Two water balloons were launched into the air at different moments and collided. the water balloons were modeled by the quadratic functions: y = −7x2 26x 3 and y = −6x2 23x 5, where y represents the height in meters and x represents the time in seconds after the launch. 2.0 seconds is the time, in seconds, that the balloons collided at the highest point
The time in seconds that the balloons collided at the highest point is; B: 2.0 seconds
We are told that the water balloons were modeled by the quadratic functions:
y = -7x² + 26x + 6 and y = -6x² + 25x + 4
where;
y = the height in meters
x = the time in seconds after the launch
The time at which they will collide has to be at the same height.
Thus;
-7x² + 26x + 6 = -6x² + 25x + 4
Rearranging this gives;
x² - x - 2 = 0.
Using an online quadratic equation solver gives us x = 2 or -1. We will take the positive one as x = 2.0 seconds
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Do the multiplication both sides,
Arrange the terms to LHS according to their variables,
Factorise this polynomial
So what we notice here is when you're multiplying two numbers you're getting 0 as answer.
So one of them must be 0.
If (x-1) is 0
then x = 1
similarly,
x-6=0
then, x= 6.
So the possible values of x are 1 and 6.
To calculate this you need to imagine triangle which points are:
boat
Top of lighthouse
Bottom of lighthouse
That triangle has 90 degrees angle at bottom of lighthouse. That means that we can use trigonometry to determine length between boat and bottom of lighthouse
tan(25) = 89/x
x = 89/tan(25)
x = 190.86
after rounding, the answer is D, 191 feet
<span>A shape has Rotational Symmetry when it still looks the same after a rotation.</span>
The unit rate per munchkin is $0.22.
<h3>
What is Division?</h3>
Division is one of the four fundamental arithmetic operations, which tells us how the numbers are combined to form a new one.
The cost of 25 munchkins cost $5.46, therefore, the unit rate of each munchkin can be written as,
Hence, the unit rate per munchkin is $0.22.
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