Answer:
Equation A = Graph 3
Equation B = Graph 4
Equation C = Graph 1
Equation D = Graph 2
Step-by-step explanation:
The first equation is y = x² - 7x + 10
This equation can be rearranged as
So, this is an equation of parabola having vertex at and the axis is parallel to positive y-axis.
Therefore, graph 3 is correct for this equation A.
The second equation is y = (x - 4)(x + 2)
⇒ y = x² - 2x - 8 = (x - 1)² - 9
⇒ y + 9 = (x - 1)²
So,this is an equation of parabola, having vertex at (1,-9) and axis is parallel to positive y-axis.
Therefore, graph 4 is correct for this equation B.
Now, in equation C, y = (x - 4)² + 2, ⇒ y - 2 = (x - 4)²
This is also an equation of parabola having vertex at (4,2) and the axis is parallel to positive y-axis.
Therefore, graph 1 is correct for this equation C.
Now, the remaining equation D is of graph 2.
(Answer)
To solve this problem you must apply the proccedure shown below:
1. You must use the formula for calculate the surface area and the volume of the tank:
2. Solve for in the second equation and substitute it into the first one.Then, you have:
3. Now, derivate:
4. When you solve for , you obtain:
5. Now, you must calculate :
Therefore, the dimensions are:
The sides of the base of the tank:
The height of the tank:
Answer:
see explanation
Step-by-step explanation:
the arc length of a circle is calculated as
arc = circumference of circle × fraction of circle
(5)
circumference (C) is calculated as
C = 2πr ( r is the radius )
here diameter = 12 , then r = 12 ÷ 2 = 6
C = 2π × 6 = 12π ≈ 37.7 m ( to the nearest tenth )
(6)
JK = 2πr ×
= 2π × 7 ×
= 14π ×
= ≈ 9.2 in ( to the nearest tenth )
(7)
7.5 = 2πr ×
7.5 = 2πr × ( multiply both sides by 3 to clear the fraction )
22.5 = 2πr ( divide both sides by 2π )
r = ≈ 3.6 ft
It takes 1.5 seconds to reach the maximum height and 1.5 seconds to fall back to the ground.
<h3>What is the axis of symmetry?</h3>Axis of symmetry is a line that divides an object into two equal halves, thereby creating a mirror-like reflection of either side of the object.
1. The function is a parabola of the form . The the formula for the axis of symmetry of a parabola is . We can infer from our function that a= -16 and b = 48, so lets replace those values in our formula:
x = 1.5
We can conclude that to the left of the line of symmetry the ball is reaching its maximum height, and to the right of the line of symmetry the ball is falling.
2. Lets check how much time the ball takes to reach its maximum height and return to the ground. To do that we are going to set the height equal to zero:
t = 0, (t-3) = 0
t = 0, t = 3
From our previous point we know that the ball reaches its maximum time at , which means that it takes 1.5 seconds to reach the maximum height and 1.5 seconds to fall back to the ground.
To learn more about axis of symmetry from the given link:
#SPJ4
