For every positive number a the functions sin x and cos x are orthogonal on the interval [−a, a]. true or false ?

Q: Write the expression as a sum and/or difference of logarithms. Express powers as factors. In…

A: Explaination of the answer is as follows

Q: Find the volume of the solid generated by revolving the shaded region about the y-axis. 0.5- x= 3…

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Q: Determine the volume of the solid generated by rotating function f(x) = √64 - ² about the x-axis on…

A: The given function is

Q: Solve the exponential equation. Express irrational solutions in exact form. 41-9x = 3X What is the…

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Q: what is the addition or subtraction on formula used to write the expressions.

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Q: Find the distance between the given parallel planes. 4x - 5y + z = 16, 8x 10y + 2z = 3

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Q: Evaluate the following indefinite integrals: a. S 1 x²√36-x² - dx b. X -9 - 11-364 c. [²√²+² d.…

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

Q: The equation of the ellipse that has a center at (7,5), a focus at (11,5), and a vertex at (2,5), is…

A: The ellipse that has a center at (7,5), a focus at (11,5), and a vertex at (2,5)Let The equation of…

Q: Verify that (sin(0) csc(0))+ (cot(0) tan(0)) = 2

A: We have to verify,

Q: Show that the given function is a solution of the differential equation. x2 dy - xy = x² + x, y = x…

A: To show that the given function is a solution of the differential equation.

Q: 1 Find the volume of the solid generated when the region bounded by y = x(8 - x) and x = 5 is…

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Q: Integrating an Exponential Function Use the Exponential Rule to find the indefinite integral. See…

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Q: Compute the gradient of the function at the given point. f(x,y)= -8x^2+10y, (6,-2)

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Q: s 1 /x√√x + x dx.

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Q: Evaluate ff ex²+y² dxdy R= {(1,0): 0< r ≤ 4, 0≤0 ≤ 2} ffer 86

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Q: two linearly independent solutions of the differential equation 3y''-7y'+2y=0 are

A: The given differential equation .The aim is to find the linearly independent solutions of the…

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: Directions: Use the digits 1 to 9, at most one time each, to fill in the boxes so that the line is…

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Q: Find the value(s) of c guaranteed by the Mean Value Theorem for Integrals for the function over the…

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Q: Find the particular solution. dy dx - 2y = 10, y = 4 when x = 0

A: Given , the differential equation, y = 4 when x=0We find the particular solution of the above…

Q: The purchasing power P of a $25,000 per year pension after t years of 4% inflation can be modeled by…

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Q: A kite 120 feet above the ground is being blown away from the person holding its string parallel to…

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Q: Let f(x) = 3x + 3 and g(x) = −3x - 3. Compute the following. (a) (fog)(x) (b) (c) (d) (fog)(8)…

A: Let .To compute the following:

Q: 12. 57%/6 sec (2x) tan (2x) dx 0

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Q: 33. Let f(x) = ax²+bx+c, a ‡0. Show that f has a local maximum at x = -b/(2a) if a 0.

A: The objective of this question is to prove that the function f(x) = ax^2 + bx + c, where a ≠ 0, has…

Q: Find the values of the trigonometric functions of t from the given information. sin(t) sec(t) < 0…

A: Given,.

Q: g (t) = = 3+t+t² √t

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Q: Find Ax and the values to be evaluated for L4 on the interval [13, 33]. Ax = 5 L4 Endpoints: 13, 18,…

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Q: 7. DETAILS SPRECALC7 7.2.017. Use an Addition or Subtraction Formula to write the expression as a…

A: Let,.We know that,

Q: 283. ys (1 − µ³) 3/2 dy -

A: By using a suitable change of variables to determine the following indefinite integral.

Q: 2. Consider a function g(x, y, z) = 1 + ln(3x + 6y +9z) and a vector u = (0, -1, 1). (a) Find the…

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Q: 77. y = cos.x, y = - sinx, x = 0, x = 1/

A: y=cos⁡x,y=−sin⁡x,x=0,x=π2

Q: Find a function f that has the derivative f '(x) and whose graph passes through the given point.…

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Q: If f(x) = cos(x)²x, find f'(π/4)

A: f(x)=cos(x)2x

Q: edback e average angular displacement is given by the slope of the secant. We calculate f(0.2) and…

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Q: r(t)= (cos t, sin t, t). Find the speed of the curve and its length function, s(t), the length of…

A: The objective of the question is to find the speed of the curve and its length function, s(t), for…

Q: Consider the following. 47 3 (a) Find the reference number t for the value of t. t= t = (b) Find the…

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Q: A coin is tossed 9 times. What is the probability of getting heads exactly one time? Round your…

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Q: Solve each equation for x by converting to exponential form. In part (b), give two forms for the…

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Q: Find all possible functions with the given derivative. f'(x) = x5 f(x) =

A: Given function

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Q: 16. Prove by induction on n that 1 Σi(i+1) i=1 for all positive integers n. n i(i+1) n+1'

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Q: Find the accumulated present value of an investment over a 7 year period if there is a continuous…

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Q: Determine all solutions of the given equation. Express your answer(s) using radian measure. (Select…

A: Given equation 2tan2x +sec2x -2=0 Using identity sec2x =1+tan2x, we get2tan2x + 1+tan2x -2=0

Q: Consider the following. (Round your answers to four decim f(x, y) = yex (a) Find f(2, 1) and f(2.8,…

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Q: Sketch each of the following cardioids. Then compute the length of each curve 1. r = 2+2cosθ

A: Since you have asked multiple questions in a single request so we will be answering only first…

Q: Explain why an exponential or logarithmic function would not be used to model the graph from…

A: An exponential or logarithm function cannot model the graph, because the graph is not monotonic.

Q: 8. Evaluate the integral. 장 T x + 1 x2 + 2x -dx

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Q: Footballs are made using a four-step process. In the stamping step, the leather is cut and stamped…

A: This is question of calculus appliedhere we have to find worker using given detail further…

Q: The equation of the hyperbola that has a center at (4, 10), a focus at (-1,10), and a vertex at…

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