Step-by-step explanation:
For a quadratic equation y = ax² + bx + c, the vertex (the maximum or minimum point) is at x = -b/(2a).
1) y = -0.5t² + 2t + 38
The maximum is at:
t = -2 / (2 × -0.5)
t = 2
The maximum height is:
y = -0.5(2)² + 2(2) + 38
y = 40
The coordinates of the vertex are (2, 40). That means the missile reaches a maximum height of 40 km after 2 minutes.
2) y = -4.9t² + 12t + 1.6
The maximum is at:
t = -12 / (2 × -4.9)
t = 1.22
The maximum height is:
y = -4.9(1.22)² + 12(1.22) + 1.6
y = 8.95
The coordinates of the vertex are (1.22, 8.95). That means the missile reaches a maximum height of 8.95 m after 1.22 seconds.
3) y = -0.04x² + 0.88x
The maximum is at:
x = -0.88 / (2 × -0.04)
x = 11
The maximum height is:
y = -0.04(11)² + 0.88(11)
y = 4.84
The maximum height of the tunnel is 4.84 meters.
The maximum width is when y = 0.
0 = -0.04x² + 0.88x
0 = -0.04x (x − 22)
x = 22
The maximum width is 22 feet.
Finding the square<span> root of a </span>number<span> is the inverse operation of squaring that </span>number<span>. Remember, the </span>square<span> of a </span>number<span> is that </span>number<span> times itself. The perfect squares are the squares of the whole </span>numbers<span>. The </span>square<span> root of a </span>number<span>, n, written below is the </span>number<span> that gives n when multiplied by itself.
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Answer:
The constant of proportionality is equal to 4
Step-by-step explanation:
The picture of the question in the attached figure
Let
y ----> the total cost in dollars
x ----> the number of bags of peanuts
we know that
A relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form 
or 
To find out the constant of proportionality, we need to take one point from the graph
take the point (1,4)
Find the value of k
substitute the value of x and the value of y
If a line is parallel to another, the slopes of both lines are the same. So for this problem, you can infer that the slope of the line you're trying to find is 3.
To find the actual equation of the line, you can use the given coordinates and plug them into the point slope form:
y - y1 = m(x - x1)
plug the given y coordinate into y1 and the given x coordinate into x1. m is the slope, so plug in 3 for m.
y - 1 = 3(x +2) Use distributive property for right side of equation
y - 1 = 3x + 6 add 1 to both sides to cancel -1 on left side of equation and isolate y
Equation of line: y = 3x + 7
It should be noted that Polygon 3 and polygon 4 are similar to polygon 1.
<h3>
What exactly is polygon?</h3>
In geometry, it should be noted that a polygon is a plane figure which is described by a finite number of straight line segments that are connected in order to form a closed polygonal chain.
In this case, the bounded plane region, the bounding circuit, may be called a polygon. Also, a similarity transformation is the conformal mapping whose transformation matrix are identical.
In this case, it should be noted that Polygon 3 and polygon 4 are similar to polygon 1.
Learn more about polygon on:
brainly.com/question/24966296
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