Mathematics, 01.09.2020 14:01 heatherballiet866

A ranger in a lookout tower spots two fires on the campground below. Fire A is 75 meters east and 40 meters south of the tower. Fire B is 37 meters west and 64 meters south of the tower.
If there is a fire hydrant located three-fourths of the way from Fire A to Fire B, find the location
of the fire hydrant relative to the tower.

Answers: 3

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Answers

Answer from: peterblessd6868

The location of the hydrant relative to the tower is $\left(-9, -58 \right)$ meters.

How to locate the coordinates of the hydrant relative to the tower

In this question we should use the vectorial formula for a line segment to determine the coordinates of the hydrant relative to the tower ( $\vec C$ ), in meters:

$\vec C = \vec A + r\cdot (\vec B - \vec A)$ (1)

Where:

$\vec A$ - Coordinates of the fire A relative to the tower, in meters. $\vec B$ - Coordinates of the fire B relative to the tower, in meters.

- Distance ratio.

Now we determine the location of the hydrant: ( $\vec A = (75, -40)\,[m]$ , $\vec B = (-37, -64)\,[m]$ , $r = \frac{3}{4}$ )

$\vec C = (75,-40) + \frac{3}{4}\cdot [(-37,-64)-(75,-40)]$

$\vec C = (75,-40) + \frac{3}{4} \cdot (-112,-24)$

$\vec C = (75,-40) + \left(-84, -18\right)$

$\vec C = \left(-9, -58 \right)\,[m]$

The location of the hydrant relative to the tower is $\left(-9, -58 \right)$ meters. $\blacksquare$

To learn more on vectors, we kindly invite to check this verified question: link

Answer from: Shubbs

the fire hydrant is 9 meters west and 58 m south of the tower

Step-by-step explanation:

Fire A and Fire B can be represented as a point in the Cartesian coordinate with the tower as the origin. Fire A is 75 meters east and 40 meters south of the tower, It can be represented as (75, -40). Fire B is 37 meters west and 64 meters south of the tower, It can be represented as (-37, -64).

If a point O(x, y) divides a line segment AB in the ratio n:m, with A( x_1,y_1 ) and B( x_2,y_2 ), the point O(x, y) is at:

$x=\frac{n}{n+m}(x_2-x_1)+x_1\\ \\y=\frac{n}{n+m}(y_2-y_1)+y_1$

The fire hydrant (x, y) divides Fire A(75, -40) and fire B(-37, -64) in the ratio 3:1(three fourth), hence:

$x=\frac{n}{n+m}(x_2-x_1)+x_1=\frac{3}{4}(-37-75) +75=\frac{3}{4}(-112)+75=-84+75\\x=-9 \\ \\y=\frac{n}{n+m}(y_2-y_1)+y_1=\frac{3}{4}(-64-(-40))+(-40)= \frac{3}{4}(-18)-40=-18-40\\y=-58$

The fire hydrant is at (-9, -58). That is the fire hydrant is 9 meters west and 58 m south of the tower

Answer from: Quest

this is a very good question

step-by-step explanation:

i got a hair cut today from my mom not to flex just to flex kim jon un is one rad fellow i'd say you'd need to take the hairline in kinda like a box shape like someone rammed a lego brick into your head. from there you really need to take the top up keeping with that boxy aesthetic, finally coat the whole thing with gel if your country economics are failing or whatever you can just coat it with the starving children's food rations. about 5 orphans per strand is a good ratio. good luck with the fresh cut my dude

Answer from: Quest

d. millimeters per hour.

step-by-step explanation:

we are given that,

carlo used a rain gauge to measure the amount of water his lawn is receiving from the sprinklers.

since, according to the options, we see that,

water cannot be measured by 'miles per hour', 'meters per second' and 'grams per seconds'.

we get that, the water can be measured by 'millimeters per hour'.

hence, the appropriate rate for describing the amount of water is 'millimeters per hour'.

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A ranger in a lookout tower spots two fires on the campground below. Fire A is 75 meters east and 4...