The light from a lightbulb radiates outward in all directions. a. Consider the interior of an imaginary sphere on which the light shines. The surface area of the sphere is directly proportional to the square of the radius. If the surface area of a sphere with a 10-m radius is 400 πm 2 , determine the exact surface area of a sphere with a 20-m radius. b. Explain how the surf ace area changed when the radius of the sphere increased from 10 m to 20 m. c. Based on your answer from part (b) how would you expect the intensity of light to change from a point 10 m from the lightbulb to a point 20 m from the lightbulb? d. The intensity of light from a light source varies inversely as the square of the distance from the source. If the intensity of a lightbulb is 200 lumen/m 2 (lux) at a distance of 10 m, determine the intensity at 20 m.
The light from a lightbulb radiates outward in all directions. a. Consider the interior of an imaginary sphere on which the light shines. The surface area of the sphere is directly proportional to the square of the radius. If the surface area of a sphere with a 10-m radius is 400 πm 2 , determine the exact surface area of a sphere with a 20-m radius. b. Explain how the surf ace area changed when the radius of the sphere increased from 10 m to 20 m. c. Based on your answer from part (b) how would you expect the intensity of light to change from a point 10 m from the lightbulb to a point 20 m from the lightbulb? d. The intensity of light from a light source varies inversely as the square of the distance from the source. If the intensity of a lightbulb is 200 lumen/m 2 (lux) at a distance of 10 m, determine the intensity at 20 m.
The light from a lightbulb radiates outward in all directions.
a. Consider the interior of an imaginary sphere on which the light shines. The surface area of the sphere is directly proportional to the square of the radius. If the surface area of a sphere with a 10-m radius is
400
πm
2
,
determine the exact surface area of a sphere with a 20-m radius.
b. Explain how the surf ace area changed when the radius of the sphere increased from 10 m to 20 m.
c. Based on your answer from part (b) how would you expect the intensity of light to change from a point 10 m from the lightbulb to a point 20 m from the lightbulb?
d. The intensity of light from a light source varies inversely as the square of the distance from the source. If the intensity of a lightbulb is 200
lumen/m
2
(lux) at a distance of 10 m, determine the intensity at 20 m.
2. [-/1 Points]
DETAILS
MY NOTES
SESSCALCET2 6.5.015.
Use the Trapezoidal Rule, the Midpoint Rule, and Simpson's Rule to approximate the given integral with the specified value of n. (Round your answers to six decimal places.)
ASK YOUR TEACHER
3
1
3 +
dy, n = 6
(a) the Trapezoidal Rule
(b) the Midpoint Rule
(c) Simpson's Rule
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This question builds on an earlier problem. The randomized numbers may have changed, but have your work for the previous problem available to help with this one.
A 4-centimeter rod is attached at one end to a point A rotating counterclockwise on a wheel of radius 2 cm. The other end B is free to move back and forth along a horizontal bar that goes through the center of the wheel. At time t=0 the rod is situated as in the diagram at the left below. The
wheel rotates counterclockwise at 1.5 rev/sec. At some point, the rod will be tangent to the circle as shown in the third picture.
B
A
B
at some instant, the piston will be tangent to the circle
(a) Express the x and y coordinates of point A as functions of t:
x= 2 cos(3πt)
and y= 2 sin(3πt)
(b) Write a formula for the slope of the tangent line to the circle at the point A at time t seconds:
-cot (3πt)
(c) Express the x-coordinate of the right end of the rod at point B as a function of t: 2 cos(3πt) +41/1
(d) Express the slope of the rod…
4. [-/1 Points]
DETAILS
MY NOTES
SESSCALCET2 6.5.024.
Find the approximations Tη, Mn, and S, to the integral
computer algebra system.)
ASK YOUR TEACHER
PRACTICE ANOTHER
4 39
√
dx for n = 6 and 12. Then compute the corresponding errors ET, EM, and Es. (Round your answers to six decimal places. You may wish to use the sum command on a
n
Tn
Mn
Sp
6
12
n
ET
EM
Es
6
12
What observations can you make? In particular, what happens to the errors when n is doubled?
As n is doubled, ET and EM are decreased by a factor of about
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'
and Es is decreased by a factor of about
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