THOMAS' CALCULUS EARLY...LL W/MYMATHLAB
14th Edition
ISBN: 9780136208013
Author: Hass
Publisher: PEARSON
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Chapter 15.7, Problem 43E
To determine
Find the value of the spherical coordinate
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Can you answer this question and give step by step and why and how to get it. Can you write it (numerical method)
Can you answer this question and give step by step and why and how to get it. Can you write it (numerical method)
There are three options for investing $1150. The first earns 10% compounded annually, the second earns 10% compounded quarterly, and the third earns 10% compounded continuously. Find equations that model each investment growth and
use a graphing utility to graph each model in the same viewing window over a 20-year period. Use the graph to determine which investment yields the highest return after 20 years. What are the differences in earnings among the three
investment?
STEP 1: The formula for compound interest is
A =
nt
= P(1 + − − ) n²,
where n is the number of compoundings per year, t is the number of years, r is the interest rate, P is the principal, and A is the amount (balance) after t years. For continuous compounding, the formula reduces to
A = Pert
Find r and n for each model, and use these values to write A in terms of t for each case.
Annual Model
r=0.10
A = Y(t) = 1150 (1.10)*
n = 1
Quarterly Model
r = 0.10
n = 4
A = Q(t) = 1150(1.025) 4t
Continuous Model
r=0.10
A = C(t) =…
Chapter 15 Solutions
THOMAS' CALCULUS EARLY...LL W/MYMATHLAB
Ch. 15.1 - In Exercises 1-14. evaluate the iterated...Ch. 15.1 - Prob. 2ECh. 15.1 - In Exercises 1-14, evaluate the iterated...Ch. 15.1 - Prob. 4ECh. 15.1 - Prob. 5ECh. 15.1 - Prob. 6ECh. 15.1 - Prob. 7ECh. 15.1 - Prob. 8ECh. 15.1 - Prob. 9ECh. 15.1 - Prob. 10E
Ch. 15.1 - Prob. 11ECh. 15.1 - Prob. 12ECh. 15.1 - Prob. 13ECh. 15.1 - Prob. 14ECh. 15.1 - Prob. 15ECh. 15.1 - Prob. 16ECh. 15.1 - In Exercises 17-24, evaluate the double integral...Ch. 15.1 - Prob. 18ECh. 15.1 - Prob. 19ECh. 15.1 - Prob. 20ECh. 15.1 - Prob. 21ECh. 15.1 - In Exercises 17–24, evaluate the double integral...Ch. 15.1 - Prob. 23ECh. 15.1 - In Exercises 17–24, evaluate the double integral...Ch. 15.1 - Prob. 25ECh. 15.1 - Prob. 26ECh. 15.1 - Prob. 27ECh. 15.1 - Prob. 28ECh. 15.1 - Find the volume of the region hounded above by the...Ch. 15.1 - Find the volume of the region bounded above by the...Ch. 15.1 - Prob. 31ECh. 15.1 - Prob. 32ECh. 15.1 - Prob. 33ECh. 15.1 - Prob. 34ECh. 15.1 - Prob. 35ECh. 15.1 - Prob. 36ECh. 15.1 - Use Fubini’s Theorem to evaluate
.
Ch. 15.1 - Prob. 38ECh. 15.1 - Use a software application to compute the...Ch. 15.1 - Prob. 40ECh. 15.2 - In Exercises 1-8, sketch the described regions of...Ch. 15.2 - In Exercises 1-8, sketch the described regions of...Ch. 15.2 - Prob. 3ECh. 15.2 - Prob. 4ECh. 15.2 - Prob. 5ECh. 15.2 - Prob. 6ECh. 15.2 - Prob. 7ECh. 15.2 - Prob. 8ECh. 15.2 - In Exercises 918, write an iterated integral for...Ch. 15.2 - Prob. 10ECh. 15.2 - Prob. 11ECh. 15.2 - In Exercises 9–18, write an iterated integral for ...Ch. 15.2 - Prob. 13ECh. 15.2 - Prob. 14ECh. 15.2 - In Exercises 9–18, write an iterated integral for ...Ch. 15.2 - In Exercises 9-18, write an iterated integral for...Ch. 15.2 - Prob. 17ECh. 15.2 - Prob. 18ECh. 15.2 - Prob. 19ECh. 15.2 - Prob. 20ECh. 15.2 - Prob. 21ECh. 15.2 - Prob. 22ECh. 15.2 - Prob. 23ECh. 15.2 - Prob. 24ECh. 15.2 - Prob. 25ECh. 15.2 - In Exercises 25-28, integrate f over the given...Ch. 15.2 - Prob. 27ECh. 15.2 - Prob. 28ECh. 15.2 - Prob. 29ECh. 15.2 - Prob. 30ECh. 15.2 - Prob. 31ECh. 15.2 - Each of Exercises 29–32 gives an integral over a...Ch. 15.2 - In Exercises 33–46, sketch the region of...Ch. 15.2 - Prob. 34ECh. 15.2 - Prob. 35ECh. 15.2 - Prob. 36ECh. 15.2 - Prob. 37ECh. 15.2 - Prob. 38ECh. 15.2 - Prob. 39ECh. 15.2 - Prob. 40ECh. 15.2 - Prob. 41ECh. 15.2 - Prob. 42ECh. 15.2 - Prob. 43ECh. 15.2 - Prob. 44ECh. 15.2 - Prob. 45ECh. 15.2 - Prob. 46ECh. 15.2 - Prob. 47ECh. 15.2 - Prob. 48ECh. 15.2 - Prob. 49ECh. 15.2 - Prob. 50ECh. 15.2 - Prob. 51ECh. 15.2 - Prob. 52ECh. 15.2 - Prob. 53ECh. 15.2 - Prob. 54ECh. 15.2 - Prob. 55ECh. 15.2 - Prob. 56ECh. 15.2 - Prob. 57ECh. 15.2 - Prob. 58ECh. 15.2 - Prob. 59ECh. 15.2 - Prob. 60ECh. 15.2 - Prob. 61ECh. 15.2 - Prob. 62ECh. 15.2 - Prob. 63ECh. 15.2 - Find the volume of the solid cut from the square...Ch. 15.2 - Prob. 65ECh. 15.2 - Prob. 66ECh. 15.2 - Prob. 67ECh. 15.2 - Prob. 68ECh. 15.2 - Prob. 69ECh. 15.2 - Prob. 70ECh. 15.2 - Prob. 71ECh. 15.2 - Prob. 72ECh. 15.2 - Prob. 73ECh. 15.2 - Prob. 74ECh. 15.2 - Prob. 75ECh. 15.2 - Prob. 76ECh. 15.2 - Prob. 77ECh. 15.2 - Prob. 78ECh. 15.2 - Prob. 79ECh. 15.2 - Prob. 80ECh. 15.2 - Prob. 81ECh. 15.2 - Prob. 82ECh. 15.2 - Prob. 83ECh. 15.2 - Prob. 84ECh. 15.3 - In Exercises 1-12, sketch the region bounded by...Ch. 15.3 - Prob. 2ECh. 15.3 - In Exercises 1-12, sketch the region bounded by...Ch. 15.3 - In Exercises 1-12, sketch the region bounded by...Ch. 15.3 - Prob. 5ECh. 15.3 - Prob. 6ECh. 15.3 - In Exercises 1-12, sketch the region bounded by...Ch. 15.3 - Prob. 8ECh. 15.3 - Prob. 9ECh. 15.3 - Prob. 10ECh. 15.3 - Prob. 11ECh. 15.3 - Prob. 12ECh. 15.3 - Prob. 13ECh. 15.3 - Prob. 14ECh. 15.3 - The integrals and sums of integrals in Exercises...Ch. 15.3 - Prob. 16ECh. 15.3 - Prob. 17ECh. 15.3 - The