Consider the function f(0) = 4 cos(20) + 2, where 0 is in radians. a. What is the amplitude of f? Preview b. What is the period of f? Preview Box 1: Enter your answer as a number (like 5, -3, 2.2172) or as a calculation (like 5/3, 2^3, 5+4) Enter DNE for Does Not Exist, oo for Infinity Box 2: Enter your answer as a number (like 5, -3, 2.2172) or as a calculation (like 5/3, 2^3, 5+4) Enter DNE for Does Not Exist, oo for Infinity Box 3: Enter your answer by drawing on the graph.

Q: |l. Find for and fy for flx,)= cOs (x)) No need to simplihy -/2 fx = cos (xy)- 1x -(-sin (xy)- y. 1x...

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A: Given: - The ordinary differential equation is, y''+2y=sec(x) To solve: - The solution of the given ...

Q: Prove that ∀n ∈Z, gcd(7n + 1, 15n + 2) = 1 *use only the definition of divisibility and gcd please!

A: we want to prove that   gcd(7n+1 , 15n+2)=1

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Q: 33. tan- (z²y) = x + xy°

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Q: (sinh(x)(x² + 7°)] 1. dx d In(x² – 4x + 13) + sin(zx) dx et d? sin? dx2 (sr + v=)|

A: a. ddxsinhxx2+7x=coshxx2+7x+2x+7xlog7sinhx      duv=uv'+vu'b.ddxlnx2-4x+13+sinπxex=1x2-4x+13×2x-4+πc...

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A: Given, P(T,V)=(8.31T)/V At centre V=12litre and T=310k

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

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Q: - fyr. For the function f(x, y) = e²´y sin(xy) show that Clairaut's Theorem holds, that is, fæy

A: Clairut's Theorem : fxy = fyx i.e, ∂2f∂x∂y =∂2f∂y∂x.

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Q: Use substitution to evaluate the integral 4 sec2 4xvtan 4xdx 4 (tan 4x) + C 3 15 (tan 4x) + C 2 (tan...

A: Given query is find the value of the integral.

Q: water heater that has the shape of a right cylindrical tank with a radius of 2 ft and ft is being dr...

A: Given thatRadius of right cylinder,r=2 ft, height ,h=6 ft dhdt=-1 ft/minTo find :dvdtSolution:Volume...

Q: 10. a) What transformation are used to turn the parent function f(x) = x³ into g(x) : -(2³ – 3) +2. ...

A: Given query is to find the transformation applied and then graph the function.

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Q: 8. Let T: R? - R³ be defined by T((a, b)) = (a, a + b, a + 2b). Find range T and a basis for range T...

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Q: 7. Determine the following general antiderivatives. | cos*(x) b. sin(x) xp- 10 10 | sin(x)cos(x)] d....

A: Please see the below picture for detailed solution. 

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A: Explanation of the answer is as follows

Q: Differentiate. sin(0) f(0) 1 + cos(0) f'(0) %3D II

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A: Comparison Test: Let ∑ an, ∑ bn be two positive sequences such that for all n,    an≤ bnIf ∑ bn conv...

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Q: 3. y/" + 6y + 8y 3e-2 + 2x

A: To find out the solution of the given differential equation. 

Q: 8. When solving an absolute value inequality, the fact of whether it is a "greater than/greater than...

A: In this question we have to solve the given question.

Q: V2 e| de 4t

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Q: Subtract and simplify. (3 – 5i) – (-8 + i) (3- 5i) – (- 8+ i) = | (Simplify your answer. Type your a...

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Q: Complete the table. Use the resulting solution points to sketch the graph of the equation. y =-2x + ...

A: NOTE: Refresh your page if you can't see any equations. . the given equation of a line is  now make...

Q: Prove that ∀n ∈ Z, gcd(7n + 1, 15n + 2) = 1.

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Q: 3. Given: r = 3 – 5 sin0 a) Sketch the curve and label 4 polar points. b) Find the slope of the tang...

A: Given polar curve r=3-5sinθSolution :b.x=rcosθ  ,y=rsinθslope of tangent ,dydx=dydθdxdθr=3-5sinθdrdθ...

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Q: Prove that there exists exactly one prime of the form n^3 −1. First express the statement symbolica...

A: Number

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Q: Simplify. 3 3+7 i

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Q: -3xdx 8. S: 2x+1

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Q: A particular country's exports of goods are increasing exponentially. The value of the exports, t ye...

A: V(t) =1.6 e0.039ta)   substitute t=0 for 2006     V(0) =1.6e0= 1.6      Value of country's export in...

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Q: A. Each week, Adriel buys cheese (C) and sausage (S) which provides him a utility of U= 6th root of ...

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Q: nd the area of the circular sector given a central angle of and a radius of 3 inch

A: θ = π5r =3

Q: Evaluate the iterated integral. SL" z dzdydz O 1 O 1/10 O 10

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A: Here is the solution

Q: 5. Find the arc length made by a central angle of radians and a radius of 10 cm.

A: Given central angle=π4 radius=10cm find arc length  

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Q: Direction: Evaluate the following indeterminate function. Once simplified draw the graph and checked...

A: Here is the solution of the given problem.  Limit evaluation at a given points x=16  Verification by...