Calculus Volume 3
16th Edition
ISBN: 9781938168079
Author: Gilbert Strang, Edwin Jed Herman
Publisher: OpenStax
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Textbook Question
Chapter 4.5, Problem 230E
For the following exercises, find dv using partial dx
derivatives.
230. Sin
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Year Month Units1 Nov 42,1611 Dec 44,1862 Jan 42,2272 Feb 45,4222 Mar 54,0752 Apr 50,9262 May 53,5722 Jun 54,9202 Jul 54,4492 Aug 56,0792 Sep 52,1772 Oct 50,0872 Nov 48,5132 Dec 49,2783 Jan 48,1343 Feb 54,8873 Mar 61,0643 Apr 53,3503 May 59,4673 Jun 59,3703 Jul 55,0883 Aug 59,3493 Sep 54,4723 Oct 53,164
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Chapter 4 Solutions
Calculus Volume 3
Ch. 4.1 - For the following exercises, evaluate each...Ch. 4.1 - For the following exercises, evaluate each...Ch. 4.1 - For the following exercises, evaluate each...Ch. 4.1 - For the following exercises, evaluate each...Ch. 4.1 - For the following exercises, find the domain of...Ch. 4.1 - For the following exercises, find the domain of...Ch. 4.1 - For the following exercises, find the domain of...Ch. 4.1 - For the following exercises, find the domain of...Ch. 4.1 - For the following exercises, find the domain of...Ch. 4.1 - For the following exercises, find the domain of...
Ch. 4.1 - Find the range of the functions. 11....Ch. 4.1 - Find the range of the functions. 12. V(x,y)=4x2+y2Ch. 4.1 - Find the range of the functions. 13. z=y2x2Ch. 4.1 - For the following exercises, find the level curves...Ch. 4.1 - For the following exercises, find the level curves...Ch. 4.1 - For the following exercises, find the level curves...Ch. 4.1 - For the following exercises, find the level curves...Ch. 4.1 - For the following exercises, find the level curves...Ch. 4.1 - For the following exercises, find the level curves...Ch. 4.1 - For the following exercises, find the level curves...Ch. 4.1 - For the following exercises, find the level curves...Ch. 4.1 - For the following exercises, find the level curves...Ch. 4.1 - For the following exercises, find the level curves...Ch. 4.1 - For the following exercises, find the level curves...Ch. 4.1 - For the following exercises, find the level curves...Ch. 4.1 - For the following exercises, find the level curves...Ch. 4.1 - For the following exercises, find the level curves...Ch. 4.1 - For the following exercises, find the level curves...Ch. 4.1 - For the following exercises, find the level curves...Ch. 4.1 - For the following exercises, find the vertical...Ch. 4.1 - For the following exercises, find the vertical...Ch. 4.1 - For the following exercises, find the vertical...Ch. 4.1 - Find the domain of the following functions. 33....Ch. 4.1 - Find the domain of the following functions. 34....Ch. 4.1 - Find the domain of the following functions. 35....Ch. 4.1 - Find the domain of the following functions. 36....Ch. 4.1 - Find the domain of the following functions. 37....Ch. 4.1 - Find the domain of the following functions. 38....Ch. 4.1 - For the following exercises, plot a graph of the...Ch. 4.1 - For the following exercises, plot a graph of the...Ch. 4.1 - For the following exercises, plot a graph of the...Ch. 4.1 - Sketch the following by finding the level curves....Ch. 4.1 - Sketch the following by finding the level curves....Ch. 4.1 - Sketch the following by finding the level curves....Ch. 4.1 - Sketch the following by finding the level curves....Ch. 4.1 - Sketch the following by finding the level curves....Ch. 4.1 - Sketch the following by finding the level curves....Ch. 4.1 - Find the level surface for the functions of three...Ch. 4.1 - Find the level surface for the functions of three...Ch. 4.1 - the level surface for the functions of three...Ch. 4.1 - Find the level surface for the functions of three...Ch. 4.1 - Find the level surface for the functions of three...Ch. 4.1 - For the following exercises, find an equation of...Ch. 4.1 - For the following exercises, find an equation of...Ch. 4.1 - For the following exercises, find an equation