Calculus question and answers for July 02, 2023
- Q 3The surface area S (in square meters) of a hot-air balloon is given by S(r) = 4x where r is the radius of the balloon (in meters). If the radius...
- Q Calculate the Taylor polynomial T4 centered at x = 1 for the function f(x) = ?x.
- Q The domain of a one-to-one function f is [7,00), and its range is [-7,00). State the domain and the range of f1.What is the domain of f?1The domain of f...
- Q Write the expression as a single logarithm.82 log?6x-1-log 6 6 (3X82 log6?6x-1-log 6 0 ( 1 )X(Simplify your answer.)+ log 68+ log 68=
- Q 1. Unlike savings accounts, banks expect people to make frequent withdrawals and deposits to checking accounts. (2 pts.)TrueFalse
- Q A traveler pulls a suitcase, as shown in the figure.LLLL0The force acting on the handle is 30 N at an angle of 8 = 40. How much work is done...
- Q 2. Banks and other financial institutions offer incentives for people to keep their money in a savings account. (2 pts.)TrueFalse
- Q 7. (a) Determine such a < 0 so that the forward Euler method with step h = 0.1 is stablwhen applied to solve(3+7 10 marks)(b) Determine for which values of...
- Q Indicate whether the following table specifies a function.Domain4812Range235Choose the correct answer below.OA. The table specifies a function.OB. The table does not specify a function.
- Q Complete the table.y = f(g(x))2x9y = sinU=u = g(x)y = f(u)y = sin u
- Q Banks and credit unions are the only types of financial institutions.O TrueOFalse
- Q Checks can be used to: (4 pts.)O pay billsOpay rentOmake purchasesall of the above
- Q C9 Consider the plane in R with vector equation1+S2+t1s,teR(a) Find parametric equations for the plane.(b) Use the parametric equations you found in (a) tofind a scalar equation for the plane.
- Q A railroad crew can lay 5 miles of track each day. They need to lay 135 miles of track. The length, L (in miles), that is left to lay after...
- Q Convert the Cartesian coordinate (4,5) to polar coordinates, 0 ? 0 < 2?r =Enter exact value.0 =
- Q . (4 pts) The volume of a sound, in decibels, is given by D = 10 logwhere I is the intensity10-1in watts per square meter. What is the volume, in...
- Q Express the vector t as a linear combination of the vectors u, v, and w.12THHH- 20. u= -4 V= 0 W = -351t=t=027Qu+v+CW15
- Q Aldo spends $16 each time he travels the toll roads. He started the month with $240 in his toll road account. The amount, A (in dollars), that he has left...
- Q (d) For any two vectors u and v in R, u xv||?|u||||v||.TrueFalseJustification:
- Q Which of the following represents vector w = -45i + 28j in trigonometric form? Round 0 to the nearest degree.Ow= 53cos 32i + 53sin 32jOw= 53cos 148i + 53sin 148jw...
- Q Solve the following system of equations.= 2X+ y + z2x + 5y + 2z-x+6y-3z =-108Select the correct choice below and, if necessary, fill in the answer boxesto complete your choice.OA....
- Q Write the vector, parametric, and symmetric equations of the line passing throughA(-1, 4, 1) and B(-1, 7, -2).
- Q The reference angle of 239 degrees is __________ degrees.The reference angle of 342 degrees is __________ degrees.The reference angle of -136 degrees is _________ degrees.
- Q Use your calculator to evaluate cos-(0.53) to at least 3 decimal places. Give the answer in radians.
- Q A rectangular pool table centered at the origin has a width of 4 ft. and a length of 8 ft., with pockets at each of the four corners of the...
- Q The cost of a can of Coca Cola in 1960 was $0.10. The function that models the cost of a Coca Cola can by year is C(t) = 0.10e??????? ,...
- Q What is the range of the data?What percentage of data is below upper quartile?What percentage of data is located between the lower quartile and the median?What percentage of data is...
