Find the general solution to the following problems: 1. (D² + 4D + 5)y = 50x + 13 e³x 2. (D² - 1)y = 2 1+ex

Q: Given P(x) 3x55x² - 4x³ – 8x² 64x + 48, and that 2i is a zero, write P in factored form (as a…

A: NOTE: Refresh your page if you can't see any equations. . the given root is  so another root must…

Q: Analyze the function f(x) = x+17 4x +15 if x < 4 if x ≥ 4

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Q: Find y as a function of t if y(0) = 4, y(0) = 1. y(t): = 64y" - 144y + 81y = 0,

A: Given: The characteristics equation is             64m2-144m+81=0⇒m=--144±-1442-4· 64· 812·…

Q: Find the general solution of the differential equation. y (5) — 11y(4) + 29y" — 11y" + 28y' = 0.…

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Q: The velocity of a particle moving along a line is a function of time given by v(t) = = the distance…

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Q: Write the quadratic function in the form f(x)=(x-4)²+k Then, give the vertex of its graph.…

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Q: a B sin(A) = cos (A) = Note: Triangle may not be drawn to scale. Suppose a = 9 and b = 2. Find an…

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Q: f(x) = In (x) + In (25-x²), (0,5)

A: 1st derivative test

Q: Use Theorem 13.9 to find the directional derivative of the function at P in the direction of the…

A: To find the directional derivative of the function at a given point in a unit direction.

Q: 12) 3 Find the first derivative of f(x)= -2 3x

A: The objective of the question is determine the first derivative of the given function.

Q: Find the area of the triangle. Round your answer to one decimal place. B = 111°,    C = 29°,    a =…

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Q: a. Which of the following are functions? Justify your answer. f(x) 5+ 4- 3- -4-3-2-1 O -2- -3+ -4-…

A: Let's find function or not.

Q: 4. Gill wants to reach a movie commercial from a building, 60 feet above the street. If Gill has a…

A: We can solve the given problem by using the trigonometric ratios

Q: 1) tan x Find the derivative of y= = e

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Q: Find the critical point(s) of the function y = 0 - 2 cos (0) at 0 € [-3, -π]. (Give your answer in…

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Q: 12. Solve the problem with given initial value. y’’-6y’+9y=0, y(0)=0,  y’(0)=2 theme: repeated…

A: To find out the solution.

Q: Find the particular solution of the differential equation that satisfies the initial condition(s).…

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Q: 10. Prove: cos²(x)-sin²(x) =sin² (x) 1-tan²(x)

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Q: CHECKPOINT 3.14 √ √ Rewrite the integral evaluate the integral). x³ √25x² dx using the appropriate…

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Q: Use the sum-to-product formulas to find the exact value of the expression. 5-2 sin 3 2 sin in

A: We can find the answer as below using the sum to product formula.

Q: 3. Evaluate S dA where R is the region between y = 2x and y² = x³ lying to the R left of x = 1.

A: Let's evaluate double integral.

Q: Q1 (a) Show that y= Ae²* + Be ³*, where A and B are constants, is the general solution of the…

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Q: Find a function f that has the derivative f '(x) and whose graph passes through the given point.…

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Q: -8-7-6 - 5 -4 -3 -2 -1 8 7 6 5 4 3 2 1- 0 ل -3 نا 2 3 4 5 6 7 8

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Q: 1. Find the divergence and curl of the following vector fields a. F = (1/y²)j b. F=y³z³i+ 2xyz³j +…

A: We have to find the divergence and curl of the given vector fields.

Q: Use the figure, which shows two lines whose equations are y₁ = m₁x + b₁ and y2 = m₂x + b₂. Assume…

A: The solution is given below

Q: A population of a particular yeast cell develops with a constant relative growth rate of 0.4373 per…

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Q: The area of the sector of a circle with radius 8 inches formed by a central angle of 100° is inches.…

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Q: Use Lagrange multipliers to find the indicated extrema, assuming that x and y are positive. Maximize…

A: By using Lagrange multipliers to find the indicated extrema, assuming that x and y are…

Q: Find the critical points and the intervals on which the function f(x) = (x³ - 2x) e* + 8 is…

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Q: If 0 = sec (0) csc(0) = - = tan(0) cot (0) = = 7 -T, enter exact values for each function. 4 7000

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Q: (True/False) For any three-dimensional vectors u and 7, we have u x vx u.

A: The given statement is true.

Q: 2. Solve the DE: -+secx(y-2sec³x+2 sec² x tan x) + y cotx=0 dx

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Q: 5) Evaluate the given expression without the aid of a calculator tan[arcsin( +1 x+ 6 --)]

A: We have to evaluate the given expression without the aid of a calculator.

Q: 10. (True/False) For any continuous function f(x, y), we have fry = fyr.

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Q: (1) -dr x(x + 1)

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Q: 2. Find the volume of the solid obtained by rotating the region bounded by the given curves about…

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Q: To find the distance between a point X and an inaccessible point Z, a line segment XY is…

A: Given   In △XYZm∠Y=34°,18'm∠Z=94°,48'and z=961 m

Q: Σ k = 1 k k 4' 249

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Q: 5 Find a parametrization for the line segment joining the points (0, 2) and (4,0) using the angle in…

A: A parametrization for the line segment joining the points (0,2) and (4,0) using the angle θ in the…

Q: Solve 11. a), b), c), d)

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Q: xp (I + ²)² [ (1) 9x)x I

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Q: Find the domain of the following rational function. 20x² H(x)= + X O A. x² +2 Select the correct…

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Q: We assume that in a village there are farmers, carpenters, and tailors, who provide the three…

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Q: Find the local maximum and minimum values of f using both the First and Second Derivative Tests.…

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Q: ∞ A function is a probability density function if it satisfies the following definition: 1: f(t)dt =…

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Q: 9. 1 Sketch the graph of g(x)=sin5x, using the amplitude and the period.

A: Solve the following

Q: 7. Find the exact values of: a) sin ¹(1) b) tan-¹(0) 5-¹ (13) 2 COS

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Q: A woman is on a lake in a rowboat located 1 mi from the closest point P of a straight shoreline (see…

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Q: 4Q Find the dot product and cross product of following vectors i a= 2i+j a= b=I-j+k b= 11. 111. a=į…

A: To find the dot product and cross product of the given vectors. Note that:…