of...Ch. 4.1 - The strength E of an electric field at point (x....Ch. 4.1 - A thin plate made of iron is located in the...Ch. 4.1 - Refer to the preceding problem. Using the...Ch. 4.1 - Refer to the preceding problem. Find the level...Ch. 4.2 - For the following exercises, find the limit of the...Ch. 4.2 - For the following exercises, find the limit of the...Ch. 4.2 - For the following exercises, find the limit of the...Ch. 4.2 - For the following exercises, evaluate the limits...Ch. 4.2 - For the following exercises, evaluate the limits...Ch. 4.2 - For the following exercises, evaluate the limits...Ch. 4.2 - For the following exercises, evaluate the limits...Ch. 4.2 - For the following exercises, evaluate the limits...Ch. 4.2 - For the following exercises, evaluate the limits...Ch. 4.2 - For the following exercises, evaluate the limits...Ch. 4.2 - For the following exercises, evaluate the limits...Ch. 4.2 - For the following exercises, evaluate the limits...Ch. 4.2 - For the following exercises, evaluate the limits...Ch. 4.2 - For the following exercises, evaluate the limits...Ch. 4.2 - For the following exercises, evaluate the limits...Ch. 4.2 - For the following exercises, evaluate the limits...Ch. 4.2 - For the following exercises, evaluate the limits...Ch. 4.2 - For the following exercises, evaluate the limits...Ch. 4.2 - For the following exercises, complete the...Ch. 4.2 - For the following exercises, complete the...Ch. 4.2 - For the following exercises, use algebraic...Ch. 4.2 - For the following exercises, use algebraic...Ch. 4.2 - For the following exercises, use algebraic...Ch. 4.2 - For the following exercises, use algebraic...Ch. 4.2 - For the following exercises, evaluate the limits...Ch. 4.2 - For the following exercises, evaluate the limits...Ch. 4.2 - For the following exercises, evaluate the limit of...Ch. 4.2 - For the following exercises, evaluate the limit of...Ch. 4.2 - For the following exercises, evaluate the limit of...Ch. 4.2 - For the following exercises, evaluate the limit of...Ch. 4.2 - Discuss the continuity of the following functions....Ch. 4.2 - Discuss the continuity of the following functions....Ch. 4.2 - Discuss the continuity of the following functions....Ch. 4.2 - Discuss the continuity of the following functions....Ch. 4.2 - For the following exercises, determine the region...Ch. 4.2 - For the following exercises, determine the region...Ch. 4.2 - Show that the function approaches different values...Ch. 4.2 - Show that the function approaches different values...Ch. 4.2 - Create a plot using graphing software to determine...Ch. 4.2 - Determine the region of the xy-plane in which the...Ch. 4.2 - Determine the region of the xv-plane in which f(x....Ch. 4.2 - At what points in space g(x,y,z)=x2+y22z2...Ch. 4.2 - At what points in space is g(x,y,z)=1x2+z21...Ch. 4.2 - Show that (x,y)(0,0)lim1x2+y2 does not exist at...Ch. 4.2 - [T] Evaluate (x,y)(0,0)limxy2x2+y2 by plotting the...Ch. 4.2 - [T] a. Use a CAS to draw a contour map of z=9x2y2...Ch. 4.2 - True or False: If we evaluate (x,y)(0,0)limf(x)...Ch. 4.2 - Use polar coordinates to find (xy)(0,0)limsin x 2+...Ch. 4.2 - Use polar coordinates to find urn...Ch. 4.2 - Discuss the continuity of f(g(x. y)) where f(i) =...Ch. 4.2 - Given f(x. v) = x2-4y. find h0limf(x+h,y)f(x,y)h.Ch. 4.2 - Given f(x,y)=x24y find h0limf(1+h,y)f(1,y)hCh. 4.3 - Lord Kelvin and the Age of Earth Figure 4.25 (a)...Ch. 4.3 - Lord Kelvin and the Age of Earth Figure 4.25 (a)...Ch. 4.3 - Lord Kelvin and the Age of Earth Figure 4.25 (a)...Ch. 4.3 - For the following exercises, calculate the partial...Ch. 4.3 - For the following exercises, calculate the partial...Ch. 4.3 - For the following exercises, calculate the sign of...Ch. 4.3 - For the following exercises, calculate the sign of...Ch. 4.3 - For the following exercises, calculate the sign of...Ch. 4.3 - For the following exercises, calculate the sign of...Ch. 4.3 - For the following exercises, calculate the partial...Ch. 4.3 - For the following exercises, calculate the partial...Ch. 