- Q Find sin(2x), cos(2x), and tan(2x) from the given informationsin(x)=8/17 , x in quadrant IA)sin(2x)B)cos(2x) =C)tan(2x)
- Q The driver of a car travelling at 45 km/h applies the brakes 50 m from a crosswalk. Assuming the driver applies a constant braking deceleration; find the deceleration required to...
- Q You take a group of 20 people to the movies, Kids' tickets cost $ 4.- each, and adults tickets cost $ 6.- each. Your total cost is $ 96.- ....
- Q Dylan invested $700 in an account paying an interest rate of 1(3/4) % compounded quarterly. Sebastian invested $700 in an account paying an interest rate of 1(1/4)% compounded daily. After...
- Q Suppose sin 2x=-(3^-2)/2Find all solutions 0 ?x ? 2?. Give exact values in radians, and type "pi" for ?.x=2?/3, 5?/6, 5?/3,11?/6 (If there is more than one answer, enter the...
- Q What are all the solutions to the equation sin 2x = 2cos x in the interval [0, 2?)?{n}{0, ?}{?/2}{?/2, 3?/2}
- Q A formula of order 4 for approximating the first derivative of a function f gives:f'(0) ? 4.50557 for h = 1f'(0) ? 2.09702 for h = 0.5By using Richardson's extrapolation...
- Q Vector has a magnitude of 3 units and it creates an angle of 160 with the positive x-axis. Find the magnitude and direction of 5?. Give the direction as an...
- Q Given vector a = (4, -2, 3) and b= (0,3,-5) find:1. lal2. a * b3. the angle between a and b4. la x blBlank #1Blank #2Blank #3Blank #4
- Q Solve the inhomogeneous equation ?u = -f in an infinite cylindrical region for zero boundary conditions (of first or second kind) and construct the...
- Q Given the complex numberz? = 30( cos 23?/12 + i sin 23?/12) and z? = 5( cos 19?/12 + i sin 19?/12), express the result of z?/z? in rectangular form...
- Q Let 0.02x+1.02 if x< -1 f(x)= -1.4x-4.4 if x> -1 ...
- Q Vector v has a magnitude of 3 units and it creates an angle of 160 with the positive x-axis.Find the magnitude and direction of 5v.Give the direction as an angle...
- Q Determine the equation of the plane that contains the point A(-2, 2, 3) and the line r = m(2, -1,7), m ? R
- Q Determine a vector equation for the plane containing the points O(0,0,0), A(-1,2,5), and C(3, -1, 7).Determine a vector equation for the plane containing the pointsP(-2, 2, 3),Q(-3, 4, 8), and...
- Q Determine parameters corresponding to the point P(5,3, 2), where P is a point on the plane with equation?:r= (2,0,1) + s(4, 2, -1) + t(-1, 1, 2), s, t?R.b. Show...
- Q (1) Determine two pairs of direction vectors that can be used to represent the xy-plane in R .(2) Write a vector and parametric equations for the xy-plane...
- Q A plane passes through the points P(-2, 3,1), Q(-2,3, 2), and R(1, 0, 1).(a) Using PQ and PR as direction vectors, write a vector equation for this plane.(b) Using QR...
- Q A plane has 7 = (-3, 5, 6) + s(-1, 1, 2) + v(2, 1, -3), s, v?R as its equation.a. Give the equations of two intersecting lines that lie...
- Q Let f(3) = ?|x - 1|.Determine the following function value. Enter DNE if the function is undefined at x = 1.f(1) = ______
- Q The function given by f(x) = cos x is(A) Decreasing in (0, 2?)(B) Increasing in (0, 2?)(C) Neither increasing nor decreasing in (0, 2?)(D) Increasing in (0, ? )
- Q Run a regression analysis on the following data set with y as the responseWhat is the predicted value of the response variable when x = 74.5?y=Round to 1 decimal place.
