Use the shell method to find the volume of the solid generated by revolving the region bounded by the given curves about the given lines.y = 4x,<img src="https://sciemce.com/files/4/ppg__10612191952__f1q85g1.jpg" alt="" style="vertical-align: -4.0px;" />y = x2; revolve about the y-axis
Use the Remainder Theorem and synthetic division to find each function value. Verify your
answers using another method.
<img src="https://sciemce.com/files/2/ppg__cognero__Section_3.3_Polynomial_and_Synthetic_Division__media__6664df1d-ad8b-484f-acac-c28244ec7720.PNG" class="wirisformula" align="middle" style="vertical-align: middle;" data-wiris-created="true" varid="variable_id_field" variablename="impvar_6266bb7901f44fa389493b146" />
Give the equation of the horizontal asymptote, if any, of the function.h(x) = <img src="https://sciemce.com/files/4/ppg__tttt0527190934__f1q111g1.jpg" style="vertical-align: -17.0px;" />
An ornamental light bulb is designed by revolving the graph of <img alt="" align="middle" class="wirisformula" data-wiris-created="true" src="https://sciemce.com/files/2/ppg__cognero__Section_7.4__media__f53e5366-5dc0-4c76-8da9-b1408c6920b4.PNG" style="vertical-align:middle;" /> about the x-axis where x and y are measured in feet. Approximate the amount of glass needed to make the bulb. (Assume that the glass is 0.016 inches thick.) Round your answer to four decimal places.
<img alt="" src="https://sciemce.com/files/2/ppg__cognero__Section_7.4__media__728035c6-9a00-4046-9a7c-f9c2a6e87d97.PNG" />
Find the component form of the specified vector.Let u = <img src="https://sciemce.com/files/4/ppg__tttt0615191204__f1q184g1.jpg" alt="" style="vertical-align: -4.0px;" />, v = <img src="https://sciemce.com/files/4/ppg__tttt0615191204__f1q184g2.jpg" alt="" style="vertical-align: -4.0px;" />. Find v - u.
Find the second derivative of the function.s = <img src="https://sciemce.com/files/4/ppg__tttt0612191036__f1q92g1.jpg" style="vertical-align: -21.0px;" />
Evaluate the function <img src="https://sciemce.com/files/3/ppg__cognero__Section_3.2_Logarithmic_Functions_and_Their_Graphs__media__646f1ab1-1d40-44c7-a650-57251b5bdb30.PNG" class="wirisformula" align="middle" style="vertical-align: middle;" data-wiris-created="true" varid="variable_id_field" variablename="impvar_1f2785662b744cbd9deebb586" /> at <img src="https://sciemce.com/files/3/ppg__cognero__Section_3.2_Logarithmic_Functions_and_Their_Graphs__media__0a86ee97-08c6-43f5-b572-fa2277af12fc.PNG" class="wirisformula" align="middle" style="vertical-align: middle;" data-wiris-created="true" varid="variable_id_field" variablename="impvar_10c958885bfd4a2783b3ee5c5" />. Round to 3 decimal places. (You may use your calculator.)
Find <img src="https://sciemce.com/files/4/ppg__tttt0610191239__f1q132g1.jpg" style="vertical-align: -17.0px;" /> by using the Chain Rule. Express your final answer in terms of t.w = cos (x2yz); x = t, y = t4, z = t2
Solve the system of linear equations and check any solution algebraically.
<img src="https://sciemce.com/files/3/ppg__cognero__Section_6.3_Multivariable_Linear_Systems__media__4ec6e001-cb2d-4f96-86ca-f342fcdfa9b8.PNG" class="wirisformula" align="middle" style="vertical-align: middle;" data-wiris-created="true" varid="variable_id_field" variablename="impvar_b594511ea712499c9a0da6086" />
Data are given for y as a power function of x. Write an equation for the power function, and state its power and constant of variation.<img src="https://sciemce.com/files/4/ppg__tttt0522191119__f1q19g1.jpg" style="vertical-align: -15.0px;" />
Select from the following which is the polynomial of degree n that has the given zero(s).
Zeros Degree <img src="https://sciemce.com/files/2/ppg__cognero__Section_3.2_Polynomial_Functions_of_Higher_Degree__media__cde1029d-18f4-44ac-b99d-c098f51faf36.PNG" class="wirisformula" align="middle" style="vertical-align: middle;" data-wiris-created="true" varid="variable_id_field" variablename="impvar_18b42cb0d71a4c2689fa61dfa" /> <img alt="" style="vertical-align:middle;" src="https://sciemce.com/files/2/ppg__cognero__Section_3.2_Polynomial_Functions_of_Higher_Degree__media__13d5b8e8-b372-4687-be3f-481ad4d25d9d.PNG" data-wiris-created="true" class="wirisformula" />
Solve the problem.Suppose that in a memory experiment the rate of memorizing is given by <img src="https://sciemce.com/files/4/ppg__dsd0530191647__f1q200g1.jpg" alt="" style="vertical-align: -4.0px;" /> where M'(t) is the memory rate, in words per minute. How many words are memorized in the first <img src="https://sciemce.com/files/4/ppg__dsd0530191647__f1q200g2.jpg" alt="" style="vertical-align: -4.0px;" /> (from t = 0 to t = 20)?
Find the mass of the wire that lies along the curve r and has density δ.C1: r(t) = (8 cos t)i + (8 sin t)j, 0 ≤ t ≤ <img src="https://sciemce.com/files/4/ppg__10611192155__f1q256g1.jpg" style="vertical-align: -17.0px;" />;C2: r(t) = 8j + tk, 0 ≤ t ≤ 1; δ = 7t5
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