4.3 - For the following exercises, calculate the partial...Ch. 4.3 - For the following exercises, calculate the partial...Ch. 4.3 - For the following exercises, calculate the partial...Ch. 4.3 - For the following exercises, calculate the partial...Ch. 4.3 - For the following exercises, calculate the partial...Ch. 4.3 - For the following exercises, calculate the partial...Ch. 4.3 - For the following exercises, calculate the partial...Ch. 4.3 - For the following exercises, calculate the partial...Ch. 4.3 - For the following exercises, calculate the partial...Ch. 4.3 - Evaluate the partial derivatives at point P(O. 1)....Ch. 4.3 - Evaluate the partial derivatives at point P(O. 1)....Ch. 4.3 - Evaluate the partial derivatives at point P(O. 1)....Ch. 4.3 - The area of a parallelogram with adjacent side...Ch. 4.3 - Express the volume of a right circular cylinder as...Ch. 4.3 - Calulate wz for w=zsin(xy2+2z) .Ch. 4.3 - Find the indicated higher-order partial...Ch. 4.3 - Find the indicated higher-order partial...Ch. 4.3 - Find the indicated higher-order partial...Ch. 4.3 - Find the indicated higher-order partial...Ch. 4.3 - Find the indicated higher-order partial...Ch. 4.3 - Find the indicated higher-order partial...Ch. 4.3 - Find the indicated higher-order partial...Ch. 4.3 - Find the indicated higher-order partial...Ch. 4.3 - Find the indicated higher-order partial...Ch. 4.3 - Find the indicated higher-order partial...Ch. 4.3 - Find the indicated higher-order partial...Ch. 4.3 - Find the indicated higher-order partial...Ch. 4.3 - Find the indicated higher-order partial...Ch. 4.3 - Find the indicated higher-order partial...Ch. 4.3 - Find the indicated higher-order partial...Ch. 4.3 - Find the indicated higher-order partial...Ch. 4.3 - Find the indicated higher-order partial...Ch. 4.3 - Find the indicated higher-order partial...Ch. 4.3 - Find the indicated higher-order partial...Ch. 4.3 - Find the indicated higher-order partial...Ch. 4.3 - Find the indicated higher-order partial...Ch. 4.3 - Find the indicated higher-order partial...Ch. 4.3 - Find the indicated higher-order partial...Ch. 4.3 - Find the indicated higher-order partial...Ch. 4.3 - Find the indicated higher-order partial...Ch. 4.3 - Suppose the sides of a rectangle are changing with...Ch. 4.3 - A Cobb-Douglas production function...Ch. 4.3 - The apparent temperature index is a measure of how...Ch. 4.4 - For the following exercises, find a unit normal...Ch. 4.4 - For the following exercises, find a unit normal...Ch. 4.4 - For the following exercises, as a useful review...Ch. 4.4 - For the following exercises, as a useful review...Ch. 4.4 - For the following exercises, as a useful review...Ch. 4.4 - For the following exercises, as a useful review...Ch. 4.4 - For the following exercises, as a useful review...Ch. 4.4 - For the following exercises, find the equation for...Ch. 4.4 - For the following exercises, find the equation for...Ch. 4.4 - For the following exercises, find the equation for...Ch. 4.4 - For the following exercises, find the equation for...Ch. 4.4 - For the following exercises, find the equation for...Ch. 4.4 - For the following exercises, find the equation for...Ch. 4.4 - For the following exercises, find the equation for...Ch. 4.4 - For the following exercises, find the equation for...Ch. 4.4 - For the following exercises, find the equation for...Ch. 4.4 - For the following exercises, find the equation for...Ch. 4.4 - For the following exercises, find the equation for...Ch. 4.4 - the following exercises, find the equation for the...Ch. 4.4 - For the following exercises, find parametric...Ch. 4.4 - For the following exercises, find parametric...Ch. 4.4 - For the following exercises, find parametric...Ch. 4.4 - For the following exercises, find parametric...Ch. 4.4 - For the following exercises, find parametric...Ch. 4.4 - For the following exercises, find parametric...Ch. 4.4 - For the following exercises, use the figure shown...Ch. 4.4 - For the following exercises, use the figure shown...Ch. 4.4 - For the following exercises, use the figure shown...Ch. 4.4 - For the following exercises, complete each task....Ch. 4.4 - For the following exercises, complete each task....Ch. 4.4 - For the following exercises, complete each task....Ch. 4.4 - For the following exercises, complete each task....Ch. 4.4 - For the following exercises, complete each task....Ch. 4.4 - For the following exercises, complete each task....Ch. 4.4 - For the following exercises, complete each task....Ch. 4.4 - For the following exercises, complete each task....Ch. 4.4 - For the following exercises, complete each task....Ch. 4.4 - The centripetal acceleration of a particle moving...Ch. 4.4 - The radius r and height h of a tight circular...Ch. 4.4 - The base radius and height of a right circular...Ch. 4.4 - The electrical resistance R produced by wiring...Ch. 4.4 - The area of an ellipse with axes of length 2a and...Ch. 4.4 - The period T of a simple pendulum with small...Ch. 4.4 - Electrical power P is given by P = V2R where V is...Ch. 4.4 - For the following exercises, find the linear...Ch. 4.4 - For the following exercises, find the linear...Ch. 4.4 - For the following exercises, find the linear...Ch. 4.4 - For the following exercises, find the linear...Ch. 4.4 - For the following exercises, find the linear...Ch. 4.4 - [T] Find the equation of the tangent plane to the...Ch. 4.4 - [T] Find the equation for the tangent plane to the...Ch. 4.4 - [T] Find the equation of the tangent plane to the...Ch. 4.5 -
Ch. 4.5 - For the following exercises, use the information...Ch. 4.5 - For the following exercises, use the information...Ch. 4.5 - For the following exercises, use the information...Ch. 4.5 - For the following exercises, use the information...Ch. 4.5 - For the following exercises, use the information...Ch. 4.5 - For the following exercises, find dfdtusing the...Ch. 4.5 - For the following exercises, find dfdtusing the...Ch. 4.5 - For the following exercises, find dfdtusing the...Ch. 4.5 - For the following exercises, find dfdtusing the...Ch. 4.5 - For the following exercises, find dfdtusing the...Ch. 4.5 - For the following exercises, find dfdtusing the...Ch. 4.5 - Let w(x. v, z) = x + y + z, x = cos t, v = sin t,...Ch. 4.5 - Let z=x2y. where x=t2 and v=t2. Find dzdt .Ch. 4.5 - Let u=exsiny, where x=t2 and y=t . Find dudtwhen x...Ch. 4.5 - For the following exercises, find dv using partial...Ch. 4.5 - For the following exercises, find dydx using...Ch. 4.5 - For the following exercises, find dydx using...Ch. 4.5 - For the following exercises, find dydx using...Ch. 4.5 - For the following exercises, find dydx using...Ch. 4.5 - For the following exercises, find dydx using...Ch. 4.5 - For the following exercises, find dydx using...Ch. 4.5 - For the following exercises, find dydx using...Ch. 4.5 - For the following exercises, find dydx using...Ch. 4.5 - For the following exercises, find dydx using...Ch. 4.5 - For the following exercises, find dydx using...Ch. 4.5 - For the following exercises, find dydx using...Ch. 4.5 - For the following exercises, find dydx using...Ch. 4.5 - For the following exercises, find dydx using...Ch. 4.5 - For the following exercises, find dydx using...Ch. 4.5 - For the following exercises, find dydx using...Ch. 4.5 - For the following exercises, find dydx using...Ch. 4.5 - For the following exercises, find dydx using...Ch. 4.5 - For the following exercises, use this information:...Ch. 4.5 - For the following exercises, use this information:...Ch. 4.5 - For the following exercises, use this information:...Ch. 4.5 - The volume of a right circular cylinder is given...Ch. 4.5 - The pressure P of a gas is related to the volume...Ch. 4.5 - The radius of a tight circular cone is increasing...Ch. 4.5 - The volume of a frustum of a cone is given by the...Ch. 4.5 - A closed box is in the shape of a rectangular...Ch. 4.5 - The total resistance in a circuit that has three...Ch. 4.5 - The temperature T at a point (x. y) is T(x. y) and...Ch. 4.5 - The x and y components of a fluid moving in two...Ch. 4.5 - Let