Suppose an arrow is shot upward on the moon with a velocity of 49 m/s, then its height in meters after seconds is given by h(t) = 49t - 0.83t². Find the average velocity over the given time intervals. [3,3.5]

Q: Which one of the following is NOT a separable first-order differential equation? A x 2-52²-1 dy ay…

A: Find which equation is not separable.

Q: 3. Write the system as a matrix equation and solve using inverses. 2x₁ - 3x₂ = 23 3x₁ + 2x₂ = -11

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Q: The function k(x, y) =e cos (5x)

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Q: h) y secx= x tan y

A: given  ysecx=xtany we know d dx(secx)=secxtanxd dx(tanx)=sec2xd dx(a.b)=a×dbdx+b×dadx

Q: A guitar factory has a cost of production C(z)-90z+ 47500 if the company needs to break even after…

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Q: Consider the Initial Value Problem: " + 5y-6y=0, y(0)=2, (0)=-1, Which one of the following is the…

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Q: Use the indicated substitution to evaluate the integral. 1 = 1 √x² - 169 (Use symbolic notation and…

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Q: Find lim lim h→0 h→0 f(5+h)-f(5) h f(5+h)-f(5) h II if f(x)=-3x - 8. (Simplify your answer.)

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Q: Let f(x) = √√x² + 3.

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Q: The point P(5, 37) lies on the curve y = x² + x + 7. If Q is the point (x, x² + x + 7), find the…

A: To find the slope of the secant line

Q: Use (a) the Trapezoidal Rule, (b) the Midpoint Rule, and (c) Simpson's Rule to approximate the given…

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Q: (Hint: Rationalize twice) (ii) Use the result of part (i) to evaluate lim #42 (Hint: It's a one line…

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Q: An open rectangular box has volume 48 cm³. What are the lengths of the edges giving the minimum…

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Q: Let f(x) = [2x +9 if x 2 Determine whether f(x) is continuous at x = 2. If f(x) is not continuous,…

A: Given query is to find function is continuous at x = 2 or not.

Q: A solid object placed along the x axis has cross sectional area at a value x equal to A(x) = e^2x.…

A: A(x)=e2xgiven interval is -1,3formula for volume isV(x)=∫abA(x)dx

Q: Find the derivative of the function using the definition of derivative. g(x)=√2-x g'(x) = 1 2√2-x…

A: Solving the following problem

Q: Calculate R5 for f(x) = 2x² + 9x over [-1, 1]. (Give an exact answer. Use symbolic notation and…

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Q: b) Given that B = ₁1 321. i) Find the eigenvalues of B. ii) Prove that the eigenvectors for matrix B…

A: Given matrix:- B=2-31-2

Q: Learning Target D1: I can find the derivative of a function, both at a point and as a function,…

A:

Q: lim x → 2 2 x²+x-6 x-2

A: Factorize the numerator and cancell the common factor.

Q: Evaluate the following path integrals Jo f(x, y, z) ds, under the following conditions. (Note that…

A:

Q: 2y(y2 - x)dy = dx

A: Given data :    2y(y2 - x) dy = dx

Q: Find the marginal profit function if cost and revenue are given by C(x) = 295 +0.9x and R(x) = 7x…

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Q: 9. Given the function f(x) = x³ - x and g(x) = x - 1, determine an equation for the the combined…

A: The given problem is solved below in detail.

Q: For the given functions f and g, find the requested function and state its domain. f(x) = x-9; g(x)…

A: given  f(x)=x-9g(x)=9x2(f+g)(x)=f(x)+g(x)

Q: 12) lim x-0 x3 + 12x2 - 5x 5x 13) lim X-2 x2 + 6x - 16 x-2

A: We are required to find the limit12. limx→0x3+12x2-5x5x13. limx→2x2+6x-16x-2

Q: Which of the following graphs exhibit ALL of the listed properties: • lim f(x) = 1, 2-00 • lim f(x)…

A: Since the student has posted multiple questions and does not mention any specific question, so we…

Q: Consider the differential equation:=-y. If the general solution is y = cet ,cER, which one of the…

A: We can solve this as follows:

Q: Find the absolute maximum and minimum of the function f(x, y) = x² + y2 subject to the constraint…

A: Given function:- fx,y=x2+y2 Let gx,y=x4+y4-1

Q: Find the critical point of the function f(x, y) = − (36x + 6y² + ln(|x + y))) . C= Use the Second…

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Q: Which one of the following is the general solution of 3 + 5y = 1? dz y=+cel -+ce where CER ++ where…

A: To find the general solution of given differential equation

Q: dy dx dy dx Find for the function y = x .-10 cos(x) 0

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Q: Using the RN approximation, express the area under the graph f(x) = 8 sin(x) over [0, 5] as a limit.…

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Q: Use the trapezoidal rule, the midpoint rule, and Simpson's rule to approximate the given integral…

A: Concept: For estimating mathematical operations, there exist numerical approaches. We use…

Q: Do b).

A: Here is the solution:

Q: 6. Consider the graph. a.) Do the points on the graph represent a sequence? b.) Find the general…

A: Since the student has posted multiple questions and has mentioned to solve multiple questions, but…

Q: he following figures show the price of gold per ounce, in dollars, for a 10-business-day period.…

A: Price variation of gold as follows  1,030, 1,026, 1,035, 1,025, 1,026, 1,022, 1,016, 1,029, 1,003,…

Q: Find the average rate of change for the function over the given interval. y=ex between x = -2 and x…

A: We know that Average rate of change of a function f(x) from x=a to x=b is given as:f(b)-f(a)b-a

Q: Use the graph of the function f shown to estimate the following limits and the function value.…

A: By using the graph of the function f shown ro estimate the following limits and the function…

Q: Let f and g be differentiable functions. Find a general formula for the derivative of y = f(x)9(x).

A: Given y = f( x )g( x )

Q: The graph of y = f(x) has the following features: lim f(x) = 3 18 ● lim f(x) = -2 #418 lim f(x) = -∞…

A: Here is the solution:

Q: Question 4 (i) Evaluate (Hint: Rationalize twice) lim x→2 19 √2x + 5 x 2 4

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Q: Suppose that functions f and g and their derivatives with respect to x have the values shown to the…

A: To find the value of the derivative at x=2.

Q: Find the derivative of the function. dy dx y = 3xe 4x || - ets

A: To find the derivative of the following function. y=3xe-4x-ex4

Q: Evaluate the integral. (Use C for the constant (arcsin(x))² dx

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Q: List the first five terms of the sequence. 2₁ = 6, an+1 = 2a + 3

A: Explanation of the answer is as follows

Q: Differentiate the following function: f'(t) = FI f(t) = √t__1 1-1/1

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Q: Consider the ODE: "-7y" -/+7y=0. Which one of the following is the general solution to this ODE?…

A: The given differential equation is: y'''-7y''-y'+7y=0 So, we can also write as: D3-7D2-D+7y=0   The…

Q: Determine the exact solutions for x on the interval [0,2π). This problem has inverse trig in the…

A: Given trignometry equation sin( 2x ) = 45

Q: ²-8 If f(x) = X-4' X = where is f not differentiable?

A: