6) Use the Binomial Expansion Theorem to determine the sixth term in the expansion of (x + 3y)8

Q: A volume is described as follows: 1. the base is the region bounded by = y² + 14y-5 and x = y² - 26y…

A: Given: x = -y^2 + 14 y - 5 x = y^2 - 26 y + 177

Q: Find the scalar equation of the plane that contains the points A(0, 4, -1), B(6, 2, 5) and C(3, -1,…

A:

Q: Find the distance from the plane 6x+y+7z=54 to the plane 6x+y+7z=30 The distance is d= (Type an…

A: given planes are 6x+y+7z=54 and 6x+y+7z=30

Q: Let ux² then dx = du 2x and so 2 2 du S ƒ ze²³d² = ƒ re² de S xe dr xe" 2x 0 0 1 S = (²-1) e" du

A:

Q: Determine a definite integral that represents the area of the region enclosed by one petal of r = 4…

A: We have,      r = 4 sin (3θ)       a = 0

Q: f(t) = t sin(at) 14. f(t) nat

A:

Q: 5. The velocity function (in meters per second) is given for a particle moving along a line. Find a)…

A:

Q: Determine the derivative of the following exponential function d. f(x)= 10* (sin sin x)

A: We have to find the derivatives of the function.

Q: Determine the marginal profit for the sale of 500 units of the product if the cost function for…

A:

Q: A dynamite blast blows a heavy rock straight up from the ground." Height = 0 when time=0" The…

A: Vt=160-32t

Q: Given: (x is number of items) Demand function: d(x) = 352.8 -0.2x² Supply function: s(x) = 0.6x²…

A:

Q: Find the volume of the solid obtained by rotating the region in the first quadrant bounded by the…

A:

Q: Let f(x) = X 3x + 1 and g(x)=√1-x.

A:

Q: A bucket begins holding 15 kgs of sand. The bucket is to be lifted to the top of a 20 meter tall…

A:

Q: Find the volume of the solid obtained by rotating the region bounded by the given curves about the…

A: We know that the volume formula int_a^b pi (f(x))^2 dx

Q: 1a Differentiate the following functions with respect to t and simplify your answer as far as…

A:

Q: Solve the given differential equation by separation of variables. (ex + 1)²e-y dx + (ex + 1)¹e-x dy…

A: We need to solve (e^y+1)^2 e^(-y)dx+(e^x+1)^4 e^(-x) dy=0.

Q: Question 4 Given that v = (0, -2) and w=(5, -8), what is w - v? A B C D (-5, -6) (-5, 6) (5,6)…

A: v =<0,-2> w = <5,-8> We have to find w-v

Q: 3. Which of the following statements are TRUE about how y=-4 arcsin 3 I. Vertical stretch of 4 II.…

A: Given a transformed trigonometric function, we need to write down the transformations.

Q: x cos(x) dx?

A: ∫xcosxdx

Q: 14x^2-13x-12 using box method

A:

Q: 2. fx. sin³3x dx

A:

Q: If f is a differentiable function and f'(x)=x4 point at =x²+2x³ - 15x²2, then f has an inflection 3

A:

Q: Find the limit. lim (x,y) → (9, 9) 3 3,,2 (x²√³ - x³y²2) -

A: Apply L'hospital rule in limit

Q: 3. Find the local extrema of the given function z(x,y)= x³ - 8y³ -12xy + 18

A:

Q: Consider the table below for lim (f (h)). Step 2 of 2: Find lim (f (h)). h-673" h 672.5 672.9 672.99…

A:

Q: Determine a definite integral that represents the arc length of = 2 cos(8), 0 ≤ 0 ≤ H2 2 do

A:

Q: x^2 - xy + y^2 = 3, find y'' Step by step solutions.

A: Given: x2-xy+y2=3 To find y''.

Q: Solve the given differential equation by separation of variables. 1 y In(x) dx = (v + ¹)² dy x³ln(x)…

A:

Q: -4x - 4, f(x) ) = { x ² + 2x - ²1₁ 1, x < -1 x ≥ −1

A:

Q: a. For the function and point below, find f'(a). b. Determine an equation of the line tangent to the…

A: f(x)=-9x2.

Q: Perform the indicated integration using RATIONALIZING SUBSTITUTION 3 dy 4 + ³√y+1 1.f.

A: Since you have posted multiple questions i can do first question as per our company guidelines…

Q: Solve the given equation 3e*+2 = 75

A:

Q: 2. Consider the function: a) Determine the derivative. y = 2sinx b) Calculate the exact value of x…

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Q: Check that the point (−1, 1, 3) lies on the given surface. Then, viewing the surface as a level…

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Q: Evaluate the integral See ex -2 dx Note: Use an upper-case "C" for the constant of integration.

A:

Q: ou want to earn 13% annual simple interest on an investment, how much should you pay for a note that…

A: We know that the formula A=p(1+rt)  Where A is an amount and  P= principal r= rate of interest  t=…

Q: Evaluate the given definite integral. -23 125 th In x

A: let D=∫123lnxxdx

Q: List the points in the xy-plane, if any, at which the function z = 8 + √√(x − 6)² + (y + 7)² is not…

A:

Q: 1/3 The integral fo²³ 3-√2-9x1² dx is to be evaluated 0 directly and using series approximation. 1)…

A:

Q: Find the scalar equation of the plane that contains a(7,1,3), b(-3,4,0) and c(1,-1,2).

A: We have, Points:- A(7, 1, 3) B(-3, 4, 0) C(1, -1, 2)

Q: One side of a triangle is increasing at a rate of 9 cm/s and a second side is decreasing at a rate…

A: One side of a triangle is increasing at a rate of 9 cm/s and a second side is  decreasing at a rate…

Q: Solve the given differential equation by separation of variables. (ex + 1)²e-y dx + (ex + 1)4e¯x dy…

A: ey+12e-y dx + ex+14e-x dy = 0

Q: 15. a) Find the limit. x²-9 lim x--3x²+2x-3 b)lim √25+h-5 h

A: (a) let H=limx→-3x2-9x2+2x-3

Q: horizontal asymptote (c) Describe the end behavior of the function. End behavior: y y → as x → ∞ as…

A:

Q: ƒ(x) = x + 1 X

A: fx=x+1x

Q: 17) Use the Binomial Expansion Theorem to determine the coefficient of xº in the expansion of (x² +…

A:

Q: 15, Suppose a company has fixed costs of $1200 and variable costs per unit of 16x + 1620 dollars,…

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Q: Suppose that f(x) = 4x³ + 5x² + 4. Using the Intermediate Value Theorem, for what values of N is…

A:

Q: What is the product of 5 and 1.0\sqrt(72) in simplest radical form? Please explain, correct answer…

A: 172 = 136*2           = 1(36)*2          =  162 now we rationalize it         = 162* 22         =…