Calculus question and answers for July 01, 2023
- Q Use a calculator to perform the indicated operation. Give the answer in rectangular form.(4 cis 2? 9)2(Type your answer in the form a + bi. Use integers or decimals for...
- Q Summarize the pertinent information obtained by applying the graphing strategy and sketch the graph of f(x) = x+6/x-6Find any vertical asymptotes of f(x). Select the correct choice below and, if...
- Q Use elimination to solve the system of equations. Identify the system as consistent or inconsistent. If the system is consistent, state whether the equations are dependent or independent.5x+y = -37x-3y=-35Select...
- Q (1 point) A ferris wheel is 28 meters in diameter and makes one revolution every 8 minutes. Suppose you board the ferris wheel at ground level when time is t...
- Q Suppose that triangle ABC is a right triangle with a right angle at C and hypotenuse c. Also note that a is the length of the side opposite angle A...
- Q A lemonade recipe calls for 1/4 cup of lemon juice for every 1 cup of water.How many cups of water would be needed if you used 1 cup of lemon...
- Q Find the volume of the given solid. enclosed by the paraboloid z = x + y2 + 1 and the planes x = 0, y = 0, z = 0,...
- Q Find the average value of f over the given rectanglef(x, y) = 4xy, R has vertices (-1,0), (-1, 4), (1, 4), (1, 0)favg=
- Q A company markets exercise DVDs that sell for $14.95, including shipping and handling. The monthly fixed costs (advertising, rent, etc.) are $14,630 and the variable costs (materials, shipping, etc.) are...
- Q Find the interest earned when $22825 is invested at 6% compounded continuously for 5 years. Round the answer to the nearest cent.A. $14,804.52B. $15,885.06C. $1,566.87D. $7,985.53
- Q Rewrite each equation as requested.(a) Rewrite as an exponential equation.log3 1/81 = -4(b) Rewrite as a logarithmic equation.8 = 64
- Q The amount of money, A(t), in a savings account that pays 3% interest, compounded quarterly for t years, with an initial investment of P dollars, is given byAt =P[1+ 0.03/4)^4tIf...
- Q In a frame of three-dimensional space, the coordinates of the points O, A, B and C as well as vector ? are:0= (0,0,0)A= (1,2,3)B= (8,6,7)C= (-2,1, 8)? = (-3.4, -1)a)...
- Q Solve for t to two decimal places.4 = e^0.08t
- Q Given a RIGHT triangle with one LEG measured 5m in length, and its LONGEST side is 6m; find the measure, in degrees, of the SMALLEST of the 3 angles in...
- Q Of all points (x,y,z) that satisfy x + 4y + z = 24, find the one that minimizes (x-1) + (y-1)+(z-1)The given function has a minimum at which satisfies x...
- Q Solve x- 2x - 4x + 8 = 0 by factoring by grouping.Smaller x =Larger x =
- Q Use long division to find the quotient and remainder.(-x +11) (x + 2)What is the quotient?What is the remainder?
- Q Find the maximum volume (in cubic units) of a rectangular box that is inscribed in a sphere of radius r units.cubic units
- Q Find the extreme values of f subject to both constraints. (If an answer does not exist, enter DNE.)f(x, y, z) = yz + xy; xy = 1, y + z...
- Q Find any points on the hyperboloid x - y - z = 1 where the tangent plane is parallel to the plane z = 4x + 4y. (If an answer...
- Q f(x, y) =x/y , P(8, 1), u = 3/5i +4/5 j(a) Find the gradient of f.Vf(x, y) =(b) Evaluate the gradient at the point P.Vf(8, 1) =(c) Find the rate...
- Q A water sprinkler sends water out in a circular pattern. Determine how large an area is watered. The radius of watering is 24 ft. Use 3.14 for ? .The area...
- Q Given a triangle with a leg of 8 km and hypotenuse 22 km, find the missing side.The length of the missing side is km.(Round to the nearest thousandth.)
- Q Solve the following equation.x? - 4x - 32 = 0
- Q Factor the following expression completely: 6z +z-1=
- Q Use the distributive property to multiplya. -6(4x - 2x - 11)b. x(x? + 8x - 11)c. 2x (2x-x-3)d. x (3x-8x - 6x)
- Q Solve logarithmic equation graphicallylog? (x + 1) - log? (x - 2) = 1
- Q Solve the following equation.x? - 81 = 0
- Q A value of sinh x or cosh x is given. Use the definitions and the identity cosh x - sinh x = 1 to find the value of the other...
- Q Rewrite the expression as an equivalent expression functions greater than 1.8 cos2x
- Q Use a half-angle formula to find the exact value of the expression.COS 5?/12
- Q Consider a ferris wheel that measures 400ft in diameter and spins at a constant speed completing a rotation once every 30 minutes. Assume you board the ferris wheel at the...
- Q Let . a,? Z[i] with prime. Prove that if ?|a, then 7 and a are relatively prime.Let , a. ? Z[i] with prime. Prove that if ?| a, then ?a...
- Q Find the position and velocity vectors of a particle that has the given acceleration and the given initial velocity and position: a(t) = tj + tk, v(1) = 5j, and...
- Q Find the equation of the plane that passes through the points (2, 2, 1) and (-1, 1, -1) and is perpendicular to the plane 2x - 3y + z =...
- Q Sketch the plane curve r(t) = ti+tj and the vectors T(t) and N(t) when t = 1.(Do NOT try to find T(t) and N(t)).Find the scalar tangential component of acceleration...
