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h=x(V-5x)
The equation shown gives the height,
h, in meters, of a spray of water from a particular lawn sprinkler at a distance,
x meters from the sprinkler when the water is traveling at a velocity,
V, in meters per second. The maximum spraying distance is the horizontal distance from the sprinkler where the water reaches the ground. If the velocity is quadrupled, how does the maximum spraying distance change?
Choose 1 answer:
(A) The maximum spraying distance is halved.
(B) The maximum spraying distance is doubled.
(C) The maximum spraying distance is quadrupled.
(D) The maximum spraying distance is multiplied by 16.

$h=x(V-5 x)$ $\newline$ The equation shown gives the height, $h$ , in meters, of a spray of water from a particular lawn sprinkler at a distance, $x$ meters from the sprinkler when the water is traveling at a velocity, $V$ , in meters per second. The maximum spraying distance is the horizontal distance from the sprinkler where the water reaches the ground. If the velocity is quadrupled, how does the maximum spraying distance change? $\newline$ Choose $1$ answer: $\newline$ (A) The maximum spraying distance is halved. $\newline$ (B) The maximum spraying distance is doubled. $\newline$ (C) The maximum spraying distance is quadrupled. $\newline$ (D) The maximum spraying distance is multiplied by $16$ .

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Evaluate a linear function: word problems

Full solution

Q.

h=x(V-5 x)

\newline

The equation shown gives the height,

h

, in meters, of a spray of water from a particular lawn sprinkler at a distance,

x

meters from the sprinkler when the water is traveling at a velocity,

V

, in meters per second. The maximum spraying distance is the horizontal distance from the sprinkler where the water reaches the ground. If the velocity is quadrupled, how does the maximum spraying distance change?

\newline

Choose

1

answer:

\newline

(A) The maximum spraying distance is halved.

\newline

(B) The maximum spraying distance is doubled.

\newline

(C) The maximum spraying distance is quadrupled.

\newline

(D) The maximum spraying distance is multiplied by

16

.

Analyze Equation $h = x(V - 5x)$ : Let's analyze the given equation $h = x(V - 5x)$ to understand how the height of the spray depends on the distance $x$ from the sprinkler and the velocity $V$ . The maximum spraying distance occurs when the height $h$ becomes zero, because that's when the water reaches the ground.
Set $h$ to zero: Setting $h$ to zero for the maximum spraying distance, we get $0 = x(V - 5x)$ . This simplifies to $V - 5x = 0$ , because if $x$ were zero, we wouldn't be talking about a distance from the sprinkler. So, we solve for $x$ to find the maximum spraying distance.
Solve for x: Solving $V - 5x = 0$ for $x$ gives us $x = \frac{V}{5}$ . This is the original maximum spraying distance with the initial velocity $V$ .
Substitute new velocity: Now, if the velocity is quadrupled, the new velocity is $4V$ . We substitute this into the equation for $x$ to find the new maximum spraying distance: $x = \frac{4V}{5}$ .
Correct substitution: However, we made a mistake in the previous step. The correct substitution should be into the original equation $V - 5x = 0$ , replacing $V$ with $4V$ . So the new equation is $4V - 5x = 0$ .

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