+2441 Obviously, two others have already posted their own solution, but I put in a solution earlier at https://web2.0calc.com/questions/helppppp_16#r1
Given that the forum title of this question is "i still dont get it," I assume that you were confused with my solution. You are always strongly encouraged to request for clarification. It is detrimental to you to pretend as if you understand.
Is there a particular section that confused you?
Do you understand what "surface area" means?
Is there a particular section where you would like more detail?
+2441 The following diagram illustrates the gist of the Fundamental Theorem of Algebra.
\(P(x)=\underbrace{ax^n+bx^{n-1}+cx^{n-2}+...+yx+z}\\ \hspace{30mm}\text{n complex roots}\)
The degree of the polynomial of \(2x^2+8x+14\) is 2, so the number of complex roots is also 2.
You can use the quadratic formula to find those roots.
| \(2x^2+8x+14=0\) | Apply the quadratic formula! |
| \(x_{1,2}=\frac{-8\pm\sqrt{8^2-4*2*14}}{2*2}\) | Now it is a matter of simplifying. |
| \(x_{1,2}=\frac{-8\pm\sqrt{64-112}}{4}\) | |
| \(x_{1,2}=\frac{-8\pm\sqrt{-48}}{4}\) | |
| \(x_{1,2}=\frac{-8\pm\sqrt{48*-1}}{4}\) | |
| \(x_{1,2}=\frac{-8\pm i\sqrt{48}}{4}\) | |
| \(x_{1,2}=\frac{-8\pm i\sqrt{16*3}}{4}\) | |
| \(x_{1,2}=\frac{-8\pm 4i\sqrt{3}}{4}\) | |
| \(x_{1,2}=-2\pm i\sqrt{3}\) | |
+2441 #1)
One way to approach this problem is to add up the sides of all the faces. All the faces are rectangular-shaped, so finding their individual area is not too difficult.
| \(A_{\text{AGFD}}=lw\) | This is the formula for the area of this side. Its length (l) is 6 units, and the width (w) is 4 units. |
| \(A_{\text{AGFD}}=6*4\) | |
| \(A_{\text{AGFD}}=24\text{ square units}\) | Area is always represented as a square unit since it measures in two dimensions. |
We can do the same calculation for the other faces.
| \(A_{\text{ABCD}}=lw\) | Use the diagram to find these lengths. |
| \(A_{\text{ABCD}}=6*2\) | |
| \(A_{\text{ABCD}}=12\text{ square units}\) | |
| \(A_{CDFE}=lw\) | We might as well find the other one, too. |
| \(A_{\text{CDFE}}=4*2\) | |
| \(A_{\text{CDFE}}=8\text{ square units}\) | |
Because the above figure is a rectangular prism, the opposite face is equal to one that I already found.
| \(SA_{total}=2(A_{\text{AGFD}}+A_{\text{ABCD}}+A_{\text{CDFE}}\) | Let's plug in the values we know. |
| \(SA_{total}=2(24+12+8)\) | One luxury unique to addition and multiplication is that you can perform the calculation in any order you desire; therefore, I will find the sum of 12 and 8 because they add up to a number where its last digit is zero. |
| \(SA_{total}=2(24+20)\) | |
| \(SA_{total}=2(44)\) | |
| \(SA_{total}=88\text{ square units}\) | |
#2)
A dihedral angle is formed when two planes intersect. \(\angle JAB\) has the same measure because it is included in the dihedral angle.