- Q Given the ellipse (x - 3)/25 + (y - 4)/36 = 1Find the center point: List the vertices (separated by a comma):
- Q Suppose sin ? = 8/17, cos ? = -15/17sin(2?) = ________cos(2?) = _________
- Q The center of the conic section with the equation x +(y+1)/=1 is 64(A) (-1,0)(B) (0, -1)(C) (0, 1)(D) (1,8)(E) (8,1)
- Q The center of the conic section with the equation x + (y+1)/64 =1 is;(A) (-1,0)(B) (0, -1)(C) (0, 1)(D) (1,8)(E) (8,1)
- Q If point P has rectangular coordinates (-8, -6), one possible pair of polar coordinates for P is:(A) (10,37)(B) (10, 53)(C) (10, 217)(D) (10, 233)(E) (10, -307)
- Q The line with vector equation 1 = (2,0, 1) + s(-4,5,5), S?R, lies on the plane T, as does the point P(1, 3, 0). Determine the Cartesian equation of T.
- Q A toy manufacturer builds three holiday-themed toys, A, B, and C, and keeps track of the sales of these three toys over the first three weeks of December. The matrix...
- Q A plane contains the point A(2, 2, -1) and the line 1 = (1, 1,5) + s(2, 1, 3),S?R. Determine the Cartesian equation of this plane. no containing the point...
- Q For sin2x + cosx = 0, use a double-angle or half-angle formula to simplify the equation and then find all solutions of the equation in the interval [0, 2?).The answers...
- Q Algebra 1 x x 1Calculate (a) Spectral decomposition of the matrix(b) Rank-1 approximation of the matrix
- Q Which of the following transformation creates a figure that is similar (but not congruent) to the original figure?(A) Translation(B) Rotation(C) Dilation
- Q Determine the Cartesian equation of the plane containing the point (-1, 1, 0) and perpendicular to the line joining the points (1, 2, 1) and (3, -2, 0). Evoloin the...
- Q Determine the angle between the planes x + 2y 3z 4 = 0 and x + 2y 1 = 0.b. Determine the Cartesian equation of the plane that passes through...
- Q What is the value of k that makes the planes 4x + ky 2z + 1 = 0 and 2x + 4y z + 4 = 0 parallel?b. What is...
- Q The function f(x) is defined by the rule "add 3, multiply by 2, and square root". Howis the inverse, f(x), defined?a) Square, divide by 2, and subtract 3.Ob) Square root,...
- Q The table provides various values, including all minimums and maximums, of a cosine function f(x) on the interval [0, ?). Angle 0 ?/4 7?/12 ...
- Q The three non collinear points P(-1, 2, 1), 2(3, 1, 4), and R(-2, 3, 5) lie on a plane.a. Using PQ and QR as direction vectors and the point R(-2,...
- Q Point P lies on the unit circle in the first quadrant at angle 8 shown below, and has coordinates (a, b).a. Kiara says that b = ?1-a. Do you agree...
- Q What is the magnitude of the vector 8i - 15j?(A) - 7(B)?23(C) 7(D) 17(E) 23
- Q If Matrix A is given by A =B could be4-6(A)-2 4(B)(C)-2 43]4624and the product Matrix AB is given by AB =-64(D)1(E) Matrix B cannot be determined by the information given.10then...
- Q 10. The asymptotes of the hyperbola with the equation(x^2)/4-(y^2)/25=1(A) y =(4/25)x(B) y =(25/4)x(C) y = (2/5)x(D) y =(5/2)x(E) y =x
- Q In ?ABC, side a=25, side b=30, and side c=45. The measure of ?C to the nearest degree is:(A) 132(B) 109(C) 71(D) 39(E) 32
- Q The center of the sphere given by the equation x + y + z = 20(A) (4, 0, -10)(B) (2, 0, -5)(C) (0, 0, 0)(D) (-2, 0, 5)(E) (-4, 0,...
- Q Which of the following points is NOT the same point as the polar coordinate point (8, ?/6)?(A) Rectangular coordinates: (4?3, 4)(B) Polar coordinates: (8, 30%)(C) Polar coordinates: (8, 390)(D) Polar...
- Q -> -> -> -> -> ->The sum of v = 4 j - 6 k and w= -i - 2 k...
- Q Let X and Y be independent and Cauchy distributed. Show that (X+Y)/2 also has a Cauchy distribution.
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