u = u(x. y, z). where x = x(w, t). y = (w. t)....Ch. 4.6 - For the following exercises, find the directional...Ch. 4.6 - For the following exercises, find the directional...Ch. 4.6 - For the following exercises, find the directional...Ch. 4.6 - For the following exercises, find the directional...Ch. 4.6 - For the following exercises, find the directional...Ch. 4.6 - For the following exercises, find the directional...Ch. 4.6 - For the following exercises, find the directional...Ch. 4.6 - For the following exercises, find the directional...Ch. 4.6 - For the following exercises, find the directional...Ch. 4.6 - For the following exercises, find the directional...Ch. 4.6 - For the following exercises, find the directional...Ch. 4.6 - For the following exercises, find the directional...Ch. 4.6 - For the following exercises, find the directional...Ch. 4.6 - For the following exercises, find the directional...Ch. 4.6 - For the following exercises, find the directional...Ch. 4.6 - For the following exercises, find the directional...Ch. 4.6 - For the following exercises, find the directional...Ch. 4.6 - For the following exercises, find the directional...Ch. 4.6 - For the following exercises, find the directional...Ch. 4.6 - For the following exercises, find the directional...Ch. 4.6 - For the following exercises, find the gradient....Ch. 4.6 - For the following exercises, find the gradient....Ch. 4.6 - For the following exercises, find the gradient....Ch. 4.6 - For the following exercises, find the gradient....Ch. 4.6 - For the following exercises, find the directional...Ch. 4.6 - For the following exercises, find the directional...Ch. 4.6 - For the following exercises, find the derivative...Ch. 4.6 - For the following exercises, find the derivative...Ch. 4.6 - [T] Use technology to sketch the level curve of...Ch. 4.6 - [T] Use technology to sketch the level curve of...Ch. 4.6 - For the following exercises, find the gradient...Ch. 4.6 - For the following exercises, find the gradient...Ch. 4.6 - For the following exercises, find the gradient...Ch. 4.6 - For the following exercises, find the gradient...Ch. 4.6 - For the following exercises, find the derivative...Ch. 4.6 - For the following exercises, find the derivative...Ch. 4.6 - For the following exercises, find the derivative...Ch. 4.6 - For the following exercises, find the derivative...Ch. 4.6 - For the following exercises, find the derivative...Ch. 4.6 - For the following exercises, find the maximum rate...Ch. 4.6 - For the following exercises, find the maximum rate...Ch. 4.6 - For the following exercises, find the maximum rate...Ch. 4.6 - For the following exercises, find equations of a....Ch. 4.6 - For the following exercises, find equations of a....Ch. 4.6 - For the following exercises, find equations of a....Ch. 4.6 - For the following exercises, find equations of a....Ch. 4.6 - For the following exercises, solve the problem....Ch. 4.6 - For the following exercises, solve the problem....Ch. 4.6 - For the following exercises, solve the problem....Ch. 4.6 - For the following exercises, solve the problem....Ch. 4.7 - For the following exercises, find all critical...Ch. 4.7 - For the following exercises, find all critical...Ch. 4.7 - For the following exercises, find all critical...Ch. 4.7 - For the following exercises, find all critical...Ch. 4.7 - For the following exercises, find the critical...Ch. 4.7 - For the following exercises, find the critical...Ch. 4.7 - For the following exercises, find the critical...Ch. 4.7 - For the following exercises, find the critical...Ch. 4.7 - For the following exercises, use the second...Ch. 4.7 - For the following exercises, use the second...Ch. 4.7 - For the following exercises, use the second...Ch. 4.7 - For the following exercises, use the second...Ch. 4.7 - For the following exercises, use the second...Ch. 4.7 - For the following exercises, use the second...Ch. 4.7 - For the following exercises, use the second...Ch. 4.7 - For the following exercises, use the second...Ch. 4.7 - For the following