Use the two methods "real number solution space basis" and "complex solution space basis" respectively to solve y''+ 1/4y = 0, y(π) = 1, y'(π) = -1

Q: can you solve this and explain the steps used along the way

A: Step 1: Simplify the integrand The integrand can be rewritten using exponents: 1/(41+x​)=(1+x)−1/4…

Q: Which of the following is the general solution to y′′ + 4y = e^2t + 12 sin(2t) ?A. y(t) = c1 cos(2t)…

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A: Thevolumeoftheparallelepipeddeterminedbythevectorsa,b,cisgivenbytheabsolutevalueofthescalartriplepro…

Q: Find the area of the shaded region. (a) 5- y 3 2- (1,4) (5,0) 1 3 4 5 6 (b) 3 y 2 Decide whether the…

A: First, we need to identify the shape of the shaded region. In part (a), the shaded region is a…

Q: could you please show the computation of this by wires

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Q: The function f is shown below. If g is an antiderivative of f such that g(6) = 2, what is the…

A: Since g is an antiderivative of f, g′(x)=f(x). This means g(x) is increasing where f(x)>0 and…

Q: DETAILS MY NOTES SESSCALCET2 6.3.012. 6. [-/1 Points] Evaluate the integral. x-4 dx x² - 5x + 6 Need…

A: 67891011

Q: Topic 2 Evaluate S x dx, using u-substitution. Then find the integral using 1-x2 trigonometric…

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Q: 31.

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Q: Question 2 (1pt). Evaluate the following (definite and indefinite) integrals (a) / (e² + ½) dx (b) S…

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Q: B G R + K Match each equation with a graph above - 3(0.9)* 1 a. green (G) 3(1.5)* b. black (K)…

A: Let's analyze the equations and match them to the graphs based on their properties:General Form: All…

Q: Find the following limit lim x-4 X-72 3x-6

A: We need to evaluate the limit:limx→2​3x−6x2−4​ Step 1: Substitute x = 23(2)−622−4​=6−64−4​=00​Since…

Q: Perform long division on the integrand, write the proper fraction as a sum of partial fractions, and…

A: Step 1:Step 2:Step 3: Step 4:

Q: 11 fr² Find√² du In(x+u)

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Q: Use undetermined coefficients to find the particular solution to y"-y+5y = 7t² +61 +3 Yp(t) =

A: Step 1: Step 2: Step 3: Step 4:

Q: Find area of the sector

A: Ans 13:Read this as answer number 13Ans 15:

Q: Suppose that R (x) is a polynomial of degree 7 whose coefficients are real numbers. Also, suppose…

A: Since R(x) is a polynomial with real coefficients, its complex roots must occur in conjugate pairs.…

Q: Find the derivative of the following function. -8e5x y= 9x+2

A: To distinguish the specified function:…

Q: The expression 3 | (3+1/+1) of the following integrals? A Ов E + + + + 18 3+1+1 3++1 3++1 (A) √2×14…

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Q: Use the two methods "real number solution space basis" and "complex solution space basis"…

A: Method 1: Real Number Solution Space Basis Step 1: Solve the Characteristic EquationThe…

Q: 3. Given the function h(x)=(x²+x-12 if x≤1 3-x if x>1' a) Graph the function h(x). Make the graph…

A: Part ABased on the given equation, the graph of the function should look like this: Desmos is used…

Q: could you explain this pleasethe answer is has sum 1but i dont know how to calculate it

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Q: a is done please show b

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Q: Find the indefinite integral using the substitution x = 5 sin(e). (Use C for the constant of…

A: Let's solve the given indefinite integral: 1. Recognizing the SubstitutionWe have the…

Q: 4. Evaluate the following integrals. Show your work. a) -x b) f₁²x²/2 + x² dx c) fe³xdx d) [2…

A: Step 1:Step 2:Step 3:Step 4:

Q: Two cables tied together at C are loaded as shown. Given: Q = 130 lb. 8 30° C B Q 3 4 Draw the…

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Q: 1. Given the vector field F(x, y, z) = -zi, verify the relation 1 VF(0,0,0) lim +0+ volume inside S…

A: The vector field is given by F(x, y, z) = -zi. The surface S is the surface of a cube centered at…

Q: Question Considering the definition of f(x) below, find lim f(x). Select the correct answer below:…

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Q: 1. Find the area of the region enclosed between the curves y = x and y = x. Sketch the region.

A: Step 1: Compute the points of intersection. Since y = x4 and y = x, then x4 = x. Transfer all terms…

Q: show work

A: Okay , so here are the solutions. 1. sec²θ - 1Using the identity: sec²θ = 1 + tan²θsec²θ - 1 =…

Q: Question 14 6+ 5 4 3 2 -8-2 2 3 4 5 6 + 2 3 4 -5 -6 The graph above is a transformation of the…

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Q: Write an integral that is approximated by the following Riemann sum. Substitute a into the Riemann…

A: We are given the Riemann sum:  ∑i=12000​((10−a)+0.001i)a1​(0.001) Step 1: Recognizing the Riemann…

Q: Let f(x) = √√x+3 and g(x) = 6x − 2. Find each of the following composite functions and state the…

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Q: practice problem please help!

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Q: For the given graph, determine the following. -3 12 УА 4 3 - -1 ° 1 2 3 x -1. -2- a. Determine for…

A: Given figure is :

Q: Find the derivative of the following function. -2 y = (3x+7)³

A: Given Function: y=(3x5+7)3−2​ Rewrite the Function Rewriting the function using exponent notation:…

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A: Step 1: Step 2:Step 3: Step 4:

Q: Find the equation of the tangent line to the graph of the given function at the given value of x. 6…

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Q: Explain how to solve all solutions of y"(x)+ay'(x)+by(x)=0 when the Characteristic Equation…

A: When solving the second-order linear differential equation y′′(x)+ay′(x)+by(x)=0 with the…

Q: the correct answer is C could you please explain

A: Step 1: Given Region D The given region D is defined by: 1≤x2+y2≤4,∣y∣≤x The inequality 1 ≤ x2 + y2…

Q: 3. Solve the equation, give the answer exactly (no calculator approximations), and show all your…

A: We solve the equation log5(2x) = 3 as follows: Step 1: Convert from Logarithmic Form to Exponential…

Q: 4.3 (A). A conveyor beam has the cross-section shown in Fig. 4.24 and it is subjected to a bending…

A: Detailed explanation:

Q: Use the method of disks to find the volume of the solid that is obtained when the region under the…

A: Step 1: Step 2: Step 3: Step 4:

Q: can you solve this question and explain the steps used along the way

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Q: 2. Suppose f(x) = 3x² - 5x. Show all your work for the problems below.

A: Step 1:Step 2: Step 3: Step 4:

Q: The twice differentiable functions fand g are defined for all real numbers of x. Values of f(x) and…

A: The value of the integral is -6.

Q: A function is defined on the interval (-π/2,π/2) by this multipart rule: if -π/2 < x < 0 f(x) = a if…

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Q: Please refer below

A: Let's solve the inequality:Step 1: Isolate the Absolute Value ExpressionStart with:…