Ans67
Step-by-step explanation:
Answer:
a) d = 36 ft. ( using Pithagoras´theorem )
b) d = 36 ft ( Using ( function sin ) trigonometry
Step-by-step explanation:
a) Using Pythagoras´Theorem:
Diagonal (d) is the hypothenuse of a right triangle of side 25 feet, and according to Pythagoras´Theorem in a right triangle.
d² = a² + b²
In this particular case a = b = 25 feet then
d² = (25)² + ( 25)²
d = √ 2 * (25)²
d = √2 * 25
d = 1,414*25
d = 35,35
d = 36 ft.
b) Using trigonometry:
We know that sin 45° = cos 45° = √2 / 2
In a right triangle
sin α = opposite side / hypothenuse (d)
sin 45° = √2 / 2 = 25/ d
√2 *d = 2* 25
d = 50/√2
d = 50 / 1,414
d = 35,36
d = 36 ft
Given that,
Total cost function, C (x) = 43x + $1850
The revenue function R (x) = $80x
To find,
The number of units that must be produced and sold to break even.
Solution,
At break even, cost = revenue
43x + $1850 = $80x
Subtract 80x from both sides.
43x + 1850 -80x = $80x -80x
1850 = 80x-43x
37x = 1850
x = 50
So, the required number of units are 50.
Step-by-step explanation: To solve this absolute value inequality,
our goal is to get the absolute value by itself on one side of the inequality.
So start by adding 2 to both sides and we have 4|x + 5| ≤ 12.
Now divide both sides by 3 and we have |x + 5| ≤ 3.
Now the the absolute value is isolated, we can split this up.
The first inequality will look exactly like the one
we have right now except for the absolute value.
For the second one, we flip the sign and change the 3 to a negative.
So we have x + 5 ≤ 3 or x + 5 ≥ -3.
Solving each inequality from here, we have x ≤ -2 or x ≥ -8.
