Answer:
45° and 135°
Step-by-step explanation:
let one angle be "x" and the other be "y"
Angles which are supplementary total to 180°. This can be represented with the equation:
x + y = 180
If angle "x" is a third of angle "y", the situation is represented with this equation:
(1/3)x = y
Since fractions are difficult to work with, multiply the whole equation by 3.
(1/3)x = y <= X 3
x = 3y
Use the equations x+y=180 and x=3y.
You can substitute x=3y into x+y=180.
x + y = 180
(3y) + y = 180 <=combine like terms
4y = 180 <=isolate y by dividing both sides by 4
y = 45
Substitute y=45 itno the equation x+y=180 to find x.
x + y = 180
x + 45 = 180 <=isolate x by subtracting 45 from both sides
x = 135
Therefore the angles are 45° and 135°.
Answer:
Step-by-step explanation:
Yes, it is a line of slope 1.
Answer:
a) see below
b) 40x20 meters
Step-by-step explanation:
Write down what you know:
- The area of the enclosure is length*width, so
- The length of the fencing is 80 meters, so
Now we have to combine these two equations above, and get rid of y in the process.
First rewrite the second as:
Then substitute for y in the first:
b) To maximize A, find the zero of the first derivative:
So y = (80-40)/2 = 20 meters.