- Q Find an equation of the normal plane to a = sin(2t), y = cos(2t), z = 4t at the point (0, 1, 2?).
- Q (a) Find the point at which the given lines intersect.r = (3, 2, 0) + t(2, -2, 3)r=(5, 0, 3) + s(-2, 2, 0)(x, y, z) =(b) Find an equation...
- Q Find two unit vectors that are orthogonal to both (5, 3, 1) and (-1, 1,0).
- Q Evaluate the Riemann sum for f(x) = ln(x) - 0.7 over the interval [1, 5] using eight subintervals, taking the sample points to be midpoints.
- Q Find the scalar equation of the plane that contains the point (2,-1,5) as well as the line (x,y,z) = (1,2,3) + t(3,4,-3)
- Q Show all work and upload a file to complete the following:Given that f = 3/1+x and g = 3x - 4,a) Find the composite function, f.gb) Determine the domain of...
- Q What is the radius of a circle in which an angle of 3 radians cuts off an arc length of 30 cm?
- Q Evaluatelog3 54/log162 3 - log3 486/log18 3
- Q From Times Square in New York City, you can see Central Park and the Empire State Building. The approximate distance from Times Square to Central Park is 2 miles, Central...
- Q Prove by definition that {(x,y,z)| x +2-6z=0} is a C^? surface.
- Q Find a second-degree polynomial P such that P(3) = 17, P'(3) = 14, and P"(3) = 6.P(x) =
- Q Graph the curve with parametric equations x = sin(t), y = 3 sin(2t), z = sin(3t).
- Q At what point on the curve x = t, y = 6t, z = t4 is the normal plane parallel to the plane 6x +12y - 8z = 3?
- Q Suppose a = 11 and b = 6.Find an exact value or give least two decimal places:tan (A) =sec (A) =csc (A) =cot (A) =
- Q Find the length of the curve correct to four decimal places. (Use your calculator to approximate the integral.)r(t) = (sin(t), cos(t), tan(t)), 0?t??/4.
- Q Find the curvature of r(t) = (7t, t, t) at the point (7, 1, 1).
- Q Find the equation of the plane through (3, -1, 2), (4, 0, 2), and (5, 3, 1).
- Q Solve the following quadratic inequality: 3x + 5x ? 2 ? 0Write your answer in interval notation.
- Q Evaluate the following expressions. The answer must be given as a fraction, NO DECIMALS. If the answer involves a square root it should be entered as sqrt. For instance, the...
- Q Solve: |4x-8| > 1Give your answer as an interval.Note: Type oo for the infinity symbol ? and U for the union symbol U.
- Q Use the hal zeros theorem to list all possible rational zeros of the following.f(x)= 10x + 6x + 8x + 4Be sure that no value in your list appears more...
- Q The y-coordinate of a particle in curvilinear motion is given by y-8.71-13.5t, where y is in inches and t is in seconds. Also, the particlehas an acceleration in the x-direction...
- Q Determine if the specified linear transformation is (a) one-to-one and (b) onto. Justify your answer.T(X?X2 X3 X4) = (0,X3 +X4X3 X4 X3 X4)a. Is the linear transformation one-to-one?1000OA. T is...
- Q Find all y-intercepts and x-intercepts of the graph of the function.f(x) = -x - 2x+48If there is more than one answer, separate them with commas.Click on "None" if applicable.y-intercept(s):x-intercept(s):None0/0X0/60,0,...53/6?
- Q Find a vector equation and parametric equations for the line. (Use the parameter t.)the line through the point (8, -5, 6) and parallel to the vector (1, 3, -2/3)r(t) =(x(t),...
- Q Let P be a point not on the line L that passes through the points Q and R. The distance d from the point P to the line L isd=la...
- Q Determine whether the lines L? and L? are parallel, skew, or intersecting.L?: x = 9 + 6t, y = 12 - 3t, z = 3 + 9tL?: x = 3...
- Q Find parametric equations for the line. (Use the parameter t.) the line through (3, 3, 0) and perpendicular to both i + j and j + k(x(t), y(t), z(t)) =...
- Q . If * x (x z) = (xy) xz, then which of the following option is correct ?(a) x and y are collinear.(b) and z are collinear.(c) y and z...
- Q (5 points) Let V be a vector space over some field Fa) (3 points) Let W be a subspace of a vector space V. Suppose x, y V are not...
- Q A Ferris wheel rotates 2852 per ride. How far would a rider seated 8 feet from the center of the Ferris wheel travel during the ride?Round your answer to the...
- Q A jet airliner, flying initially 300 mi/hr due east, suddenly enters a region where the wind is blowing 100 mi/hr, pushing the aircraft in the direction 30 north of east....
- Q Use the ? - ? definition of limit to show that lim z?1+i (2z + 3i) = 2 + 5i.
- Q Graph the parabola. y=x + 4x+7 Plot five points on the parabola: the vertex, two points to the left of the vertex, and two points to the right of the...
- Q Consider the following functions. f?(x) = x, f?(x) = x, f3(x) = 5x - 4x g(x) = c1f1(x) + c2f2(x) + c3f3(x) Solve for C1, C2, and C3 so that...
- Q For the polynomial below, - 1 is a zero.g(x)=x + 5x + x - 3Express g (x) as a product of linear factors.
- Q Divide.(-2x4-12x-4x +15x+18) (-2x+4)Write your answer in the following form: Quotient +
- Q Suppose you deposit $5000 at 3% interest compounded continously. Find the average value of youaccount during the first 4 years.
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