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k(x)=5x^(2)
The function models
k, the kinetic energy in joules of a silver carp with a mass of 10 kilograms as it swims at a speed of
x meters per second. Which of the following statements is the best interpretation of the ordered pair
(2.4,28.8) ?
Choose 1 answer:
(A) A silver carp can swim 28.8 meters in 2.4 seconds.
(B) The maximum kinetic energy of a 2.4-kilogram silver carp is 28.8 joules.
(C) The kinetic energy of a 10-kilogram silver carp is 2.4 joules when it is swimming at a speed of 28.8 meters per second.
(D) The kinetic energy of a 10-kilogram silver carp is 28.8 joules when it is swimming at a speed of 2.4 meters per second.

$k(x)=5 x^{2}$ $\newline$ The function models $k$ , the kinetic energy in joules of a silver carp with a mass of $10$ kilograms as it swims at a speed of $x$ meters per second. Which of the following statements is the best interpretation of the ordered pair $(2.4,28.8)$ ? $\newline$ Choose $1$ answer: $\newline$ (A) A silver carp can swim $28$ . $8$ meters in $2$ . $4$ seconds. $\newline$ (B) The maximum kinetic energy of a $2$ . $4$ -kilogram silver carp is $28$ . $8$ joules. $\newline$ (C) The kinetic energy of a $10$ -kilogram silver carp is $2$ . $4$ joules when it is swimming at a speed of $28$ . $8$ meters per second. $\newline$ (D) The kinetic energy of a $10$ -kilogram silver carp is $28$ . $8$ joules when it is swimming at a speed of $2$ . $4$ meters per second.

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Solve quadratic equations: word problems

Full solution

Q.

k(x)=5 x^{2}

\newline

The function models

k

, the kinetic energy in joules of a silver carp with a mass of

10

kilograms as it swims at a speed of

x

meters per second. Which of the following statements is the best interpretation of the ordered pair

(2.4,28.8)

?

\newline

Choose

1

answer:

\newline

(A) A silver carp can swim

28

.

8

meters in

2

.

4

seconds.

\newline

(B) The maximum kinetic energy of a

2

.

4

-kilogram silver carp is

28

.

8

joules.

\newline

(C) The kinetic energy of a

10

-kilogram silver carp is

2

.

4

joules when it is swimming at a speed of

28

.

8

meters per second.

\newline

(D) The kinetic energy of a

10

-kilogram silver carp is

28

.

8

joules when it is swimming at a speed of

2

.

4

meters per second.

Understand Function $k(x)$ : Understand the function $k(x)=5x^{2}$ and what it represents. $\newline$ The function $k(x)$ gives us the kinetic energy in joules of a silver carp with a mass of $10$ kilograms when it swims at a speed of $x$ meters per second. The variable $x$ represents the speed of the carp in meters per second, and $k(x)$ represents the kinetic energy in joules.
Interpret Ordered Pair: Interpret the ordered pair $(2.4, 28.8)$ . The ordered pair $(2.4, 28.8)$ means that when $x$ (the speed of the carp in meters per second) is $2.4$ , $k(x)$ (the kinetic energy in joules) is $28.8$ . This does not give us any information about the time it takes for the carp to swim a certain distance or the mass of the carp, only the relationship between its speed and kinetic energy.
Evaluate $k(x)$ at $x=2.4$ : Evaluate the function $k(x)$ at $x=2.4$ to verify the ordered pair. $\newline$ $k(2.4) = 5 \times (2.4)^2$ $\newline$ $k(2.4) = 5 \times 5.76$ $\newline$ $k(2.4) = 28.8$ joules $\newline$ This calculation confirms that the ordered pair $(2.4, 28.8)$ is correct for the given function.
Match Ordered Pair with Interpretation: Match the ordered pair $(2.4, 28.8)$ with the correct interpretation. $\newline$ (A) This option is incorrect because the function does not provide information about distance traveled over time. $\newline$ (B) This option is incorrect because the mass of the carp is given as $10$ kilograms, not $2.4$ kilograms. $\newline$ (C) This option is incorrect because it reverses the values for speed and kinetic energy. $\newline$ (D) This option is correct because it accurately describes the kinetic energy of a $10$ -kilogram silver carp swimming at a speed of $2.4$ meters per second.

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