Consider the polar equation defined by r= 5 cos(2 sin 6), where 0<0< 2x. Determine the missing values of r in the table below. Round off your answers to two decimal places. Sr (approx.) (A) (D 0.78 (B) (C) --0.80 2.70 3 Il (appren.) (E) -2.08 (G) (H) 2.70 0.78 (F) -0.50

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A: we know that  The deck has cards in two colours red and black

Q: dæ is equivalent to Using the substitution u = x + 1 Vx + 1 1 -du 1/2 du du -1/2 du - 1) /u2

A:

Q: (4) Evaluate S SR e™y-2dA where R is the region enclosed by y = 4x, y = }, y = ± and y = 1.

A: Let's find.

Q: 4- The number of element in the sample space when you flip 3 coins together c) 6 d) 12

A: We can solve this as follows:

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Q: dy Use an appropriate technique to find dx from x? + y? = (2x² + 2y² – x)*.

A: We can solve this as follows:

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A:

Q: 00 n³n² COS 5n³ +3, 1

A: See the answer below

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A:

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A: This question can be solved using the concept of area bounded by two curves.

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A: Given : Sixth derivative of a sixth degree polynomial is a line. To find: State whether the above…

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A: Explained below

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A:

Q: Radioactive Carbon-14 The percentage Pof radioactive carbon- 14 remaining in a fossil after t years…

A: Note: As P and b for the first question are not given in the data provided by you. Solved the second…

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A:

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A: we have to find area.

Q: Sketch the graph the integrands and use areas to evaluate the integrals. 1. L'lx| dx Sketch the…

A: The graph is shown below, where the shaded region represents the area.

Q: Find the area of the surface generated by revolving the given curve about the y-axis. 8ry 2y+1,…

A:

Q: Xt v X + l x t ...

A:

Q: Q(x) = Jx + Vx + Vx + ·…

A:

Q: Let f(x) = 1, for all x E (0,1). Is f continuous on (0, 1)? Is f uniformly continuous on (0, 1)?…

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Q: An iron block weighs 5.2 N and has a volume of 272 cm³. What is the density of the block in kilogra…

A:

Q: Select all of the following tables which represent y as a function of x. y -2 -1 -2 -5 -1 2 1 2 1 1…

A:

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A: Domain of a function y=f(x) is the set of values of x for which f(x) is defined Range of a function…

Q: 1- P is equal : a) 1 b) 120 c) 5 2- C is equal : a) 455 b) 544 c) 4542.

A:

Q: Given the three vectors å ,b and ở in 3D. The following question is t termine if operation involving…

A: We can solve this as follows:

Q: ||r'(t) × r"(t)|| ||r(t)||* Use the formula k(t) to find k(t). 13 r(t) = t'i+5j 390 t14 K(t) = %| (4…

A:

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A:

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A: To find which discontinuity is at x=4.

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A:

Q: 4. Find the arc length of r = cos? (0/2), 0 s 0 s 2n.

A:

Q: The general solution of the D.E.  ( x + y)dx + (x-y)dy = 0.

A:

Q: 2. Find all the derivatives of f, given f(x) = x8 – 5x7 + 4x6 – nx* + 3x3 + 11.

A:

Q: Find all the derivatives of f, given f(x) = x8 – 5x7 + 4x6 – nx* + 3x³ + 11.

A:

Q: Without eliminating the parameter t, find a Cartesian equation for the line tangent to the curve C,…

A: Let's find.

Q: dr

A: To find integration.

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A: We need to find equation of tangent

Q: Next, simplify. - 3t dt = dx

A:

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A:

Q: y² = csc*5x cot°sx aS C

A: Here, the given function is: y2=csc25x cot25x⇒y=±csc 5x cot 5x...(1)

Q: 16) Rewrite the integral 10 3(1 – z/10) 7(1 – y/3 – z/10) dx dy dz in the order dz dy dx.

A: To rewrite the integral ∫010∫031-z10∫071-y3-z10 dx dy dz in the order dz dy dx

Q: j. r (0)=tanh (cas o)+ cos h (e)

A:

Q: 1. Use mathematical induction to prove the given statements below. 2 3+2 32+....+ 2· 3n-1 = 3" – 3…

A:

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A:

Q: Sketch the graph the integrands and use areas to evaluate the integrals. | Ix| dx -2

A: Follow the procedure given below.

Q: Use power series to show that sinh(z) + cosh(x)= e".

A:

Q: B: .A card is drawn from a well shuffled pack of 52 cards. Find the probability of: (iv) a card of…

A: Given that a card is drawn from a well-shuffled pack of 52 cards To find the probability of (iv) a…

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A:

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Q: B: .A card is drawn from a well shuffled pack of (iv) a card of diamond (v) a king or a queen

A: