Use the given transformation to evaluate the integral.<img src="https://sciemce.com/files/4/ppg__tttt0613191206__f1q22g1.jpg" alt="" style="vertical-align: -4.0px;" /> <img src="https://sciemce.com/files/4/ppg__tttt0613191206__f1q22g2.jpg" alt="" style="vertical-align: -4.0px;" /> <img src="https://sciemce.com/files/4/ppg__tttt0613191206__f1q22g3.jpg" alt="" style="vertical-align: -4.0px;" /> <img src="https://sciemce.com/files/4/ppg__tttt0613191206__f1q22g4.jpg" style="vertical-align: -10.0px;" /> Rwhere R is the interior of the ellipsoid <img src="https://sciemce.com/files/4/ppg__tttt0613191206__f1q22g5.jpg" alt="" style="vertical-align: -17.0px;" />
Referring to triangle ABC, find the area of the triangle.
<img src="https://sciemce.com/files/3/ppg__cognero__Section_7.4_The_Area_of_Triangle__media__d644fe39-3a4c-4099-bb24-cdd447d2020a.PNG" class="wirisformula" align="middle" style="vertical-align: middle;" data-wiris-created="true" varid="variable_id_field" variablename="impvar_33551fa72c5d4145b91080c82" />
Round to three significant digits.
Use the formula for the sum of the first n terms of a geometric sequence to evaluate the sum.<img src="https://sciemce.com/files/4/ppg__tttt0604191018__f1q182g1.jpg" style="vertical-align: -23.0px;" />
Find the location of the indicated absolute extremum for the function.Maximum<img src="https://sciemce.com/files/4/ppg__tttt0604190811__f1q141g1.jpg" alt="" style="vertical-align: 0.0px;" height="224" width="224" />
Solve the problem.Let D be the smaller cap cut from a solid ball of radius 10 units by a plane 7 units from the center of the sphere. Set up the triple integral for the volume of D in rectangular coordinates.
Solve the problem.A heavy-duty shock absorber is compressed 1 cm from its equilibrium position by a mass of 500 kg. How much work is required to compress the shock absorber 4 cm from its equilibrium position? (A mass of 500 kg exerts a force (in N) of 500g, where g ≈ 9.8 m/s2.)
Provide an appropriate response.True or false? The statement sin-1(sin x) = x for all real numbers in the interval - <img src="https://sciemce.com/files/4/ppg__ads0528191716__f1q195g1.jpg" style="vertical-align: -17.0px;" /> < x < <img src="https://sciemce.com/files/4/ppg__ads0528191716__f1q195g2.jpg" style="vertical-align: -17.0px;" />?
Provide an appropriate response.The region shown here is to be revolved about the y-axis to generate a solid. Which of the methods (disk, washer, shell) could you use to find the volume of the solid? How many integrals would be required in each case?<img src="https://sciemce.com/files/4/ppg__tttt0609191436__f1q121g1.jpg" alt="" style="vertical-align: 0.0px;" height="180" width="180" /><img src="https://sciemce.com/files/4/ppg__tttt0609191436__f1q121g2.jpg" alt="" style="vertical-align: -4.0px;" />y = 4x- x2
Given that f(x) = sin x, g(x) = cos x, and h(x) = tan x, evaluate the given function. The point (x, <img src="https://sciemce.com/files/4/ppg__tttt0523191219__f1q132g1.jpg" style="vertical-align: -4.0px;" />), on the circle <img src="https://sciemce.com/files/4/ppg__tttt0523191219__f1q132g2.jpg" alt="" style="vertical-align: -4.0px;" />, also lies on the terminal side of an angle α in quadrant II. The point <img src="https://sciemce.com/files/4/ppg__tttt0523191219__f1q132g3.jpg" alt="" style="vertical-align: -17.0px;" />, on the circle <img src="https://sciemce.com/files/4/ppg__tttt0523191219__f1q132g4.jpg" alt="" style="vertical-align: -4.0px;" />, also lies on the terminal side of an angle β in quadrant III.h(2β)
Use the shell method to find the volume of the solid generated by revolving the shaded region about the indicated line.About the line y = 1x = 6<img src="https://sciemce.com/files/4/ppg__tttt0615191048__f1q174g1.jpg" style="vertical-align: -4.0px;" /> (solid)<img src="https://sciemce.com/files/4/ppg__tttt0615191048__f1q174g2.jpg" alt="" style="vertical-align: 0.0px;" height="184" width="200" /><img src="https://sciemce.com/files/4/ppg__tttt0615191048__f1q174g3.jpg" alt="" style="vertical-align: -4.0px;" />
Shade the Venn diagram to represent the set.B ∪ (A ∩ C')<img src="https://sciemce.com/files/4/ppg__tttt0530191057__f1q238g1.jpg" alt="" style="vertical-align: 0.0px;" height="150" width="168" />
Use a CAS integration utility to evaluate the triple integral of the given function over the specified solid region.<img src="https://sciemce.com/files/4/ppg__10615191636__f1q262g1.jpg" alt="" style="vertical-align: -4.0px;" /> over the tetrahedron bounded by the coordinate planes and the plane <img src="https://sciemce.com/files/4/ppg__10615191636__f1q262g2.jpg" alt="" style="vertical-align: -4.0px;" />
Solve the problem.Consider the region R bounded by the graph of f(x) = <img src="https://sciemce.com/files/4/ppg__tttt0610191537__f1q92g1.jpg" style="vertical-align: -17.0px;" /> on the interval [0, 1]. Find the volume of the solid formed when R is revolved about the y-axis.
If $600 is invested at interest, compounded annually, then after n years the investment is worth <img src="https://sciemce.com/files/4/19e29b9445cad021(2) FIGURE 1.png" class="w-image" /> dollars. Find the size of investment after 7 years.
Fill in the blank with the correct inequality symbol.If x > -3, then -4x <img src="https://sciemce.com/files/4/ppg__wdeasd0527191728__f1q62g1.jpg" style="vertical-align: -10.0px;" /> 12.
An experiment is conducted for which the sample space is <img src="https://sciemce.com/files/4/ppg__tttt0530191057__f1q28g1.jpg" alt="" style="vertical-align: -4.0px;" /> Decide if the given probability assignment is possible for this experiment. If the assignment is not possible, tell why. <img src="https://sciemce.com/files/4/ppg__tttt0530191057__f1q28g2.jpg" style="vertical-align: -40.0px;" />
Use a graphing utility to graph the equation. Use the graph to approximate the values of x that satisfy each inequality.
Equation:
<img src="https://sciemce.com/files/3/ppg__cognero__Section_2.7_Nonlinear_Inequalities__media__3a9d2f4a-f4a6-4f8b-8991-dfc6b8864865.PNG" class="wirisformula" align="middle" style="vertical-align: middle;" data-wiris-created="true" varid="variable_id_field" variablename="impvar_3e254cdad07c41c6b46ce9e68" />
Inequality:
<img alt="" style="vertical-align:middle;" src="https://sciemce.com/files/3/ppg__cognero__Section_2.7_Nonlinear_Inequalities__media__9ba73a81-3156-43f6-9999-4836e206d288.PNG" data-wiris-created="true" class="wirisformula" />
Write an equation for the quadratic function whose graph contains the given vertex and point.Vertex ( -5, 6) , point (0, 56) (Write your answer in vertex form.)
Perform the multiplication. Simplify the result when possible.<img src="https://sciemce.com/files/3/ppg__cognero__Section_4.2_Multiplying_and_Dividing_Rational_Expressions__media__c9fbec70-967a-4143-b030-29e0c25e0548.GIF" style="vertical-align:-9px;" varid="variable_id_field" variablename="impvar_4fde4ad3bc474587a05f4b59b" class="wirisformula" />
Graph the set of numbers on a number line.<img src="https://sciemce.com/files/4/ppg__dada0527192330__f1q125g1.jpg" alt="" style="vertical-align: -4.0px;" /><img src="https://sciemce.com/files/4/ppg__dada0527192330__f1q125g2.jpg" alt="" style="vertical-align: 0.0px;" height="38" width="356" />
Find the derivative of the function <img src="https://sciemce.com/files/2/ppg__cognero__Section_5.1__media__961cee03-8b1f-41f0-a3d2-109f8f3e3d7d.PNG" class="wirisformula" align="middle" style="vertical-align: middle;" data-wiris-created="true" varid="variable_id_field" variablename="impvar_19afb21d351f41e88e71f010e" />.
