A rectangular box has length 11 inches, width 20 inches, and a height of 7 inches. Find the angle between the diagonal of of the box and the diagonal of its base. The angle should be measured in radians. angle =

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A: The given piecewise function, fx=2x+3 for x<15for x=1-4x+9for 1<x<34for x=3x-6for x>3…

Q: 20) Differentiate f(x) = cos(e*)

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Q: lim x→→3 x³-7x-6 2x³-11x²+12x+9 ³√x -1 lim X→1 X-1 sina sin 2α lim a-0 1-cos a

A: To evaluate the following limits.i limx→3 x3-7x-62x3-11x2+12x+9ii limx→1 x3-1x-1iii limα→0 sin α sin…

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Q: 6. Which of the following expresses (3√32 + √√8 ) in simplest form ? a) 3√40 b) 6√10 c) 3√2 d) 14√2

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Q: Use the graph of f to estimate the (a) local extrema and (b) absolute extrema. (a) Estimate any…

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Q: By choosing x, find a maximum of xre-x, if r>2, otherwise the function goes to infinity at x=0.

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Q: Use the following information for Questions 4 and 5. f is a continuous function with a domain [-3,…

A: (5) Given that , fx=3,          -3≤x≤0-x+3,    0≤x≤6 -3,          6≤x≤9 and gx=∫-2xftdt Find gx in…

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Q: . Find the equation of the parabola with x-intercepts -7 and 3, and that 2, -11). Express your…

A: Given parabola has two x-intercepts, (-7, 0) and (3, 0). Clearly its either upward or downward…

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A: Topic:- function

Q: If q (x) = ln (6x² + 2x+2), find q' (x). O 12x + 2 In(6x² + 2x + 2) O 3x² + x + 1 6x +1. 6x +1…

A: The given function qx=ln6x2+2x+2 use  the derivative formulas, ddxxn=nxn-1ddxa=0ddxln…

Q: base salary $60 week. and commission $1.25 for all units sold in excess of 50. The bonus is $25 if…

A: Base salary per week=$60If sales exceeds 50 units, thenCommission for per unit=$1.25and bonus for…

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Q: Use exponential regression to find an exponential function that best fits this data. f(x) = Use…

A: Answer is in next step.

Q: solve the differential equation 3(3x^2 + y^2)dx - 2xydy = 0 (A) y=c(9x^2 + y^2) B) x= c (9x^2 +9y^2)…

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Q: Homework: Ex dx 7.S √√x + ³√x

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

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Q: -1.5 (-1,5) -1. (-0.707,4.237) -0.5 7 34 1 (0, 3) -1 -3L (0.707, 1.762) 0.5 1. (1, 1) 1.5 x

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Q: In March 2020, the PH coronavirus cases recorded was 2 089. By month of August 2020, the number of…

A: Here is the function we can use to calculate this. P= P° × e^rt Where p= population affected after…

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A: We can find the answers in the following steps.

Q: 13. What is the maximum value of the parabola ? 5 0 5 a) y = 3 b) x = 4.9 -Cr- 5 c) y = -1 d) There…

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Q: Demonstrate that the function f(x)= e^-x sin (x) is a solution for the differential equation f(x) +…

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Q: 4 Jo - xp (x), us (A) TWEN 6 2 (8) 7 (8) 46 9 3 (C) 0 (C) 0 (D) 1 (a)

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Q: Estimate the instantaneous rate of change of f(x) = -3x + 2 at x = -2.

A: The instantaneous rate of change of a function f(x) is the first derivative of a given function and…

Q: 5.5 dy √y.evy 6. Š dx X+ e 7. fete d dx 8. fdx

A: Here we have to find the integral.

Q: Let f(x) = 6.3x² - 2.4x. Find the equation of the secant line on the graph of f(x) between *₁ = 3…

A: We can find the answer in the following steps.

Q: dx x (In x)5

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Q: Determine the open intervals on which the graph is concave upward or concave downward. (Enter your…

A: Given function f(x)=x4-3x3 A function is said to be concave up if f''(x)&gt;0 and concave down if…

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Q: Consider the function f(x)=x²- 5x. Compute the derivative using the definition f(x+h)-f(x) h by…

A: To find the derivative f'(x)

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Q: Find all relative extrema of the function. Use the Second Derivative Test where applicable. (If an…

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Q: 3) f₁ dx do - cos 0

A: Note: As per our company guidelines we are supposed to answer the first question only. Kindly ask…

Q: Find the point on the line 3x + 3y - 3 = 0 which is closest to the point (-2, 1). )

A: To find closest point on the line, draw perpendicular from the given point to the given line. The…

Q: 1 If f(x) = -2x2² +8x-4, find the following value. f(5)-f(-7) 5-(-7) Give answer as an integer or…

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Q: i) Use the substitution v to find the general solution to dy xy = dr x² + 6y².

A: Note: As per our company guidelines we are supposed to answer the first question only as they as…

Q: The following table represents Canada's population in specific years over the last century. Year…

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Q: 4.y=log10 (x4 + 3x² + 1) 5.y = log5 √x² +1 1-x² 6.y-log10 |2–5x3

A: Given 4. y=log10x4+3x2+1 5. y=log5x2+1 6. y=log101-x22-5x3         Derivative of the log functions…

Q: (a) Find the slope of the curve y=x²-2x-2 at the point P(2-2) by finding the limit of the secant…

A: Here given curve y=x²-2x-2 Slope to the curve is  m= limx-&gt;2(f(x)-f(2))/(x-2)…