integrals and sums of integrals in Exercises...Ch. 15.3 - Prob. 19ECh. 15.3 - Which do you think will be larger, the average...Ch. 15.3 - Prob. 21ECh. 15.3 - Prob. 22ECh. 15.3 - Prob. 23ECh. 15.3 - Prob. 24ECh. 15.3 - Bacterium population If f(x, y) = (10,000ey)/ (1 +...Ch. 15.3 - Prob. 26ECh. 15.3 - Prob. 27ECh. 15.3 - Prob. 28ECh. 15.3 - Prob. 29ECh. 15.3 - Prob. 30ECh. 15.4 - In Exercises 1-8, describe the given region in...Ch. 15.4 - Prob. 2ECh. 15.4 - In Exercises 1-8, describe the given region in...Ch. 15.4 - Prob. 4ECh. 15.4 - Prob. 5ECh. 15.4 - Prob. 6ECh. 15.4 - Prob. 7ECh. 15.4 - Prob. 8ECh. 15.4 - Prob. 9ECh. 15.4 - Prob. 10ECh. 15.4 - Prob. 11ECh. 15.4 - Prob. 12ECh. 15.4 - Prob. 13ECh. 15.4 - Prob. 14ECh. 15.4 - In Exercises 9-22, change the Cartesian integral...Ch. 15.4 - Prob. 16ECh. 15.4 - Prob. 17ECh. 15.4 - In Exercises 9-22, change the Cartesian integral...Ch. 15.4 - Prob. 19ECh. 15.4 - Prob. 20ECh. 15.4 - In Exercises 9–22, change the Cartesian integral...Ch. 15.4 - Prob. 22ECh. 15.4 - Prob. 23ECh. 15.4 - Prob. 24ECh. 15.4 - In Exercises 23–26, sketch the region of...Ch. 15.4 - In Exercises 23–26, sketch the region of...Ch. 15.4 - Prob. 27ECh. 15.4 - Prob. 28ECh. 15.4 - Prob. 29ECh. 15.4 - Prob. 30ECh. 15.4 - Prob. 31ECh. 15.4 - Prob. 32ECh. 15.4 - Prob. 33ECh. 15.4 - Prob. 34ECh. 15.4 - Prob. 35ECh. 15.4 - Prob. 36ECh. 15.4 - Prob. 37ECh. 15.4 - Prob. 38ECh. 15.4 - Prob. 39ECh. 15.4 - Prob. 40ECh. 15.4 - Prob. 41ECh. 15.4 - Prob. 42ECh. 15.4 - Prob. 43ECh. 15.4 - Prob. 44ECh. 15.4 - Prob. 45ECh. 15.4 - Prob. 46ECh. 15.4 - Prob. 47ECh. 15.4 - Prob. 48ECh. 15.5 - Evaluate the integral in Example 3, taking F(x, y,...Ch. 15.5 - Prob. 2ECh. 15.5 - Prob. 3ECh. 15.5 - Prob. 4ECh. 15.5 - Prob. 5ECh. 15.5 - Prob. 6ECh. 15.5 - Prob. 7ECh. 15.5 - Prob. 8ECh. 15.5 - Prob. 9ECh. 15.5 - Prob. 10ECh. 15.5 - Prob. 11ECh. 15.5 - Evaluate the integrals in Exercises 7–20.
12.
Ch. 15.5 - Prob. 13ECh. 15.5 - Prob. 14ECh. 15.5 - Prob. 15ECh. 15.5 - Prob. 16ECh. 15.5 - Prob. 17ECh. 15.5 - Prob. 18ECh. 15.5 - Prob. 19ECh. 15.5 - Prob. 20ECh. 15.5 - Here is the region of integration of the...Ch. 15.5 - Here is the region of integration of the...Ch. 15.5 - Prob. 23ECh. 15.5 - Prob. 24ECh. 15.5 - Prob. 25ECh. 15.5 - Prob. 26ECh. 15.5 - Prob. 27ECh. 15.5 - Prob. 28ECh. 15.5 - Prob. 29ECh. 15.5 - Prob. 30ECh. 15.5 - Prob. 31ECh. 15.5 - Prob. 32ECh. 15.5 - Find the volumes of the regions in Exercises...Ch. 15.5 - Find the volumes of the regions in Exercises...Ch. 15.5 - Prob. 35ECh. 15.5 - Prob. 36ECh. 15.5 - Prob. 37ECh. 15.5 - Prob. 38ECh. 15.5 - Prob. 39ECh. 15.5 - Prob. 40ECh. 15.5 - Evaluate the integrals in Exercises 41–44 by...Ch. 15.5 - Prob. 42ECh. 15.5 - Prob. 43ECh. 15.5 - Prob. 44ECh. 15.5 - Prob. 45ECh. 15.5 - Prob. 46ECh. 15.5 - Prob. 47ECh. 15.5 - Prob. 48ECh. 15.6 - Prob. 1ECh. 15.6 - Prob. 2ECh. 15.6 - Prob. 3ECh. 15.6 - Prob. 4ECh. 15.6 - Prob. 5ECh. 15.6 - Prob. 6ECh. 15.6 - Prob. 7ECh. 15.6 - Prob. 8ECh. 15.6 - Prob. 9ECh. 15.6 - Prob. 10ECh. 15.6 - Prob. 11ECh. 15.6 - Prob. 12ECh. 15.6 - Prob. 13ECh. 15.6 - Prob. 14ECh. 15.6 - Prob. 15ECh. 15.6 - Prob. 16ECh. 15.6 - Prob. 17ECh. 15.6 - Center of mass, moments of inertia Find the center...Ch. 15.6 - Prob. 19ECh. 15.6 - Prob. 20ECh. 15.6 - Prob. 21ECh. 15.6 - Prob. 22ECh. 15.6 - Center of mass and moments of inertia A solid...Ch. 15.6 - Prob. 24ECh. 15.6 - a. Center of mass Find the center of mass of a...Ch. 15.6 - Prob. 26ECh. 15.6 - Prob. 27ECh. 15.6 - Prob. 28ECh. 15.6 - Prob. 29ECh. 15.6 - Prob. 30ECh. 15.6 - Prob. 31ECh. 15.6 - In Exercises 31 and 32, find
the mass of the...Ch. 15.6 - Prob. 33ECh. 15.6 - Prob. 34ECh. 15.6 - Prob. 35ECh. 15.6 - Prob. 36ECh. 15.6 - Prob. 37ECh. 15.6 - Prob. 38ECh. 15.6 - Prob. 39ECh. 15.6 - Prob. 40ECh. 15.6 - Prob. 41ECh. 15.6 - Prob. 42ECh. 15.6 - Prob. 43ECh. 15.6 - Prob. 44ECh. 15.7 - In Exercises 1–12, sketch the region described by...Ch. 15.7 - In Exercises 1–12, sketch the region described by...Ch. 15.7 - In Exercises 1–12, sketch the region described by...Ch. 15.7 - In Exercises 1–12, sketch the region described by...Ch. 15.7 - In Exercises 1–12, sketch the region described by...Ch. 15.7 - In Exercises 1–12, sketch the region described by...Ch. 15.7 - In Exercises 1–12, sketch the region described by...Ch. 15.7 - In Exercises 1–12, sketch the region described by...Ch. 15.7 - In Exercises 1–12, sketch the region described by...Ch. 15.7 - In Exercises 1–12, sketch the region described by...Ch. 15.7 - Prob. 11ECh. 15.7 - Prob. 12ECh. 15.7 - Prob. 13ECh. 15.7 - Prob. 14ECh. 15.7 - Prob. 15ECh. 15.7 - Prob. 16ECh. 15.7 - Prob. 17ECh. 15.7 - Prob. 18ECh. 15.7 - Prob. 19ECh. 15.7 - In Exercises 13−22, sketch the region described by...Ch. 15.7 - Prob. 21ECh. 15.7 - Prob. 22ECh. 15.7 - Evaluate the cylindrical coordinate integrals in...Ch. 15.7 - Evaluate the cylindrical coordinate integrals in...Ch. 15.7 - Evaluate the cylindrical coordinate integrals in...Ch. 15.7 - Prob. 26ECh. 15.7 - Prob. 27ECh. 15.7 - Prob. 28ECh. 15.7 - Prob. 29ECh. 15.7 - Prob. 30ECh. 15.7 - Prob. 31ECh. 15.7 - Prob. 32ECh. 15.7 - Let D be the region bounded below by the plane z =...Ch. 15.7 - Let D be the region bounded below by the cone and...Ch. 15.7 - Give the limits of integration for evaluating the...Ch. 15.7 - Prob. 36ECh. 15.7 - Prob. 37ECh. 15.7 - In Exercises 37–42, set up the iterated integral...Ch. 15.7 - In Exercises 37–42, set up the iterated integral...Ch. 15.7 - In Exercises 37–42, set up the