The horizontal distance from the firefighter at which the maximum height of water occurs is 10.83m
<u>Explanation:</u>
Given:
h(x) = -0.026x² + 0.563x + 3
where,
h(x) is the height of the water
Initial speed, u = 14m/s
angle, θ = 30°
(a)
Horizontal distance = ?
h(x) = ax² + bx + c
the vertex is found at x = -b/2a
where,
x = distance to the maximum height
As compared to the equation given:
a = -0.026
b = 0.563
Thus,

Therefore, horizontal distance from the firefighter at which the maximum height of water occurs is 10.83m
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<em>We will assume the tent is in the shape of a triangular prism.</em>
The volume of a triangular prism can be found with the following formula, where
is the width at the base,
is the height, and
is the length.

Substitute in the known values.

Simplify — use multiplication.



Simplify — use division.

The volume — or in this case, the amount of living space — is
.
Answer:
Actual length of the Bridge = 8983.33 feet.
Step-by-step explanation:
The scale is 1 unit = 19,600.
Height of the postcard is 3.5 inches.
So, original height of the bridge = 3.5 × 19,600 = 68,600 inches
= 5716.67 feet
Width of the postcard is 5.5 inches.
So, original width of the bridge = 5.5 × 19,600 = 107,800 inches
= 8983.33 feet
Step-by-step explanation:
f(x) = x² + 1, where x >= 0.
Let y be f(x).
=> y = x² + 1
=> x² = y - 1
=> x = √(y - 1) because x is non-negative.
Hence f^-1(x) = √(x - 1), where x >= 1.