You can factor a parabola by finding its roots: if
has roots , then you have the following factorization:
In order to find the roots, you can use the usual formula
In the first example, this formula leads to
So, you can factor
The same goes for the second parabola.
As for the third exercise, simply plug the values asking
you get
Add 3 to both sides:
Divide both sides by 1.5:
Answer:
<u>Step-by-step explanation:</u>
9x² + 4 = 0
<u> -4 </u> <u>-4 </u>
9x² = -4
x² =
Answer:
2656.31
Step-by-step explanation:
To calculate the surface area, we need to find the area of all the faces, and add them together.
The faces of the cylinder are: the rectangular base, the curved top, and the two semicircles on the side.
Rectangular base:
A = length x width
A = 29.3 x 16.2
A = 474.66
Two semicircles:
A = x
(I'm using the formula for a circle, because the two semicircles are identical, so together they form a circle)
radius = 29.3/2 = 14.65
A = x
A = 674.256 (rounded to 3 decimal places)
Curved top:
The curved top, when flattened out, becomes a rectangle with a length of 16.2. The width is equal to half the circumference of the circle formed by the two semicircles.
To find the width, use the circumference (C) formula.
C = x diameter
diameter = 29.3
C = x 29.3
C = 93.049 (rounded to 3 DP)
Area (of curved top) = length x width
A = 16.2 x 93.049
A = 1507.394 (rounded to 3 DP)
Surface Area
SA = 474.66 + 674.256 + 1507.394
SA = 2656.31