Answer:
29.4 cm
Step-by-step explanation:
The length of the space diagonal can be found to be the root of the squares of the three orthogonal edge lengths. For a cube, those edge lengths are all the same, so the diagonal length is ...
d = √(17^2 + 17^2 +17^2) = 17√3 ≈ 29.4 . . . . cm
_____
Consider a rectangular prism with edge lengths a, b, c. Then the face diagonal of the face perpendicular to edge "a" has length ...
(face diagonal)^2 = (b^2 +c^2)
and the space diagonal has length ...
(space diagonal)^2 = a^2 + (face diagonal)^2 = a^2 +b^2 +c^2
So, the length of the space diagonal is ...
space diagonal = √(a^2 +b^2 +c^2)
when the prism is a cube, these are all the same (a=b=c). This is the formula we used above.
Step-by-step explanation:
<h2><em>Factor the </em><em>expression</em></h2>
<em>
</em>
<h2><em>Separate into possible cases</em></h2>
<em>
</em>
<h2><em>Solve the equation</em></h2>
<em>![n = 0[tex]n = 0 \: \: \: \: \: \: \: \: [tex]n = 0 \: \: \: \: \: \: \: \: 2n ^ 2 - 3n + 2 = 0](https://tex.z-dn.net/?f=n%20%3D%200%3C%2Fem%3E%3C%2Fp%3E%3Cp%3E%3Cem%3E%5Btex%5Dn%20%3D%200%20%5C%3A%20%20%5C%3A%20%20%5C%3A%20%20%5C%3A%20%20%5C%3A%20%20%5C%3A%20%20%5C%3A%20%20%5C%3A%20%3C%2Fem%3E%3C%2Fp%3E%3Cp%3E%3Cem%3E%5Btex%5Dn%20%3D%200%20%5C%3A%20%20%5C%3A%20%20%5C%3A%20%20%5C%3A%20%20%5C%3A%20%20%5C%3A%20%20%5C%3A%20%20%5C%3A%202n%20%5E%202%20-%203n%20%2B%202%20%3D%200)
</em>
<h2><em>Find the union</em></h2>
<em>![n = 0[tex]n = 0 \: \: \: \: \: \: [tex]n = 0 \: \: \: \: \: \: n = R](https://tex.z-dn.net/?f=n%20%3D%200%3C%2Fem%3E%3C%2Fp%3E%3Cp%3E%3Cem%3E%5Btex%5Dn%20%3D%200%20%5C%3A%20%20%5C%3A%20%20%5C%3A%20%20%5C%3A%20%20%5C%3A%20%20%5C%3A%20%3C%2Fem%3E%3C%2Fp%3E%3Cp%3E%3Cem%3E%5Btex%5Dn%20%3D%200%20%5C%3A%20%20%5C%3A%20%20%5C%3A%20%20%5C%3A%20%20%5C%3A%20%20%5C%3A%20n%20%3D%20%20R)
</em>
<h2><em>there </em><em>for </em></h2>
<em></em>
<em>hope </em><em>it</em><em> help</em>
<em>#</em><em>c</em><em>a</em><em>r</em><em>r</em><em>y</em><em> </em><em>on</em><em> learning</em>
Answer: 1) x> -21
2) x is less than or equal to -21
3) x is less than or equal to 16
4) x less than or equal to 3/4
As you may already be familiar, these functions f(x) and g(x) are piecewise. They consist of multiple functions with different domains.
1. For #1, the given input is f(0). Since 0≤1, you should use the first equation to solve. f(0)=3(0)-1 ➞ f(0)=-1
2. Continue to evaluate the given input for the domains given. 1≤1, therefore f(1)=3(1)-1➞f(1)=2
3. 5>1, therefore f(5)=1-2(5)➞f(5)=-9
4. -4≤1; f(-4)=3(-4)-1➞f(-4)=-13
5. -3<0<1; g(0)=2
6. -3≤-3; g(-3)=3(-3)-1➞g(-3)=-10
7. 1≥1; g(1)=-3(1)➞g(1)=-3
8. 3≥1; g(3)=-3(3)➞g(3)=-9
9. -5≤-3; g(-5)=3(-5)-1➞g(-5)=-16
Hope this helps! Good luck!
