Given a curve r(t) = < sin(7t), cos(7t), 3t >. Find the arc length for 4 < t < 7. Give your answer correct to two decimal places.

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A: Note: Since multiple questions are asked, I am answering the first question.please repost other ques...

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A: This question is based on solution of Homogeneous differential equation.

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A: Follow the procedure given below.

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A: Topic:- derivatives

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A:  we have to integrate the given integration 

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Q: 8. The differential equation (2x-xy-2y+3}dx-(x*y+2xkty = 0 is exact because ÔM ON

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Q: Find the interval of convergence of (-1)"(x – 4)" Σ Vn2 + 10 n=0 (Use symbolic notation and fraction...

A: Here,          an=limn→∞-1n+1x-4n+1n+12+10-1nx-4nn2+10   =limn→∞ -x-4n2+10n2+2n+11   =limn→∞ x-4n2+1...

Q: 4. Homogeneous Differential Equation: (r+2ry –4y' dx-(r² -&ry-4y'dy =0 x=2; Use the substitution y- ...

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Q: ded. Give your answers as intervals in the form (*, *). Use symbol iate type of parenthesis " (", ")...

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Q: Q11

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Q: Find the differential equation of the family of circles with fixed radius, r=a+b,and tangent to the ...

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

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Q: Please show your answers to at least 4 decimal places. Suppose that f(x, y) = x°y. The directional d...

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Q: Solve the given differential equation (3x+y- 2) da + (x +y + 4) dy = 0 O 3(x – 3)2 + 4 (2 - 3) (y + ...

A: Given differential equation, (3x+y-2)dx+(x+y+4)dy=0 So, dydx=(2-3x-y)(x+y+4)....(A)

Q: solve for t. SC

A: Follow the procedure given below.

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A: Finding dy/dx

Q: Direction: Read and understand the statement before answer. Click "TRUE" if the statement is correct...

A: ## we want to find out that the given statement is true or false.. The statement is as follows: * If...

Q: 4. Homogeneous Diffe rential Equation: (r* + 2.xy – 4y° kx-(x²-8ry-4y dy 0 Use the substitution y = ...

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Q: Findi Fx, fox, frg, for Fag fox F(X ) = Eai () %3D

A: We find out the partial derivative of given function.

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Q: 4л — 6, 2 <г -

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Q: Separation of Variable s: x(y+1)dx + dy = 0

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A: Here, the given equation is: log4(5)+log4(a) Note that: logpx+logpy=logp(xy)...(1)

Q: If y = x/T, then y' – 1/*. Select one: O True False

A: Given - y = x/π  To show :- y' = 1/π    

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Q: Instruction: Determine if f is continuous at x = c. Also, determine if f is differentiable at x = c....

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Q: Find the general solution to the differential equation. y' = 2t   t2 + 64 y =

A: Follow the procedure given below.

Q: 26.The derivative of a sum is the sum of the derivatives. AEalse. B.True

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Q: *- 2- 2 - - 2 = 0 dx dx

A: The solution is given below-

Q: Tori is draining her pool for winter. After the pool had started draining, Tori began to wonder how ...

A: To find out the equation d-1(y).