Sunlight is absorbed in water, and as a result the light intensity in oceans, lakes, and ponds decreases exponentially with depth. The percentage of visible light, P (in decimal form), at a depth of x meters is given by P = e − k t , where k is a constant related to the clarity and other physical properties of the water. The graph shows models for the open ocean, Lake Tahoe, and Lake Erie for data taken under similar conditions. Use these models for Exercises 73-76. Determine the depth at which the light intensity is 20% of the value from the surface for each body of water given. Round to the nearest tenth of a meter.
Sunlight is absorbed in water, and as a result the light intensity in oceans, lakes, and ponds decreases exponentially with depth. The percentage of visible light, P (in decimal form), at a depth of x meters is given by P = e − k t , where k is a constant related to the clarity and other physical properties of the water. The graph shows models for the open ocean, Lake Tahoe, and Lake Erie for data taken under similar conditions. Use these models for Exercises 73-76. Determine the depth at which the light intensity is 20% of the value from the surface for each body of water given. Round to the nearest tenth of a meter.
Solution Summary: The graph shows models for the open ocean, Lake Tahoe, and Lake Erie for data taken under similar conditions.
Sunlight is absorbed in water, and as a result the light intensity in oceans, lakes, and ponds decreases exponentially with depth. The percentage of visible light, P (in decimal form), at a depth of x meters is given by
P
=
e
−
k
t
, where k is a constant related to the clarity and other physical properties of the water. The graph shows models for the open ocean, Lake Tahoe, and Lake Erie for data taken under similar conditions. Use these models for Exercises 73-76.
Determine the depth at which the light intensity is 20% of the value from the surface for each body of water given. Round to the nearest tenth of a meter.
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Unit Test
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Which statement is true about the graph of the equation y = csc¯¹(x)?
There is a horizontal asymptote at y = 0.
उद
There is a horizontal asymptote at y = 2.
There is a vertical asymptote at x = 0.
O There is a vertical asymptote at x=-
R
Mark this and return
C
Save and Exit
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ے ملزمة احمد
Q (a) Let f be a linear map from a space X into a space Y and (X1,X2,...,xn) basis for X, show that fis one-to-
one iff (f(x1),f(x2),...,f(x) } linearly independent.
(b) Let X= {ao+ax₁+a2x2+...+anxn, a;ER} be a vector space over R, write with prove a hyperspace and a
hyperplane of X.
مبر خد احمد
Q₂ (a) Let M be a subspace of a vector space X, and A= {fex/ f(x)=0, x E M ), show that whether A is
convex set or not, affine set or not.
Write with prove an
application of Hahn-Banach theorem.
Show that every singleton set in a normed space X is closed and any finite set in X is closed (14M)
Let M be a proper subspace of a finite dimension vector space X over a field F show that
whether: (1) If S is a base for M then S base for X or not, (2) If T base for X then base for M
or not.
(b) Let X-P₂(x) be a vector space over polynomials a field of real numbers R, write with L
prove convex subset of X and hyperspace of X.
Q₂/ (a) Let X-R³ be a vector space over a over a field of real numbers R and
A=((a,b,o), a,bE R), A is a subspace of X, let g be a function from A into R such that
gla,b,o)-a, gEA, find fe X such that g(t)=f(t), tEA.
(b) Let M be a non-empty subset of a space X, show that M is a hyperplane of X iff there
Xiff there
exists fE X/10) and tE F such that M=(xE X/ f(x)=t).
(c) Show that the relation equivalent is an equivalence relation on set of norms on a space
X.
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