Answer:
The following are not permitted: g = 0, g + -4 and g= 3
Step-by-step explanation:
Recall that division by zero is not defined or allowed. Thus, we take the denominator, g^3+g^2−12g and set it equal to zero, to identify the x values at which the den. is zero:
g^3+g^2−12g = 0
g(g^2 + g - 12) = 0
g(g+4)(g-3) = 0 => g = 0, g + -4 and g= 3.
These three x values constitute the domain restrictions; they are not permitted.
First distribute 2a+8-2a-8
The answer is 0
Answer:
Therefore the angle that the line through the given pair of points makes with the positive direction of the x-axis is 45°.
Step-by-step explanation:
Given:
Let
A(x₁ , y₁) = (1 , 4) and
B( x₂ , y₂ ) = (-1 , 2)
To Find:
θ = ?
Solution:
Slope of a line when two points are given is given bt
![Slope(AB)=\dfrac{y_{2}-y_{1} }{x_{2}-x_{1} }](https://tex.z-dn.net/?f=Slope%28AB%29%3D%5Cdfrac%7By_%7B2%7D-y_%7B1%7D%20%7D%7Bx_%7B2%7D-x_%7B1%7D%20%7D)
Substituting the values we get
![Slope(AB)=\dfrac{2-4}{-1-1}=\dfrac{-2}{-2}=1\\\\Slope=1](https://tex.z-dn.net/?f=Slope%28AB%29%3D%5Cdfrac%7B2-4%7D%7B-1-1%7D%3D%5Cdfrac%7B-2%7D%7B-2%7D%3D1%5C%5C%5C%5CSlope%3D1)
Also Slope of line when angle ' θ ' is given as
![Slope=\tan \theta](https://tex.z-dn.net/?f=Slope%3D%5Ctan%20%5Ctheta)
Substituting Slope = 1 we get
![1=\tan \theta](https://tex.z-dn.net/?f=1%3D%5Ctan%20%5Ctheta)
![\tan \theta=1\\\theta=\tan^{-1}(1)](https://tex.z-dn.net/?f=%5Ctan%20%5Ctheta%3D1%5C%5C%5Ctheta%3D%5Ctan%5E%7B-1%7D%281%29)
We Know That for angle 45°,
tan 45 = 1
Therefore
![\theta=45\°](https://tex.z-dn.net/?f=%5Ctheta%3D45%5C%C2%B0)
Therefore the angle that the line through the given pair of points makes with the positive direction of the x-axis is 45°.
Another way of presenting this question is to ask: what is the volume of the prism. Sometimes, you can get tripped up on the terminology and fail to discover what it is the question is really asking. To find the volume of this concave prism, we can divide it into two boxes: top box and bottom box. Imagine slicing a knife through the line where the two "steps" intersect. From there, we can apply the basic formula for a rectangular prism and add up the volumes.
Top Box:
A = height x length x width
A = 10 x 40 x 20
(the height is 10 because it is equal to the tallest height minus the shorter height)
A = 8000 in. cubed
Bottom Box:
A = height x length x width
A = 20 x 60 x 20
A = 24000 in. cubed
Total Volume = 24000 in. cubed + 8000 in. cubed = 32000 in. cubed
Hoped this helped!