Plot the complex number 2 - i√3. Then write the complex number in polar form. You may express the argument in degrees or radians.

Q: Derivatives Find and simplify the derivative of the followingfunctions

A: It is given that, fx=e2x+8x2ex+16x4We have to find the derivatives.  

Q: Find the volume of the described solid S A cap of a sphere with radius r  and height h

A: Given:  A solid S is cap of a sphere with radius r and height h, To find: The volume of the solid.

Q: Derivatives Find the derivatives of the following functions.

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Q: Determine the location of a point (x, y, z) that satisfies the condition xyz > 0

A: In four of the eight octants xyz>0 1) x>0, y<0, z<0 (2) x<0, y>0, z<0 (3) x<...

Q: Find the derivative. Simplify where possible. f(x)  =tanh (1 + e2x)

A: Here given as fx=tanh1+e2x Since  ddxtanhx=sech2x

Q: The pressure in P = 10T/V     of a gas in a cylinder is given by   with T in kelvins (K) and V in m3...

A: Given as : P=10TV By differentiating it with respect to t: dPdt=10VdTdt-TdVdtV2 ......1 1). If T is ...

Q: use an exponential model and a graphing calculatorto estimate the answer in each problem. Suppose th...

A: In any given year the number of cases of a disease is reduced by 20% and there are 10,000 cases toda...

Q: Find the indefinite integral

A: To evaluate: ∫2x+1ex2+xdx Let substitute t=x2+x dtdx=2x+1dt=2x+1dx Substituting the value, ∫2x+1ex2+...

Q: Write a formula for the general term (the nth term) of the arithmetic sequence a1 = 200, d = -20. Do...

A: Formula of nth term is an=a1+(n-1)da1 is the first termd is the common difference

Q: 4. Explain what 42 means, then calculate 42 in two different ways: (42) or (4')

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Q: Calculate the derivative of the following functions

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Q: A colony of bacteria is grown under ideal conditions in a laboratory so that the population increase...

A: Exponential functiony= a bx a is the initial population

Q: Use a calculator to solve the equation cos x = -2/5 correct to four decimal places, on the interval ...

A: Given equation is cosx=-25. Solving the given equation. cosx=-25x=cos-1-25x=113.5781°    

Q: Hello Please answer b,c,d Thanks   Mahboob

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Q: Multiply or divide as indicated.: (x2 - 4)/x ÷ (x + 2)/(x - 2)

A: x2-4x÷x+2x-2

Q: Show that the triangle with vertices A(0, 0), B(1, √3), and C(2, 0) is equilateral.

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Q: A particle is moving with the given data. Find theposition of the particle.   a(t)  =10Sin t + 3Cost...

A: It is given that, a(t)  =10Sin t + 3Cost  ,  s(0)  =0 ,   s(2π) =12 We have to find the position of ...

Q: Find the union of the sets. {1, 2, 3, 4} ∪ {2, 4, 5}

A: In set theory, the union (denoted by ∪) of a collection of sets is the set of all elements in the co...

Q: Use the Leading Coefficient Test to determine the end behavior of the graph of the given polynomial ...

A: Given the function: fx=-x4+1 Given the graphs:

Q: Fill in the blank/s: |x - 7| > 2 can be rewritten without absolute value bars as ...................

A: Given: The inequation x-7>2 To write: The given inequation without absolute bar.

Q: If f(x) =x 3 -x find a formula for  f '(x)

A: Given fx=x3-x

Q: Evaluate the vector-valued function at each given value of t.                         r(t) = (2t + 1...

A:  Definition used -               For evaluating vector-valued function we have to substitute the giv...

Q: Evaluate the expression without using a calculator: log41

A: To evaluate the expression log41.

Q: Q#1 Find: (a) the intervals on which f'is increasing, (b) the intervals on which fis decreasing, (c)...

A:

Q: Use properties of logarithms to expand the logarithmic expression logb(x2y) as much as possible. Whe...

A: logbx2y

Q: Rationalize the denominator: (7 + 4√2) / (2 - 5√2)

A: Given fractions is 7+422-52

Q: Use L’Hôpital’s Rule to evaluate the limit.

A: L'Hospital's Rule states that, The given limit is:

Q: What can you conclude about log2 16, or log2(32/2)?

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Q: Find an equation of the curve that passes through the point (1, −2), and has the given slope y′ = y/...

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Q: The domain of g(x) =3/(x - 2)consists of all real numbers except 2,represented in interval notation ...

A: To Determine: The domain of g(x) interval notation as (- ∞, 2) ∪________. Given: we have a function ...

Q: Use the alternative form of the derivative to find the derivative at x = c, if it exists. f(x) = (x ...

A: Given function is fx=x-623. To find the derivaitve of the function at x=c. Differentiating with resp...

Q: Find derivative of f(x) = (x^3-6)(x+5)

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Q: find the mass and the indicated coordinate of the center of mass of the solid region Q of density ρ ...

A: To find the mass and the indicated coordinates of the center of mass of the solid region Q

Q: Fill in the blank/s : The factors of the first denominator are .............The factors of the secon...

A: x-1x2+x-6-x-2x2+4x+3 Consider the first denominator, x2+x-6=x2+3x-2x-6=xx+3-2x+3=x+3x-2 Consider the...

Q: Find all solutions of the equation 5 sin θ + 1 = 3 sin θ.

A: 5sinθ+1=3sinθ

Q: Use the formula t =ln 2/k that gives the time for a population with a growth rate k to double.The gr...

A: The growth model is given as A=4.3e0.01t. a The New Zealand’s growth rate is, The general form of eq...

Q: Find the derivative of the function. g(x) = 3(4 − 9x)5/6

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Q: Solve this  y" - 7y' + 12y = 0

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Q: Evaluate and simplify y'. 422 + u y 8и + 1

A: Given, y=4u2+u8u+1