exercises, use the second...Ch. 4.7 - For the following exercises, use the second...Ch. 4.7 - For the following exercises, use the second...Ch. 4.7 - For the following exercises, use the second...Ch. 4.7 - For the following exercises, use the second...Ch. 4.7 - For the following exercises, use the second...Ch. 4.7 - For the following exercises, use the second...Ch. 4.7 - For the following exercises, use the second...Ch. 4.7 - For the following exercises, use the second...Ch. 4.7 - For the following exercises, use the second...Ch. 4.7 - For the following exercises, use the second...Ch. 4.7 - For the following exercises, use the second...Ch. 4.7 - For the following exercises, use the second...Ch. 4.7 - For the following exercises, use the second...Ch. 4.7 - For the following exercises, use the second...Ch. 4.7 - For the following exercises, determine the extreme...Ch. 4.7 - For the following exercises, determine the extreme...Ch. 4.7 - For the following exercises, determine the extreme...Ch. 4.7 - Find the absolute extrema of the given function on...Ch. 4.7 - Find the absolute extrema of the given function on...Ch. 4.7 - Find the absolute extrema of the given function on...Ch. 4.7 - Find the absolute extrema of the given function on...Ch. 4.7 - Find three positive numbers the sum of which is...Ch. 4.7 - Find the points on the surface x2yz=5that are...Ch. 4.7 - Find the maximum volume of a rectangular box with...Ch. 4.7 - The sum of the length and the girth (perimeter of...Ch. 4.7 - A cardboard box without a lid is to be made with a...Ch. 4.7 - Find the point on the surface f(x,y)=x2+y2+10...Ch. 4.7 - Find the point in the plane 2xy+2z=16 that is...Ch. 4.7 - A company manufactures two types of athletic...Ch. 4.7 - A shipping company handles rectangular boxes...Ch. 4.7 - Find the maximum volume of a cylindrical soda can...Ch. 4.8 - For the following exercises, use the method of...Ch. 4.8 - For the following exercises, use the method of...Ch. 4.8 - For the following exercises, use the method of...Ch. 4.8 - For the following exercises, use the method of...Ch. 4.8 - For the following exercises, use the method of...Ch. 4.8 - For the following exercises, use the method of...Ch. 4.8 - For the following exercises, use the method of...Ch. 4.8 - For the following exercises, use the method of...Ch. 4.8 - For the following exercises, use the method of...Ch. 4.8 - For the following exercises, use the method of...Ch. 4.8 - For the following exercises, use the method of...Ch. 4.8 - For the following exercises, use the method of...Ch. 4.8 - For the following exercises, use the method of...Ch. 4.8 - For the following exercises, use the method of...Ch. 4.8 - For the following exercises, use the method of...Ch. 4.8 - For the following exercises, use the method of...Ch. 4.8 - For the following exercises, use the method of...Ch. 4.8 - For the following exercises, use the method of...Ch. 4.8 - For the following exercises, use the method of...Ch. 4.8 - For the following exercises, use the method of...Ch. 4.8 - For the following exercises, use the method of...Ch. 4.8 - For the following exercises, use the method of...Ch. 4.8 - For the next group of exercises, use the method of...Ch. 4.8 - For the next group of exercises, use the method of...Ch. 4.8 - For the next group of exercises, use the method of...Ch. 4.8 - For the next group of exercises, use the method of...Ch. 4.8 - Show that, of all the triangles inscribed in a...Ch. 4.8 - For the next group of exercises, use the method of...Ch. 4.8 - For the next group of exercises, use the method of...Ch. 4.8 - For the next group of exercises, use the method of...Ch. 4.8 - For the next group of exercises, use the method of...Ch. 4.8 - For the next group of exercises, use the method of...Ch. 4.8 - For the next group of exercises, use the method of...Ch. 4.8 - For the next group of exercises, use the method of...Ch. 4.8 - For the next group of exercises, use the method of...Ch. 4.8 - For the next group of exercises, use the method of...Ch. 4 - For the following