Basic Math question and answers for August 14, 2023
- Q Find the exact volume of the solid obtained by rotating theregion { (x, y) : 4 ≤ x ≤ 6; √8x ≤ y ≤ x^2 } aboutthe line x =...
- Q A canned soup company wishes to design an optimal can for makinga profit. The cost of the tin used for the can is 5 cents per cm^2.Suppose each can must...
- Q Use the product rule or quotient rule, as appropriate, tocompute each of the following derivatives:A. sin^2(x)B. sin(x) cos(x)C. sec(x) tan(x)D. x^2ln(x)E. xtan(x)
- Q A ball of radius 17 has a round hole of radius 7 drilled throughits center. Find the volume of the resulting solid.
- Q Show that this function has a positive maximum on the interval0<_x_<1:f(x)=x(x-1)e^x
- Q Approximate the arc length of the curve over the interval usingSimpson’s Rule SN with ?=8. ?=2?^(−?^2), on ?∈[0,2] (Use decimalnotation. Give your answer to four decimal places.) ?8≈
- Q In the following problems provide a complete explanation of whyit is true(1) Letnbe an integer. Justify the followingstatements.(a) The last digit ofnis even if and only ifnisdivisible by 2.(b) The...
- Q Find the largest volume V = xyz of a box for which the point (x,y, z) is on the ellipsoid x^2 + 4y^2 + 16z^2 = 48
- Q Consider the tetrahedron with vertices A= (0;1;1); B= (4;0;1);C=(2;1;3), and D= (2;2;0). a) What is the area of the parallelogramspanned by vector AB and vector AD? b) Determine the angle...
- Q Do a news search on coronavirus, specifically the mathematicalmodeling of its spread. Explain how the mathematics we are studyingapplies to this modeling.
- Q Use Lagrange multipliers to find the point on the plane 2x + y +2z = 6 which is closest to the origin
- Q 1a.Find the equation of the tangent plane to the surface √ x +√y + √ z = 4 at P(1, 1, 4).1b.Let f be a function of x and y...
- Q Verify the Divergence Theorem for the vector field and region:?=〈9?,3?,8?〉 and the region ?2+?2≤1, 0≤?≤8 ∬s F * ds = âˆrdiv(?)??=
- Q A tank contains 2340 L of pure water. A solution that contains0.07 kg of sugar per liter enters a tank at the rate 9 L/min Thesolution is mixed and drains...
- Q (1 point) The temperature at a point (x,y,z) is given by?(?,?,?)=200?−?2−?2/4−?2/9, where ? is measured in degrees Celsiusand x,y, and z in meters. There are lots of places to make...
- Q II. Free Response. Please show all work to receive full credit.Take the derivatives of the following functions, using anymethod.a. If f(x)=8-(6)/(\sqrt(x))+(10)/(x^(2)) , find f'(x).b. If g(x)=(2-x)^(79), find g'(x).c. If h(x)=(x^(3)+7x-1)(5x+2),...
- Q 8.All the real zeros of the given polynomial are integers. Findthe zeros. (Enter your answers as a comma-separated list. Enter allanswers including repetitions.)P(x) = x3 + 6x2 − 32x =Write...
- Q 1- Use calculus to find the absolute maximum and minimum valuesof the following functions on the given intervals. Give youranswers exactly and show supporting work.f(x) = (7x − 1)e^−2x on...
- Q FInd the limit.2a) lim (x,y)-->(0,0) (-5x^2)/(2x^2+3y^2)2b) lim (x,y)-->(0,0) tan(x^2+y^2)arctan(1/(x^2+y^2))2c) lim (x,y)-->(2,4) (y^2-2xy)/(y-2x)
- Q Find the coefficients for expanding y=1 in a Fourier seriesover the interval [-1,1].Find the coefficients for expanding y=x in a Fourier seriesover the interval [-1,1].
- Q 4. When the ticket price for a concert at the opera house was$50, the average attendance was 4000 people. When the ticket pricewas raised to $52, the average attendance was...
- Q There are two main ways to describe how loud a sound is. One isthat you can describe its intensity, I, measured in W/m2, which isthe amount of energy per unit...
- Q 1. y = 2x3 - 3x + 1 [-2,2]2. y = 7 - x2 [-1,2]3. y = ex [0,ln4]for each of the following 1-3, is the instantaneous rate ofchange equal...
- Q 4 parts following these instructionsFind the critical numbers for f and the open intervals on whichf is increasing (decreasing)For the first question, your answer should be a comma-separatedlist of x...
- Q for parts 1-2 foruse these answers/rulesFind the relative extrema of the function Specifically:The relative maxima of f occur at x =The relative minima of f occur at x =The value...
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