Suppose that an object that is originally at room temperature of 32 ° C is placed in a freezer. The temperature T ( x ) ( in ° C ) of the object can be approximated by the model T ( x ) = 320 x 2 + 3 x + 10 , where x is the time in hours after the object is placed in the freezer. a. What is the horizontal asymptote of the graph of this function and what does it represent in the context of this problem? b. A chemist heeds a compound cooled to less than 5 ° C . Determine the amount of time required for the compound to cool so that its temperature is less than 5 ° C .
Suppose that an object that is originally at room temperature of 32 ° C is placed in a freezer. The temperature T ( x ) ( in ° C ) of the object can be approximated by the model T ( x ) = 320 x 2 + 3 x + 10 , where x is the time in hours after the object is placed in the freezer. a. What is the horizontal asymptote of the graph of this function and what does it represent in the context of this problem? b. A chemist heeds a compound cooled to less than 5 ° C . Determine the amount of time required for the compound to cool so that its temperature is less than 5 ° C .
Solution Summary: The author explains how to calculate the horizontal asymptote for the temperature equation given by T(x)=320x
Suppose that an object that is originally at room temperature of
32
°
C
is placed in a freezer. The temperature
T
(
x
)
(
in
°
C
)
of the object can be approximated by the model
T
(
x
)
=
320
x
2
+
3
x
+
10
, where x is the time in hours after the object is placed in the freezer.
a. What is the horizontal asymptote of the graph of this function and what does it represent in the context of this problem?
b. A chemist heeds a compound cooled to less than
5
°
C
. Determine the amount of time required for the compound to cool so that its temperature is less than
5
°
C
.
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Unit Test
Unit Test Review Active
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2
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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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