The height of a stream of water from the nozzle of a fire hose is modeled by h(x) =-0.03x2+ 2x + 38 where h(x) is the height in feet, of the stream of water x feet from the fire truck. 1. What is the maximum height the water from this nozzle can reach? What is the maximum distance from the firetruck a firefighter can stand and still reach the fire?

height: 71.33 feetreach: 82.10 feet

Step-by-step explanation:

The equation can be rewritten to vertex form:

  h(x) = -0.03(x² - 200/3x) +38

  h(x) = -0.03(x² -200/3x +(100/3)²) +38 +.03(100/3)²

  h(x) = -0.03(x -33 1/3)² +71 1/3

The vertex is (33 1/3, 71 1/3), so the maximum height the water will reach is 71 1/3 feet.

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When h(x) = 0, the water reaches as far as it possibly can.

  0 = -0.03(x -33 1/3)² +71 1/3

  (-71 1/3)/(-0.03) = (x -33 1/3)² . . . subtract 71 1/3; divide by -0.03

  √(2377.78) = x -33.33 . . . . . . . . positive square root

  82.10 ≈ x

The maximum distance the water will reach is 82.10 feet.

Answer: question no. 1 -a. yes, the sides are in the ratio 2 : 5.question no. 2 -b. 59°question no. 3 -c. angles x and y are remote interior angles.question no. 4 -d. 90°, 45° and 45°question no. 5 -b. mn and qrstep-by-step explanation: question no. 1 -rs : xu = 3 : 7.5 = 2 : 5rt : x? = 6.4 : 16 = 2 : 5st : u? = 6 : 15 = 2 : 5as the ratios of all sides are equivalent, the triangles must be congruent and the sides must be proportional.therefore, the answer is: a. yes, the sides are in the ratio 2 : 5.question no. 2 -in the second diagram, angle b is the only letter not shown. therefore, the number must be equivalent to angle b.if we substitute the value of angle b as being 22° in the first diagram, we can now use the angle sum of a triangle to obtain the value of angle a.angle sum of a triangle = 180°therefore: let angle a = aa + 99 + 22 = 180a = 180 - 99 - 22a = 59°therefore, the answer is: b. 59°question no. 3 -angles x and y don't share the vertex of the triangle with the exterior angle w. remote interior angles don't share a vertex of a triangle with an exterior angle. this means that angles x and y are remote interior angles.therefore, the answer is: c. angles x and y are remote interior angles.question no. 4 -the sum of all interior angles of a triangle must be equivalent to 180°.90°, 45° and 45° are the only set of angle measures that are equivalent to 180°.therefore, the answer is: d. 90°, 45° and 45°question no. 5 -the only pair of sides stated in the options which are corresponding are mn and qr.therefore, the answer is: b. mn and qr.