Solve the system of equations by the substitution method. Check your solutions. For any dependent equations, write your answer in ordered pair form.<img src="https://sciemce.com/files/4/ppg__tttt0523190902__f1q53g1.jpg" alt="" style="vertical-align: -4.0px;" />
Solve the problem.The slope of the tangent line to the hyperbola 5x2 - 7y2 - 217 = 0 at two points on the hyperbola is - <img src="https://sciemce.com/files/4/ppg__ttt0610191111__f1q330g1.jpg" style="vertical-align: -17.0px;" />. What are the coordinates of the points of tangency?
Find the volume of the described solid.The solid lies between planes perpendicular to the x-axis at x = - 4 and x = 4. The cross sections perpendicular to the x-axis are semicircles whose diameters run from <img src="https://sciemce.com/files/4/ppg__tttt0609191436__f1q237g1.jpg" alt="" style="vertical-align: -4.0px;" /> to <img src="https://sciemce.com/files/4/ppg__tttt0609191436__f1q237g2.jpg" alt="" style="vertical-align: -4.0px;" />
A deposit of $ 5000 is made in an account that earns 4 % interest compounded quarterly. The balance in the account after n quarters is given by
<img src="https://sciemce.com/files/2/ppg__cognero__Section_11.1_Sequences_and_Series__media__b3fae419-65e2-49af-84d8-736ee64f39e8.PNG" class="wirisformula" align="middle" style="vertical-align: middle;" data-wiris-created="true" varid="variable_id_field" variablename="impvar_657fb2d33a4042bda461cc6e1" />
Find the balance in the account after 10 years by finding the 40th term of the sequence. Round to the nearest penny.
Find values of x, y, and λ that satisfy the system. These systems arise in certain optimization problems in calculus, and λ is called a Lagrange multiplier.
<img src="https://sciemce.com/files/3/ppg__cognero__Section_6.3_Multivariable_Linear_Systems__media__63fe63b3-c136-4ee9-8917-94eb9c2d6690.PNG" class="wirisformula" align="middle" style="vertical-align: middle;" data-wiris-created="true" varid="variable_id_field" variablename="impvar_950535d9a77e4a78a0ecdd37a" />
Find the variance of the probability density function to the nearest hundredth.f(x) = <img src="https://sciemce.com/files/4/ppg__tttt0530191123__f1q92g1.jpg" style="vertical-align: -17.0px;" /> - <img src="https://sciemce.com/files/4/ppg__tttt0530191123__f1q92g2.jpg" style="vertical-align: -17.0px;" />; [3, 4]
Evaluate without the use of a calculator.arctan<img src="https://sciemce.com/files/4/ppg__awdesd0521192336__f1q49g1.jpg" alt="" style="vertical-align: -17.0px;" />
Evaluate the function for the indicated values.
f (x) = 5[[x + 3]] - 5
(i) f (3) (ii) f (-63.30) (iii) f (<img src="https://sciemce.com/files/2/ppg__cognero__Section_2.4_A_Library_of_Parent_Functions__media__55201bde-42d9-4587-921a-0b2fc742f742.PNG" class="wirisformula" align="middle" style="vertical-align: middle;" data-wiris-created="true" varid="variable_id_field" variablename="impvar_f0a04def3d9d43fda39af432e" />)
A cardiac monitor is used to measure the heart rate of a patient after surgery. It compiles the number of heartbeats after t minutes. When the data in the table are graphed, the slope of the tangent line represents the heart rate in beats per minute. The monitor estimates this value by calculating the slope of a secant line. Use the data to estimate the patient's heart rate after 42 minutes using the secant line between the points with t=38 and t=42.
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