Calculus question and answers for July 01, 2023
- Q Zachary wants to build a rectangular pen for his animals. One side of the pen will be against the barn; the other three sides will be enclosed with wire fencing....
- Q At the movie theatre, child admission is $5.80 and adult admission is $8.90. On Tuesday, 163 tickets were sold for a total sales of $1246.10. How many adult tickets were...
- Q Find a plane through the points (-3, 7 ,-4), (-3, -1, 8), (3, 1, -3).
- Q A person standing close to the edge on top of a 28-foot building throws a ball vertically upward. The quadratic function h = - 16t + 108t + 28 models...
- Q Use the Pythagorean identity to find cos x.sin x = 9/13cos x=
- Q Find all solutions of the system of equations. (If there is no solution, enter NO SOLUTION.)xy = 24{ 2x2.(x, y) =(x, y) =- y + 4 = 0(smaller x-value)(larger x-value)
- Q In Exercises 7-10, find the slope of the line passing through the pair of points. Then use a graphing utility to plot the points and use the draw feature to...
- Q In a solar system, two comets pass near the sun, which is located at the origin. Comet E is modeled by (Y+162(y+13) x21, where all measurements are in astronomical units.Part...
- Q In how many ways can the expression a b c be rewritten as a product without exponents?
- Q Assume A and B are independent events with P(A) = 0.9 and P(B) = 0.6. Find (a) P(A n B), (b) P(AUB), (c) P (A' B'), (d) P (A'NB), and...
- Q Use the Test for Independence to determine if events A and B are independent.P(A)=0.5, P(B) = 0.8, P(An B) = 0.3Choose the correct answer below.A. Events A and B are...
- Q Find r and a? for the geometric sequence with a?= 2 and a?= 1/16r= ____ (Simplify your answer.)
- Q Find all solutions of the equation 2sinx - cos x =1in the interval [0, 2?) with x1 < x2 < x3.The answers areX1 = ______x2 = ______x3 = ______
- Q Use the tangent identity to find tan x.sin x = 2?10/7 COS X = 3/7tan x =
- Q The plane containing the point (7,-7,6) and parallel to the plane 2x+8y-5z=3 has equation Ax+By+Cz=D.If A=2 find the following:B = __________________C = __________________D = __________________
- Q Calculate the Fourier Transform in ContinuousDomain (CFDF) of the following signs:15 f(t) = e??tu(t)cos 3t=
- Q For what values of a and b will make the two complex numbers equal?5-2i = 10a + (3 + b)i
- Q Find t for the following terminal points, 0 < t < 2?(a) P(0, 1), t =(b) P ( - V2/2 , V2/2),t=(c) P(-1,0), t =(d) P ( - V2/2, -...
- Q Given p with magnitude of 40 and a direction of 25, q with magnitude of 75 and a direction of 270, and r with magnitude of 30 and a direction...
- Q If vector r = <4, 6> and s= <8, -3> then which is r-s?
- Q Solve 2x-3x-11x <-6. Include an Interval Chart/Number Line.
- Q The magnitude and direction of vectors t, u, and v are shown in the table.Vector Magnitude Directiont 7 ...
- Q Vector u has a magnitude of 30 and a direction of 70. Vector v has a magnitude of 40 and a direction of 220. What is the direction of u...
- Q Rewrite the expression without the log of a product, power or root.log?(x? ?y?) =_______________
- Q Match the words with their definition.1. simple interest2. principal3. compound interesta. When you deposit money into a savings accountb. interest paid only on the principalc. the bank pays on the...
- Q Complete the square for the following in order to rewrite the equation of the conic in standardform. State any applicable characteristics, including center, vertex (vertices), focus (foci), directrixand/or equations of...
- Q a) Explain the difference between a positive angle and a negative angle. b) Consider the time 11:30 where the initial side is the hour hand and terminal side is the...
- Q Algebraically find the inverse of f(x) = 3 cos (2x), showing your steps. State the domain and range of both f(x) and f-(x).
- Q A club with nine members is to choose three officers: president, vice-president, and secretary-treasurer. If each office is to be held by one person and no person can hold more...
- Q Assume A and B are independent events with P(A) = 0.8 and P(B)=0.5. Find (a) P(A ? B), (b) P(AUB), (c) P (A' ? B'), (d) P (A'?B), and (e)...
- Q A 5-digit phone number cannot start with 0. Assume that there are no restrictions on the remaining 4 numbers. How many telephone numbers are possible in which all 5 digits...
- Q Let x be a continuous random variable with a standard normal distribution. Using the accompanying standard normal distribution table, find P(0 ?x?2.23).
- Q The population of a colony of rabbits grows exponentially. The colony begins with 10 rabbits; 5 years later there are 340 rabbits. Using your solution from question 19, find and...
- Q For the probability density function f defined on the random variable x, find (a) the mean of x, (b) the standard deviation of x, and (c) the probability that the...
- Q Your parents have a credit card with a balance of $2,748.56. The interest rate is 10.5% APR. A late payment fee of $40.00 is added to the principal if they...
- Q Solve AABC subject to the given conditions, if possible. Round the lengths of the sides and measures of the angles (in degrees) to 1 decimal place if necessary. Round intermediate...
