11.Show that if a11, a12, a21, and a22 are constants with a12 and a21 not both zero, and if the functions g1 and g2 are differentiable, then the initial value problem x′1=a11x1+a12x2+g1(t),x1(0)=x01x′2=a21x1+a22x2+g2(t),x2(0)=x02 can be transformed into an initial value problem for a single second-order equation. Can the same procedure be carried out if a11, …, a22 are functions of t?

Q: Answer the following questions about the equation 1 4x³ − y² + ²⁄yz² − x(y − x)e² +1=0. (1) Does the…

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Q: 9. Suppose you sell Dried Chile Mangoes and Biscochitos, each by the pound. Your profit function is…

A: Let x represents the pounds of chile mangoes sold and y represents the pounds of biscochitos sold.…

Q: . The Minimum point of y = x3 3x+6

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Q: 1. if f(x)= x2-4,  g(x)=x3 , F(x)=1/(x-3) a. F(g(y)) b. f(square root of x4+2)

A: F(g(y)) can be obtained by replacing x by g(y) in F(x)

Q: 1. Consider the following function: f(x) = 3 + 6x + 5x2 + 3x3 + 4x4 Locate the minimum by finding…

A: Note: We'll answer the first question since the exact one wasn't specified. Please submit a new…

Q: 17. Analyze the following quadratic function: f(x) =x* - 4x³ – 3x? +10x +8 12 pts Domain:…

A: From the given biquadratic function : f(x)=x4-4x3-3x2+10x+8 Being the polynomial function, domain is…

Q: 11. Suppose that a firm that uses 2 inputs has the production function f(x₁, x₂) = 12xx and faces…

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Q: 7. Find the Domain of cach of the following functions. a) f(x) =2-V-4 b) f(x) =5x² - x+17

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Q: x-3 1. f(x) = x2 + 1 g(x)= v1–x h(x) = v(x) =-9 w (x) = 4x +3 r(x): %3D x+7 Find the following and…

A: Given that:                      f(x)=x2+1g(x)=1-xh(x)=5xv(x)=4x2-9w(x)=4x+3r(x)=x-3x+7   NOTE: As…

Q: 1. -1 1 f(x) -6 3 6. 3 -6 A. y = 3x2 + 3 В. у %3D-3x2 + 6х + 3 C. y = -3x? + 6x – 3 D. y = -3x2 - 3…

A: To choose the correct function:

Q: If f(x)=3x-²-5x¯³+1 and g(x)=√√x, then derivative of (gof)(x) is: a. b. C. 1/1/23 1 2 3x ² 5x 3 1 d.…

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Q: 9. Let f(x) = x³ – 3x² + 3. a. Find the y-intercept of the function; b. Find all critical points of…

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Q: 11. If f(x) = 2x and g(x) = x² – 15, what is (g−ƒ)(3)? ✓✓✓

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Q: Tomato Corp produces cans of tomato paste using inputs of labour and capital as follows Q = 4.0625 –…

A: Since you have posted a question with multiple sub-parts, we will solve the first three sub-parts…

Q: Experiments indicate the braking distance, d, before a car comes to rest from a speed, v (Table 2).…

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Q: 4. If g(x+2) = f(x-7) and if point A(4, -1) is on g(x), then a. Find a point A' on f(2x) b. a…

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Q: Given that f(x) = x² – 9x and g(x) = x + 4, calculate (f o g)(x) or f(g(x))

A: Given f(x)=x2-9x and g(x)=x+4

Q: 4. The quadratic function f(x) has a turning point at (-3,6). The quadratic y=÷f(x)+3 would have a…

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Q: 6. Let f(x) = V2x + 1, find as Ax - Ax

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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.