iterated integral...Ch. 15.7 - In Exercises 37–42, set up the iterated integral...Ch. 15.7 - In Exercises 37–42, set up the iterated integral...Ch. 15.7 - Evaluate the spherical coordinate integrals in...Ch. 15.7 - Evaluate the spherical coordinate integrals in...Ch. 15.7 - Evaluate the spherical coordinate integrals in...Ch. 15.7 - Prob. 46ECh. 15.7 - Prob. 47ECh. 15.7 - Prob. 48ECh. 15.7 - Prob. 49ECh. 15.7 - Prob. 50ECh. 15.7 - Prob. 51ECh. 15.7 - Prob. 52ECh. 15.7 - Prob. 53ECh. 15.7 - Prob. 54ECh. 15.7 - In Exercises 55–60, (a) find the spherical...Ch. 15.7 - In Exercises 55–60, (a) find the spherical...Ch. 15.7 - In Exercises 55–60, (a) find the spherical...Ch. 15.7 - In Exercises 55–60, (a) find the spherical...Ch. 15.7 - In Exercises 55–60, (a) find the spherical...Ch. 15.7 - In Exercises 55–60, (a) find the spherical...Ch. 15.7 - Set up triple integrals for the volume of the...Ch. 15.7 - Let D be the region in the first octant that is...Ch. 15.7 - Let D be the smaller cap cut from a solid ball of...Ch. 15.7 - Let D be the solid hemisphere x2 + y2 + z2 ≤ 1, z ...Ch. 15.7 - Find the volumes of the solids in Exercises...Ch. 15.7 - Find the volumes of the solids in Exercises...Ch. 15.7 - Find the volumes of the solids in Exercises...Ch. 15.7 - Find the volumes of the solids in Exercises...Ch. 15.7 - Find the volumes of the solids in Exercises...Ch. 15.7 - Prob. 70ECh. 15.7 - Prob. 71ECh. 15.7 - Prob. 72ECh. 15.7 - Prob. 73ECh. 15.7 - Cone and planes Find the volume of the solid...Ch. 15.7 - Prob. 75ECh. 15.7 - Prob. 76ECh. 15.7 - Prob. 77ECh. 15.7 - Sphere and cylinder Find the volume of the region...Ch. 15.7 - Prob. 79ECh. 15.7 - Prob. 80ECh. 15.7 - Prob. 81ECh. 15.7 - Prob. 82ECh. 15.7 - Cylinder and sphere Find the volume of the region...Ch. 15.7 - Prob. 84ECh. 15.7 - Prob. 85ECh. 15.7 - Prob. 86ECh. 15.7 - Prob. 87ECh. 15.7 - Prob. 88ECh. 15.7 - Prob. 89ECh. 15.7 - Prob. 90ECh. 15.7 - Prob. 91ECh. 15.7 - Prob. 92ECh. 15.7 - Prob. 93ECh. 15.7 - Prob. 94ECh. 15.7 - Prob. 95ECh. 15.7 - Prob. 96ECh. 15.7 - Prob. 97ECh. 15.7 - Prob. 98ECh. 15.7 - Prob. 99ECh. 15.7 - Prob. 100ECh. 15.7 - Prob. 101ECh. 15.7 - Prob. 102ECh. 15.7 - Prob. 103ECh. 15.7 - Prob. 104ECh. 15.7 - Vertical planes in cylindrical coordinates
Show...Ch. 15.7 - Prob. 106ECh. 15.7 - Prob. 107ECh. 15.7 - Prob. 108ECh. 15.8 - Solve the system
for x and y in terms of u and v....Ch. 15.8 - Prob. 2ECh. 15.8 - Prob. 3ECh. 15.8 - Prob. 4ECh. 15.8 - Prob. 5ECh. 15.8 - Prob. 6ECh. 15.8 - Use the transformation in Exercise 3 to evaluate...Ch. 15.8 - Prob. 8ECh. 15.8 - Let R be the region in the first quadrant of the...Ch. 15.8 - Prob. 10ECh. 15.8 - Prob. 11ECh. 15.8 - The area of an ellipse The area πab of the ellipse...Ch. 15.8 - Use the transformation in Exercise 2 to evaluate...Ch. 15.8 - Use the transformation x = u + (1/2)v, y = v to...Ch. 15.8 - Use the transformation x = u/v, y = uv to evaluate...Ch. 15.8 - Prob. 16ECh. 15.8 - Prob. 17ECh. 15.8 - Prob. 18ECh. 15.8 - Evaluate
