Verify the identity: 1/csc 2x = (2 tan x)/(1 + tan2 x)

Q: Find the magnitude and direction (in degrees) of the vector, assuming 0 ≤ θ < 360. (Round the dir...

A: Answer is  Magnitude is= 10 and Angle = 53.13°

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Q: Find the second degree polynomial with the following characteristics: P(0)=4, P'(2)=10, P"(17)=6

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Q: Let f be a differentiable function defined on (−∞, ∞). a) Show that if f is even, then f ' is odd. H...

A: Part(a):   Let fx is even function then,f-x=fxNow differentiating this:ddxf-x=ddxfxf'-xddx-x=f'xddxx...

Q: Consider the following rational function: 4(x- 1)(x+2) _ 4x² +4x-8 qlx)= 2(x+ 1)(x- 3) 2x² – 4x-6 Fi...

A: We have given rational function  qx=4x-1x+22x+1x-3 We have to find domain, x-intercepts, y-intercept...

Q: Sketch the graphs of y = x and y = tan x.

A: Given y=x and y = tanx

Q: Question 10. Find the angle between the curve r(t) = (t, sint, cos t), and the curve y + z2 = 1, x =...

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Q: Find the area of a triangle bounded by the y axis, f(x) = 6- 4/7x, and the line perpendicular to f (...

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Q: y = V16 - x2 y 3 2 -4 -2 2 4 -1F

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Q: Suppose the two-variable equation y = 800 + 10x models the cost y of manufacturing x flash drives. I...

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Q: Use logarithmic differentiation to find the derivative of the function. y = x6 cos(x)

A: We have,

Q: Integration by parts, please help

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Q: 13.7    3

A: The given equation x2+y2=13f=x2+y2-13 Gradient f = 2xi+2yj The unit vector normal to the XY plane is...

Q: Draw the polar region {(r, θ): 1 ≤ r ≤ 2, 0 ≤ θ ≤ π/2}. Why is it called a polar rectangle?

A: Concept: The calculus helps in understanding the changes between values that are related by a functi...

Q: Equation of the plane that passes through the point (8, -6, 4) and contains the line of the given eq...

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Q: Please enclose the answers in order

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Q: Sketch the graph of the function. y = −sin 2x/3

A: If y=Asin(Bx-C)+D Amplitude = A Period = 2πB Phase shift =-CB Vertical shift = D

Q: Determine whether the infinite geometric series converges or diverges. If it converges, find its sum...

A: The given expression is, ∑k=1∞14×9k-1 The given expression can be rewritten as, ∑k=1∞14×9k-1=∑k=1∞14...

Q: 3. Find parametric equations and symmetric equations for the line through the point (2, -1, 1) and p...

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Q: f(0) = sin (0), g(0) = cos (0). Find the exact value of the function f(-0) if 0 = 60°. Do not use a ...

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Q: Consider the following function. f(x) = { 3x + 1,     x ≤ −1 x2 − 3,     x > −1 (a) Find ...

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Q: Name the quadrant in which the angle 0 lies. sin 0 > 0, tan 0 > 0

A: Given that sinθ >0tanθ >0 Therefore the angle θ lies in first (1st) quadrant.

Q: Suppose the demand function for a product is given by p =  1 3  ln   5,000 − q q...

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Q: I need help with number two, thank you!

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Q: step by step how to apply l hospitals rule

A: Answer is e^3.

Q: A 13-g sample of radioactive iodine decays in such a way that the mass remaining after t days is giv...

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Q: Implicit differentiation Carry out the following steps.a. Use implicit differentiation to finddy/dx....

A: a.. The given equation is x3+y43=2. Differentiate the both sides of the above equation as follows.  

Q: What is the functional form of the particular solution y"+ 4 +4y = te-24 OY = (At? + Bt +C) e-* OY =...

A: Given: We have the 2nd order non-homogeneous linear differential equation: y''+4y'+4y=t2e-2t...........

Q: 6.y″ − 2y′ − 2y = 0

A: the given differential equation is: y''-2y'-2y=0 the above differential equation can be written as: ...

Q: f(t)=ln(ln(6t))+ln(ln2) f′(t)=

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Q: Question 2 What is the functional form of the particular solution V +y = sin(2t) + sin t Oy- At sin(...

A: consider the equation    y2+y=sin2t+sint    

Q: let logb 2 = A and logb 3 = C. Write the expression in terms of A and C, logb 3/2

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Q: The angles in each of two triangles are in G.P. The least angle of one of them is three times the le...

A: Given: Consider two triangles are△ABC and △abc The angles in each of the two triangles are in G.P. A...

Q: The population of a town increased by 2.47% per year from the beginning of 2000 to the beginning of ...

A: 1) The population at the beginning of 2000 = 74,540 Rate = 2.47% Growth factor = r = 0.0247    

Q: Calculus Question

A: Given integral is, ∫014114-xdx Integrate the above expression to get, ∫014114-xdx=∫01414-x-12dx=14-x...

Q: Determine whether the lines intersect, and if so, find the point of intersection and the cosine of t...

A: The two lines namely as L1 and L2. L1 : x-03=y-2-1=z+11L2: x-14=y+21=z+3-3 The slope of line L1 is (...

Q: Air pressure at sea level is 30 inches of mercury. At an altitude of h feet above sea level, the air...

A: Hey, since there are multiple subparts posted, we will answer the first 2 question. If you want any ...

Q: Determine the l-unit growth factor for g.

A: Given Data: g1=229.5g2=344.25g3=516.375g5=1161.84375   (i) The 1 unit growth factor of g is, R=g2g1 ...

Q: Find the maximum rate of change of the function f(x,y) = sin (xy) at the point (4,0) and the directi...

A: The given function is f(x,y)=sin (xy) and the point is (4,0)=(a, b). to find : Maximum rate of chang...

Q: I need help

A: Given data: *The cost of the sunglass is $8. The cost required to buy 12 sunglass is given by: C=12×...

Q: The profit from the sale of x units is P(x)=30x−200−x2a) How many units do they need to sell in orde...

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