib of salt per gallon is…

A: Given , A tank originally contains 100 gal of fresh water. Then water containing (1/2) lb of salt…

Q: (xy)=efr sin), Plo,0l Q(5,1)

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Q: Determine the derivative of у. /20x+6 y = ev y =

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Q: Find the conservative vector field for the potential function by finding its gradient. f(x, y, z) =…

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Q: Evaluate the integral by choosing a convenient order of integration: x cos(xy) cos' (Tx) dA; R 0, x…

A: Given

Q: Write a definite integral that represents the area of the region. (Do not evaluate the integral.) Y1…

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Q: r2 cose dr de valuate the iterated integrals A) 1

A: ∫0π∫01-sinθr2cosθdrdθ

Q: Determine the area of the region bounded by y=2x^2+10 and y = 4x+16

A: To find the area of the region bounded by the given curves.

Q: (c) Sketch a graph of the path, and sketch the velocity and acceleration vectors at the given point.…

A: When a particle move on a circular path , the direction of velocity of the particle along the…

Q: Sketch the region enclosed by the curves and find its area. y = cos 4.x, y = 0, x 8' 4 NOTE: Enter…

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Q: Find an equation of the plane with the given characteristics. The plane passes through the points…

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Q: Evaluate the line integral along the path C given by x = 2t, y = 6t, where 0 sts 1.

A: The given integral is ∫c(x+3y2)dy   and the curve C is x=2t,  y= 6t   where 0≤t≤1 Now, y=6t⇒dy =…

Q: Find the surface area of that portion of the surface Z = 4 -x that lies above the rectangle R in the…

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Q: Find the volume of the solid that results when the region enclosed by the given curves is revolved…

A: This question can be solved using the concept of volume of solid of revolution.

Q: n-1 1. b) Determine whether the series is convergent or divergent. If it's convergent, 4" n=1 find…

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Q: Use the gradient to find the directional derivative of the function at P in the direction of PQ.…

A: Directional derivative: D f = del f • unit vector of direction

Q: Express the iterated integral as an equivalent integral with the order of integration reversed.…

A: Express the iterated integral as an equivalent integral with the order of integration reversed.

Q: Find the principal unit normal vector to the curve at the specified value of the parameter. r(t) =…

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Q: Find the volume of the solid that results when the shaded region is 8 revolved about the indicated…

A: Volume of revolution

Q: Use a triple integral to find the volume of the solid in the firsy octant bounded by the coordinate…

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Q: n? +1 2. Determine whether the series is convergent or divergent. If it's 2n² +1 n=1 convergent,…

A: The given series,        ∑n=1∞n2+12n2+1

Q: 1-sine Evaluate the iterated integrals J. J. r2 cose dr de A) 1 B 2 c) o D) 3

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Q: (x + 1) f' (x) = f(1) = 5 x,

A: Solution is given below:

Q: Where is each function continuous? (a) f(x) = Vi %3D

A: According to the company rule we can answer only first question and rest can be reposted.

Q: V4-y? cv8-x²-y² Use cylindrical or spherical coordinates to evaluate the integral. JoJ Vx?+y? A 32…

A: To find the value of the given integral.

Q: Find V. (V × F), if F(x, y, z) = e²i+ 3xe"j – 7ev*k. - V · (V × F)

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Q: first octant 2 4- x+y dy dx -

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Q: (1 point) Use the Divergence Theorem to calculate the flux of the vector fields F, = -Szi + 5xk and…

A: Find your answer below

Q: Represent the line segment from P to Q by a vector-valued function. (P corresponds to t = 0. Q…

A: Given

Q: 27х3-8а3 y3= y= 3x-2a Зх-2а

A: Y'=?

Q: Find div F and curl F if F(x, y, z) = 13y*z'i – 11a'2®j – 5xy*k. div F= curl F=

A: We can solve as follows

Q: for the given path. C: x = 2 cos(8), y = sin(@), o se s 27

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Q: Evaluate the definite integral. (9ti + 3+j + Vik) dt 9ti + 3tj tk dt

A: Topic = Integration

Q: Find the area of the surface that is generated by revolving the portion of the curve y= X between x=…

A: We can solve as follows