Find real numbers a, b, and c such that the graph of the function y = ax²+bx+c contains the points (1, 2), (2, 11), and (-3, -14). Find f(-2)

Q: Find the equation for an exponential function that passes through the pair of points given below.…

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Q: Find a formula for the general term an of the sequence, assuming that the pattern of the first few…

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Q: Solve the initial value problem y" - 3y' — 40y = 0, y(0) = a, y′(0) = −35. Find a so that the…

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Q: Find the constant a such that the function is continuous on the entire real line. -√8x², a = ax - 8,…

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Q: The shape of a colony of bacteria on a Petri dish is circular. Find the approximate increase in its…

A: topic- application of derivatives

Q: Find f'(x) and find the equation of the line tangent to the graph of f at the indicated value of x.…

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Q: Use the Integral Test to determine if the series shown below converges or diverges. Be sure to check…

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Q: Find a vector-valued function whose graph is the indicated surface. The plane z = 4y r(u, v) =

A: Solution ) the plane      z = 4y   Let's make substitution  x =u , y = v  Hence  z = 4v   r ( u, v)…

Q: Find the average value over the given interval. 32) y = 5x2; [-1,2]

A: We can find the average value as below.

Q: Suppose the function y=h(x) is nonnegative and continuous on [x3], which implies that the area…

A: We want to find area bound by the astroid

Q: What we know: outer green square box has a side length of 10 inches, inner square has a side of 6…

A: Concept: Area of the square: A=side2 The diagonal of the square is : d=2side Area of circle: A=πr2…

Q: Represent the line segment from P to Q by a vector-valued function. (P corresponds to t = 0. Q…

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Q: Find a vector-valued function whose graph is the indicated surface. The plane x + y + z = 2 r(u, v)…

A: Given plane    x+y+z = 2                 this gives   z = 2-x-y            Now, let  x=u    and…

Q: 2 -2 [ 3x² + 4y dy dx = [[ 3x² + 4y' dx dy. We have Select one: True False

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Q: Let f(x, y) = x²y³, then Vf(1,2)= Select one: True False

A: Given problem:- fx,y=x2y3 Then ∇f1,2=16,12?

Q: 1. Which of the following values would be obtained using 10 circumscribed rectangles of equal width…

A: The integral is  ∫01 x2 dx

Q: a) Determine if the geometric series 8n-1 90+1 n=1 is convergent or not, and find its sum if it is…

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Q: Find the radius of convergence for n! n=1 -xn nn

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Q: Assume that x = x(t) and y=y(t). Let y = x³ +5 and dt Find dt dy dt when x = 3. (Simplify your…

A: Here is the solution:

Q: please solve d-f now. thanks.

A: We have to find the composition of functions.

Q: Consider the following. 7|x - 21 x-2 Find the x-value (if any) at which f is not continuous. Is the…

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Q: I'm not understanding what the answer is here? 77 and 71? Because that is not correct.

A: A rectangular page is to contain 76 square inches of print. The margins on each side are 1 inch. To…

Q: Without using a calculator, for the following, determine the definite integral that represents the…

A: Here, the given curve is r=3-4cos θ. The graph of the curve is: To find the area of the shaded(red)…

Q: dy_y-x dx y + x

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Q: [ 1² dx dy = 1/2 Select one: True False

A: Evaluating the definite integral

Q: 4. Terms of a sequence from sampling a signal. In electrical engineering, a continuous function like…

A: Please see the below picture for detailed solution.

Q: Question 1 Consider the matrix A- - (a) (b = 64 -1 1 -1 0 3 -2 -2 2 1 Compute the adjoint matrix…

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Q: Sketch the system. Identify the type of graph within the system. Find the intersection y = x² + 2x +…

A: Given data÷   y=x2+2x+1 and  x-y=-3   y=x2+2x+1 is a parabola and  x-y=-3 is a straight line

Q: The subset in the form [3]. Select one: O TER and y = -x. O None of these O r = -y and y ≤ 0. Or#0…

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Q: The gradient vector of the function f(x, y, z)= ln(yz) - x² is: 2 Select one: 0 (-2x,1,1) O None of…

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Q: Evaluate F F. dr using the Fundamental Theorem of Line Integrals. Use a computer algebra system to…

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Q: If A = 1 -9 -9 -6 -4 and AB = 1 D -1 9 -3 -3 6 ww -6 ? a ? ? PP ?? 9 5 B-1 9 ∞ C 3-8 1 what is the…

A: We have to multiply the two matrices then find the value of a.

Q: Evaluate the integral given below. Check your answer by differentiating. NOTE: Enter the exact…

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Q: Evaluate the indefinite integral 7X+17 (x+2) (x+3) dX

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Q: Use the given information to find the indicated probability. A and B are mutually exclusive. P(A) =…

A: As per our guidelines we can solve only one question at a time.  Please upload separately for more…

Q: 7. Convert the angle 5л 3 into degrees.

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Q: Choose the area of the region enclosed by the curves -6 4x 0 x=0, x=6, y = 4x², y = 4x. 4x2 6 SO SAX…

A: Given.

Q: Without using a calculator, convert the parametric equations of a curve into rectangular form. No…

A: Given that parametric equation and convert this equation into rectangular form and State the domain…

Q: Consider the following function and graph. f(x) = x + 2 1 -3+ Determine whether f(x) approaches ∞ or…

A: In this question, we want to find the left hand limit and right hand limit of the function.

Q: After a large number of drinks, person has a blood alcohol level of 200 mg/dL (milligrams per…

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Q: dz Find given: dt z = xe²y, x = t³, y = - 5 + 6t dz dt ||

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Q: 8. Eliminate the parameter to find a Cartesian equation of the curve: x(t) = t, and y(t) = 3t+4, t≥…

A: To eliminate the pararmeter to find a Cartesian equation of the curve: xt=t, and yt=3t+4, t≥0.To…

Q: Problem 8 ). Find the Maclaurin polynomials of orders n = 0, 1, 2, and 3, for the function f(x) =…

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Q: 5. The tank shown below is full of water. Find the work required to pump the water out of the spout.…

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Q: Find the work done by the force field F in moving an object from P(-3, 7) to Q(7,5). 2x F(x, y) = -

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Q: 2. Let f(x) = nx² - 2x + 5 and g(x) = 6x² - 5x + m. The functions are combined to form the new…

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Q: Find an equation of the tangent to the curve at the given point by two methods: without eliminating…

A: The given curve and the point is x=sin(t), y=cos2(t) ; 32,14

Q: Evaluate the integral. I sin sin (3x) cos(6x) dx = NOTE: Enter the exact answer. + C

A: We can answer the integration as below.

Q: Classify the following diferential equations. Write the order, linearity and the homogeneity of the…

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Q: Without using a calculator, for the following, determine whether the graph of the polar equation is…

A: Given that    r = 2 secθ            we know that    x(θ) =  r cosθ      and      y(θ) = r sinθ…