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Korvikt [17]
3 years ago
6

To control an infection, a doctor recommends that a patient who weighs 92 pounds be given 320 milligrams of antibiotic. If the a

ntibiotic is given proportionally according to the patient's weight, how much antibiotic should be given to a patient who weighs 138 pounds?
A 400 milligrams
B 480 milligrams
C 550 milligrams
D 600 milligrams
Mathematics
1 answer:
Goshia [24]3 years ago
6 0

Answer:

480 milligrams

Step-by-step explanation:

92 pounds → 320 milligrams

138 pounds → 320/92 x 138 = 480 milligrams

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Answer:

\{T(v_1), T(v_2), T(v_3)\} is linearly dependent set.

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Given:  \{v_1,v_2,v_3\} is a linearly dependent set in set of real numbers R

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Solution:

If \{v_1,v_2,v_3,...,v_n\} is a set of linearly dependent vectors then there exists atleast one k_i:i=1,2,3,...,n such that k_1v_1+k_2v_2+k_3v_3+...+k_nv_n=0

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A linear transformation T: U→V satisfies the following properties:

1. T(u_1+u_2)=T(u_1)+T(u_2)

2. T(au)=aT(u)

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As T is a linear transformation,

k_1T(v_1)+k_2T(v_2)+k_3T(v_3)=0\\T(k_1v_1)+T(k_2v_2)+T(k_3v_3)=0\\T(k_1v_1+k_2v_2+k_3v_3)=0\\

As \{v_1,v_2,v_3\} is a linearly dependent set,

k_1v_1+k_2v_2+k_3v_3=0 for some k_i\neq 0:i=1,2,3

So, for some k_i\neq 0:i=1,2,3

k_1T(v_1)+k_2T(v_2)+k_3T(v_3)=0

Therefore, set \{T(v_1), T(v_2), T(v_3)\} is linearly dependent.

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