Answer:
Distance is 8.485
Midpoint is (3,4)
Step-by-step explanation:
Use the points (-1,7) and (5,1)
Insert them into the equation and solve for D
Insert points into second equation to find midpoint
Answer:
The length of the segment F'G' is 7.
Step-by-step explanation:
From Linear Algebra we define reflection across the y-axis as follows:
, 
(Eq. 1)
In addition, we get this translation formula from the statement of the problem:
, 
(Eq. 2)
Where:
- Original point, dimensionless.
- Transformed point, dimensionless.
If we know that 
and 
, then we proceed to make all needed operations:
Translation
Reflection
Lastly, we calculate the length of the segment F'G' by Pythagorean Theorem:
![F'G' = \sqrt{(5-5)^{2}+[(-1)-6]^{2}}](https://tex.z-dn.net/?f=F%27G%27%20%3D%20%5Csqrt%7B%285-5%29%5E%7B2%7D%2B%5B%28-1%29-6%5D%5E%7B2%7D%7D)
The length of the segment F'G' is 7.
Answer:
The age of the horse, in human years, when Alex was born can be determined by simply deducting the Current age of Alex from the Current age of the horse in human years.
Therefore, the age of the horse, in human years, when Alex was born was 42 years.
Step-by-step explanation:
Current age of Alex = 8
Current age of the horse in human years = 50
Since the age of the horse is already stated in human years, it implies there is no need to convert the age of the horse again.
Therefore, since Alex is a human who was born 8 years ago, the age of the horse, in human years, when Alex was born can be determined by simply deducting the Current age of Alex from the Current age of the horse in human years as follows:
The age of the horse, in human years, when Alex was born = 50 - 8 = 42
Therefore, the age of the horse, in human years, when Alex was born was 42 years.
This can be presented in a table as follows:
Age of Alex Age of the Horse (in human years)
Eight years ago 0 42
Current age 8 50
∫ e^(3x)*(cosh(2x)dx
= ∫ [e^(3x)*(e^(2x)+e^(-2x))/2]dx
= ∫ [(e^(5x)+e^x)/2]dx
=e^(5x)/10+e^x/2+C
=(1/10)(e^(5x)+5e^x)+C
