I realize that the equation is different, but do it in the same way, it'll help! It is given that the water taxi's path can be modeled by the equation y =0.5(x - 14)^2. Therefore, this is one of the equations in this system. Find a linear equation that will model the path of the water skier, which begins at the point (6,6) and ends at the point (8,-4). The slope is (-5). Use the slope and one point on the line to find the y-intercept of the line. The y-intercept of the line that passes through the points (6,6) and (8,-4) is (0,36). Thus, the equation is y=-5x+36. Now, to determine if it is possible for the water skier to collide with the taxi, we have to determine if there is a solution to the system of equations. To determine if there is a solution to the system of equations, solve the system using substitution. First, write the equation that models the water taxi's path in standard form. y=0.5(x - 14)^2-->0.5x^2-14x+98. Use substitution. Substitute for y in the equation and then solve for x. As the expression on the left side of the equation cannot easily be factored, use the Quadratic Formula to solve for x. Do x=-b(plusorminus)sqrrtb^2-4ac/2a. Identify a, b, and c. a=0.5, b=-9, and c=62. Substitute into the Quadratic Formula. If there is a negative number under the radical, there are NO solutions. Thus, the path of the water skier will never cross the path of the taxi.
In conclusion: It is not possible that the water skier could collide with the taxi as the two paths never cross.
Answer:
<u>135.94 feet</u>
Step-by-step explanation:
Split the problem into two parts :
- Distance between viewer and building
- Height of the top part of the building
<u>Distance between viewer and building</u>
- The lower part of the building is 40 feet, as it is mentioned the viewer is 40 feet above street level
- Let the distance be called 'd'
- Therefore, tan37° = 40/d
- tan37° = 3/4 = 0.75
- ⇒ 40/d = 0.75
- ⇒ d = 40/(3/4) = 40 x 4/3 = 160/3 = 53.3 feet
<u>Height of the top part of the building</u>
- Let the height of the top part be 'h'
- Therefore, tan61° = h/d = h/53.3
- tan61° = 1.8
- ⇒ h/53.3 = 1.8
- ⇒ h = 53.3 x 1.8 = 95.94 feet
<u>Total height of building</u>
- Lower part + Top part
- 40 + 95.94
- <u>135.94 feet</u>
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Answer:
Horizontal, 0, y
Step-by-step explanation:
9514 1404 393
Answer:
- relative minimum -6√3 at x = -√3
- relative maximum 6√3 at x = √3
- decreasing on x < -√3 and x > √3
- increasing on -√3 < x < √3
- see below for a graph
Step-by-step explanation:
I find it convenient to draw the graph first when looking for relative extrema.
The function can be differentiated to get ...
f'(x) = -3x^2 +9
This is zero when ...
-3x^2 +9 = 0
x^2 = 3
x = ±√3 . . . . . x-values of relative extrema
Then the extreme values are ...
f(±√3) = x(9 -x^2) = (±√3)(9 -3) = ±6√3
The lower extreme (minimum) corresponds to the lower value of x (-√3), so the extrema are ...
(x, y) = (-√3, -6√3) and (√3, 6√3)
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Since the leading coefficient is negative and the degree is odd, the function is decreasing for values of x below the minimum and above the maximum. It is increasing for values of x between the minimum and the maximum.
decreasing: x < -√3, and √3 < x
increasing: -√3 < x < √3