exercises, determine whether the...Ch. 4 - For the following exercises, determine whether the...Ch. 4 - For the following exercises, determine whether the...Ch. 4 - For the following exercises, determine whether the...Ch. 4 - For the following exercises, sketch the function...Ch. 4 - For the following exercises, sketch the function...Ch. 4 - For the following exercises, evaluate the...Ch. 4 - For the following exercises, evaluate the...Ch. 4 - For the following exercises, find the largest...Ch. 4 - For the following exercises, find the largest...Ch. 4 - For the following exercises, find the largest...Ch. 4 - For the following exercises, find the largest...Ch. 4 - For the following exercises, find all second...Ch. 4 - For the following exercises, find all second...Ch. 4 - For the following exercises, find the equation of...Ch. 4 - For the following exercises, find the equation of...Ch. 4 - For the following exercises, find the equation of...Ch. 4 - For the following exercises, find the equation of...Ch. 4 - For the following exercises, find the equation of...Ch. 4 - For the following exercises, find the equation of...Ch. 4 - For the following exercises, find the gradient....Ch. 4 - For the following exercises, find the gradient....Ch. 4 - For the following exercises, find and classify the...Ch. 4 - For the following exercises, find and classify the...Ch. 4 - For the following exercises, use Lagrange...Ch. 4 - A machinist is constructing a right circular cone...Ch. 4 - A trash compactor is in the shape of a cuboid....
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- Consider the table of values below. x y 2 63 3 70 4 77 5 84 Fill in the right side of the equation y= with an expression that makes each ordered pari (x,y) in the table a solution to the equation.arrow_forwardfind the value of each variablearrow_forwardConsider the following system of equations, Ax=b : x+2y+3z - w = 2 2x4z2w = 3 -x+6y+17z7w = 0 -9x-2y+13z7w = -14 a. Find the solution to the system. Write it as a parametric equation. You can use a computer to do the row reduction. b. What is a geometric description of the solution? Explain how you know. c. Write the solution in vector form? d. What is the solution to the homogeneous system, Ax=0?arrow_forward
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- Please could you explain how to do integration by parts for this question in detail pleasearrow_forwardThere were 426 books sold in one week. The number of biology books sold was 5 times that of the number of psychology books. How many books each were sold?arrow_forwardI worked out the answers for most of this, and provided the answers in the tables that follow. But for the total cost table, I need help working out the values for 10%, 11%, and 12%. A pharmaceutical company produces the drug NasaMist from four chemicals. Today, the company must produce 1000 pounds of the drug. The three active ingredients in NasaMist are A, B, and C. By weight, at least 8% of NasaMist must consist of A, at least 4% of B, and at least 2% of C. The cost per pound of each chemical and the amount of each active ingredient in one pound of each chemical are given in the data at the bottom. It is necessary that at least 100 pounds of chemical 2 and at least 450 pounds of chemical 3 be used. a. Determine the cheapest way of producing today’s batch of NasaMist. If needed, round your answers to one decimal digit. Production plan Weight (lbs) Chemical 1 257.1 Chemical 2 100 Chemical 3 450 Chemical 4 192.9 b. Use SolverTable to see how much the percentage of…arrow_forward
- Population decreases 5% each year. Starts with a starting population of 3705. Find that population after 5 years.arrow_forwardsolve using substitution -2x-3y=-15 -3x+9y=12arrow_forwardSuppose that 7000 is placed in an accout that pays 4% interest. Interest compunds each year. Assume that no withdraws are made. How much would the account have after 1 year? And how much would the account have after 2 years?arrow_forward
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