over the solid ellipsoid D,
(Hint: Let...Ch. 15.8 - Let D be the region in xyz-space defined by the...Ch. 15.8 - Prob. 21ECh. 15.8 - Prob. 22ECh. 15.8 - Prob. 23ECh. 15.8 - Substitutions in single integrals How can...Ch. 15.8 - Centroid of a solid semiellipsoid Assuming the...Ch. 15.8 - Prob. 26ECh. 15.8 - Prob. 27ECh. 15.8 - Prob. 28ECh. 15 - Prob. 1GYRCh. 15 - Prob. 2GYRCh. 15 - Prob. 3GYRCh. 15 - Prob. 4GYRCh. 15 - Prob. 5GYRCh. 15 - Prob. 6GYRCh. 15 - How are double and triple integrals in rectangular...Ch. 15 - Prob. 8GYRCh. 15 - How are triple integrals in cylindrical and...Ch. 15 - Prob. 10GYRCh. 15 - Prob. 11GYRCh. 15 - Prob. 1PECh. 15 - Prob. 2PECh. 15 - Prob. 3PECh. 15 - Prob. 4PECh. 15 - Prob. 5PECh. 15 - Prob. 6PECh. 15 - Prob. 7PECh. 15 - Prob. 8PECh. 15 - Prob. 9PECh. 15 - Prob. 10PECh. 15 - Prob. 11PECh. 15 - Prob. 12PECh. 15 - Prob. 13PECh. 15 - Prob. 14PECh. 15 - Prob. 15PECh. 15 - Prob. 16PECh. 15 - Prob. 17PECh. 15 - Prob. 18PECh. 15 - Prob. 19PECh. 15 - Prob. 20PECh. 15 - Prob. 21PECh. 15 - Prob. 22PECh. 15 - Prob. 23PECh. 15 - Prob. 24PECh. 15 - Prob. 25PECh. 15 - Prob. 26PECh. 15 - Prob. 27PECh. 15 - Volume Find the volume of the solid that is...Ch. 15 - Prob. 29PECh. 15 - Prob. 30PECh. 15 - Prob. 31PECh. 15 - Rectangular to cylindrical coordinates (a) Convert...Ch. 15 - Prob. 33PECh. 15 - Prob. 34PECh. 15 - Prob. 35PECh. 15 - Prob. 36PECh. 15 - Prob. 37PECh. 15 - Prob. 38PECh. 15 - Prob. 39PECh. 15 - Prob. 40PECh. 15 - Prob. 41PECh. 15 - Prob. 42PECh. 15 - Prob. 43PECh. 15 - Prob. 44PECh. 15 - Prob. 45PECh. 15 - Prob. 46PECh. 15 - Prob. 47PECh. 15 - Prob. 48PECh. 15 - Prob. 49PECh. 15 - Prob. 50PECh. 15 - Prob. 51PECh. 15 - Prob. 52PECh. 15 - Prob. 53PECh. 15 - Prob. 54PECh. 15 - Prob. 1AAECh. 15 - Water in a hemispherical bowl A hemispherical bowl...Ch. 15 - Prob. 3AAECh. 15 - Sphere and paraboloid Find the volume of the...Ch. 15 - Prob. 5AAECh. 15 - Prob. 6AAECh. 15 - Prob. 7AAECh. 15 - Prob. 8AAECh. 15 - Prob. 9AAECh. 15 - Prob. 10AAECh. 15 - Prob. 11AAECh. 15 - Prob. 12AAECh. 15 - Prob. 13AAECh. 15 - Prob. 14AAECh. 15 - Minimizing polar inertia A thin plate of constant...Ch. 15 - Prob. 16AAECh. 15 - Prob. 17AAECh. 15 - Prob. 18AAECh. 15 - Prob. 19AAECh. 15 - Prob. 20AAECh. 15 - Suppose that f(x, y) can be written as a product...Ch. 15 - Prob. 22AAECh. 15 - Prob. 23AAECh. 15 - Prob. 24AAECh. 15 - Prob. 25AAECh. 15 - Prob. 26AAECh. 15 - Prob. 27AAECh. 15 - Prob. 28AAE
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