The effective focal length f of a camera is the distance required for the lens to converge light to a single focal point. The angle of view α of a camera describes the angular range (either horizontally, vertically, or diagonally) that is imaged by a camera. a. Show that α = 2 arctan d 2 f where d is the dimension of the image sensor or film. b. A typical 35 -mm camera has image dimensions of 24 mm (vertically) by 36 mm (horizontally). If the focal length is 50 mm , find the vertical and horizontal viewing angles. Round to the nearest tenth of a degree.
The effective focal length f of a camera is the distance required for the lens to converge light to a single focal point. The angle of view α of a camera describes the angular range (either horizontally, vertically, or diagonally) that is imaged by a camera. a. Show that α = 2 arctan d 2 f where d is the dimension of the image sensor or film. b. A typical 35 -mm camera has image dimensions of 24 mm (vertically) by 36 mm (horizontally). If the focal length is 50 mm , find the vertical and horizontal viewing angles. Round to the nearest tenth of a degree.
The effective focal length
f
of a camera is the distance required for the lens to converge light to a single focal point. The angle of view
α
of a camera describes the angular range (either horizontally, vertically, or diagonally) that is imaged by a camera.
a. Show that
α
=
2
arctan
d
2
f
where
d
is the dimension of the image sensor or film.
b. A typical
35
-mm
camera has image dimensions of
24
mm
(vertically) by
36
mm
(horizontally). If the focal length is
50
mm
, find the vertical and horizontal viewing angles. Round to the nearest tenth of a degree.
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) =…
Use a graphing utility to find the point of intersection, if any, of the graphs of the functions. Round your result to three decimal places. (Enter NONE in any unused answer blanks.)
y = 100e0.01x
(x, y) =
y = 11,250
×
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