Find the solution of the given initial value problem in explicit form. sin(2r) da + cos(6y) dy = 0, y(5) = %3D %3D 6. y(x) :

Q: Find the area of the region bounded by the curves y = x, x = 1 and y = 0. %3D A. 1 В. C. 1 3 D. 1 4 ...

A: Area = integration of upper curve - lower curve and put the limits.

Q: Solve for x, y, z and w. (Enter your ansv x + y y + z 3 5 z + w 8 5 (x, y, z, w) =

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Q: 2 COS os²(5æ) sin*(5æ)dr 4

A: This is a problem of integration. Based on the general formula of integration we will solve the prob...

Q: Since lim k→+0 (k + 1)!/3k+1 k!/3* k+1 lim k→+∞ 3 +00, k! the series (converges/diverges/inconclusiv...

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Q: 2. Let x+1 r -1 Determine if lim f(x) exists. r-1

A: The objective is to determine if the limit exists or not. 

Q: A population of protozoa develops with a constant relative growth rate of 0.7943 per member per day....

A: A population of protozoa develops with a constant relative growth rate of `0.7943` per member per da...

Q: The path r(t)=(5 sin t) i+(5 cos t) j describes motion on the circle x^2+y^2=25. Find the​ particle'...

A: We have to find ​ particle's velocity and acceleration vectors at t=π/3 and π/6 . Given  r(t)=(5 sin...

Q: A trough is 50 ft long and has semicircular ends, with the flat side facing up. The semicircles have...

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Q: Use implicit differentiation to find the derivative y' of the following: y²+2ye2x у?е2x + хуз — 1%3D...

A: Given :6. y2e2x+xy3-1=07. xey+3y-10x=0To find: Implicit differentiation to the derivative y'.  

Q: Give a vector parametric equation for the line that passes through the point (–2, 1, –2), parallel t...

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Q: The graph of f (x) is shown below. Which of the following statements are true? 7- 6- 4 %3D %3D -7 -6...

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Q: -n ) Σe n=1 1 d) Σ+ 3 п n=1 8

A: C) Given that ∑n=1∞e-n By the integral test, ∫1∞e-x dx=limt→∞∫1te-x dx                              ...

Q: Use the given graph of the function to find the z-values for which f is not differentiable. 1.A Answ...

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Q: Find (f^-1)'(a).  f(x)=4x^3+3x^2+8x+9,    a=9 (f^-1)'(a)=

A: Topic:- function and derivatives

Q: ip dt + y* = tys (MULTIPLE CHOICE) Which of the following is(are) true about the equation (A) The di...

A: Given that Diffrancial equation t4dydt+y4=ty3Solution :t4dydt+y4=ty3dydt+y4t4=ty3t4dydt+yt4=yt3this ...

Q: Determine the standard equation of the ellipse that satisfies the given properties: 16 3, horizontal...

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Q: A tank in the shape of an inverted right circular cone is full of water. The water weighs 62.4 pound...

A: Work done on an object is defined by,         W=F.S, Where F is the force exerted on the object and...

Q: If f(x)=10sin(x)+3cos(x) , find a function g so that g"(x)=f(x) given that g(0)=0 and g(2)=12 . g(x)...

A: Given query is to find g(x).

Q: 2) Determine dz/dx and dz/dy for z* – y? + x² = 6x²y³z? %3D

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Q: 1. Find a linear differential operator (of lowest order) that annihilates the given function: flr) -...

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Q: 3. Find the determinant of the following matrices: -5 0 1 2 -1 -1 -2 3 C. -4 -5 -6 -3 4 1 7 -8 9. T-...

A: We have to find the determinants of the below matricies.

Q: A balloon is rising vertically above a level, straight road at a constant rate of 4 ft/sec. Just whe...

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Q: Determine the solution to the second order homogeneous initial value differential equation 1 y"+ 3 y...

A: Topic:- differential equations

Q: What are the coordinates of the foci in the equation - 4 *5=1? A F1(1,0); F2(-1,0) B F1(3,0); F2(-3,...

A: The given equation is: x25+y24=1                               (1) Equation (1) is compared with the...

Q: Find lim x→∞ h(x), if it exists. f(x) = 9x2 + 2x + 7   (a)     h(x) =  f(x) x lim x→∞ h(x) =

A: We are asked to find the limit of the function.

Q: The figure to the right shows d 1 sin x and y = sin x + 4 1 4 1 sin x? Find values 4 Which graph is ...

A: Graph of sine function

Q: as, consider the different

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Q: Evaluate the following definite integrals, t(1 -t)² dt = а.

A: Solution: ∫-11t(1-t)2dt Expand=∫-11t-2t2+t3dt

Q: Is the integral of 2x wrt x equal to 2x^(1+1)/(1+1)?

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Q: Find the derivative as indicated: 1) y = 3 cos x + 2 sin x ; find y' %3D 2) f(t) t sint ; find f'()

A: Given: 1: y=3cosx+2sinx2: f(t)=t sint   To Find: 1: y'2:f'(3π2)    

Q: A tank in the shape of an inverted right circular cone is full of water. The water weighs 62.4 pound...

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Q: t nd the arc length parameter along the curve from the point where t= 0 by evaluating the integral s...

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Q: The figure below shows contours of g(x, y) on the region R, with 3 < x < 9 and 2 < y < 8. 8 -1 6 1 2...

A: Let's find. 

Q: dy find dx t - 1 If y = t and æ = t+1 dy A. 2t(t + 1)2 dx В. dy = t(t+1)² dx dy 2t С. dx (t + 1)? dy...

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Q: Integrate the following functions: 1. S sin 2x dx

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Q: Solve the following problem related to function. (Show your solution) 4. What is the equation of the...

A: Given, fx=x+1 We have to write the equation of the graph of a function when fx=x+1 Vertically stret...

Q: Find the slope of the line tangent to the graph of f(x) = 3x² - x- 5 at x = 1. %3D Provide your answ...

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Q: An object moves along the a-axis, its position at each time t > 0 is given by æ(t) = t" 3 4 +t. Dete...

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Q: Evaluate f tan²xsec*xdx using trigonometric integrals

A: Our Aim is to evaluate the integral given below:-∫tan2 (x) sec4 (x) dx -(i)

Q: Compute the first 6 terms of the sequence {an} where An-1+n a1 = 1 and an for n > 2.

A: The given sequence,a1=1 and an=an-1+n2 for n≥2

Q: dy for: (x + y) = x – y + 8 da 1. Find 2. If a ball is thrown vertically upward with a velocity of 8...

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Q: Answer this question please.

A: Rotation of matrix about a line through origin : Change the given point into polar form and check th...

Q: Given an infinite series, discuss a strategy for deciding what convergence test to use

A: First i have written an infinite series and told about convergence test of similar series named p-te...

Q: The distance from the center of a hyperbola to its vertex is larger than the distance from its cente...

A: Given query is to find that statement is true or false.

Q: Find the area of the cardioid r = 2(1+ cos 0). Α. 2π В. 47 С. D. 67 E. none of the above

A: Given r= 2.(1+cos@) To find area of cardioid

Q: solve for nonbermagnenous dilkeremrial equation . 4x

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Q: Vr csc Vx ,2

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Q: Find the position function s(t) for the given acceleration function and conditions: a(t) = −2t+7, s(...

A: The acceleration function,a(t)=-2t+7, s(1)=8, v(2)=-3

Q: If the relationship between Y and X is negative (as X increases Y decreases), then there are more po...

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Q: Express the integrand as a sum of partial fractions and then evaluate the integra 4x2 xp. 4 1

A: We have to find out