- Q Suppose f(x) = 4* and g(x) = -3x - 2. Find a simplified formula for the function:h(x) = (g(f(x)))
- Q Solve the equation.8x+16=27x64/319/6O No solutionO {12}
- Q Write the linear function whose graph passes through the points(4, 5) and (2, 13).Write the answer in the form f(x) = mx + b.Do not enter any spaces in the...
- Q A test has many multiple-choice items, each with seven answer choices. A student receives 1 point for every correct answer, and each incorrect answer brings a penalty (loss) of a...
- Q Solve the equation for the unknown variable.3+(n-1)7=17
- Q Find the length and width of a rectangle that has perimeter 48 meters and a maximumarea.12 m; 12 m.16 m; 9 m.1m; 23 m.13 m; 11 m. 6 m; 18...
- Q A student was asked to prove the trigonometric identity tan1/2x + cot1/2x = 2cscx. Which of the following could be the first step in proving the identity?I. 1-cosx/sinx + 1-cosx/sinx...
- Q Which of the following identities is equal to sec??
- Q Find the area of the surface S, where S is the part of the paraboloidz 1 -x-y that lies above the plane z = -2.
- Q Find the directional derivative of the function f(x, y) = xe^-y at the point P(-2,0) in the direction v = (2, -3).
- Q Given f(x, y, z) = xy + yz + xz, P(1, 2, 4)I. Find Vf.II. Evaluate Vf at a point P.III. Find the maximum rate of change of f at...
- Q Find v*v for the given vector.v=-4i +2j + 4kSelect the correct choice below and fill in the answer box(es) within your choice.A. The answer is a vector. v*v = ai...
- Q Write the given rule as an equation using function notation. Find the output when the input is 1, 2, 3, and 4.Rule: raise 2 to the power of the input....
- Q Determine whether the following relation is a function.Input ...
- Q Solve the linear programming problem.MaximizeP = 40x+ 50ySubject to2x+y ? 16x+y ? 9x+2y = 14x, y ? 0What is the maximum value of P?Select the correct choice below and fill...
- Q Give the first four terms of the sequence.an = 3n+2 n
- Q Give the first four terms of the sequence.an = -(?7)n-1a1 =
- Q Find the common difference for the arithmetic sequence.{4, 12, 20, 28, 36,...}
- Q The first term of a geometric sequence is 5 and the common ratio is 3. Find the 6th term.
- Q The first four terms of a geometric sequence are given. Find a12.an = {3, -6, 12, -24,...}
- Q Find the first five terms of the arithmetic sequence given the first term and common difference.a? = ?35, d = -9
- Q Find the first term a? of the arithmetic sequence in which a9 = 23 and a17 = 95.
- Q The figure below is translated left 2 units. What are the coordinates of the image of point A after this transformation?
- Q What is the end behavior of the function f(x)=-1 4x?As a ??, f(x) ?-?As ?-?, f(x) ?-?As x??, f(x) ? ?As ?-?. f(x)?-?As x??, f(x) ? ?As x?-?, f(x) ?...
- Q Find the vertex, focus, and directrix of the parabola. Then sketch the parabola.(x + 5) + (y-2) = 0vertex (x, y) = (focus (x, y) = (directrix
- Q Figure N is the result of a transformation on Figure M. Which transformation would accomplish this?A reflection over the y -axis A reflection over the x-axisA translation 3 units up...
- Q Solve for x. If there is no solution, enter DNE.x 5 - 14x - 72x + 9 x + 3 x + 12x + 27
- Q Suppose f(x) = x + 4 and g(x) = x + 2. Calculate f(2)g(-3).
- Q Suppose f(x) = ?2x and g(x) = x2 2. Show that f(x) and g(x) are inverse functions using algebra.
- Q The vector < 18,5> has initial point (-10,-4).The terminal point of the vector is:
- Q The unit circle can alternatively be parametrized by the equations:x(t) = -t + 1 / t + 1y(t)= t + 1 / 2tEveryone point on the unit circle except (-1,0)...
- Q Where do the graphs of f(x) = cos(x/2) and g(x) = ?3-cos(x/2) intersect on the interval [0, 360)?
- Q Given the following information about two spherical tanks that are connected,calculate the work required to fill both tanks from the ground.The first tank: Radius = 1mThe second tank: Radius =...
- Q An archaeological site is to be made accessible for viewing by the public. To do this, archaeologists built two straight paths from point A to point B and from point...
- Q For the following exercises, plot the points.45. (-2, ?/3)46. (?1, -?/2)
- Q Identify the polar coordinate that is not equivalent to(-3,5?/6)a. (3,11?/6)b. (3 ,-?/6)c. (-3,-7?/6)d. (3,-5?/6)
- Q For the following function, one zero is given. Find the other zeros.P(x)=x-7x +7x+15; -1The other zeros are x =(Simplify your answers. Type an integer or a fraction. Use commas to...
- Q Determine the period of the following function.y = 3 sin 2(x + 90) - 1a) 180c) 720b) 360d) 1080
- Q Find a.b.|a| = 20, |b| = 70, the angle between a and b is 3?/4.
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