Answer:
See answers and explanations below (along with a visual graph)
Step-by-step explanation:
For the function
:
Amplitude: 
Period: 
Phase shift: 
Vertical shift: 
Therefore, for
:
Amplitude:
, which is 2 units above and below the midline (see d)
Period:
, so the cycle will repeat every 3π units
Phase shift:
, or π units to the left
Vertical shift:
, or 1 unit down
X = short section of rope
4x = longer section of rope
x + 4x = 25
5x = 25
x = 5
…or in other words the shorter piece of rope is 5 feet long
Answer:
y = 3x + 15
Step-by-step explanation:
1. Find the reciprocal of the slope and change signs: -3
2. y = 3x + b
3. Plug in x and y --> b = 15
4. Make your equation using y = mx + b: y = 3x + 15
Answer:
1 1/4
Step-by-step explanation:
3 1/8 - 1 7/8
I like to line them up vertically
3 1/8
- 1 7/8
---------------
We need to borrow from the 3
Take 1 from the 3 and make it 8/8
2 (1/8+8/8)
- 1 (7/8)
---------------------
2 (9/8)
- 1 (7/8)
---------------------
1 2/8
Simplify the fraction by dividing by 2 on the top and bottom
1 1/4
Answer:
a.
and 41.6
b. 52.1
Step-by-step explanation:
a.
Considering the left side triangle the blue dotted side is the side "opposite" to the angle given and the side 24 is the side that is "adjacent" to the angle given. The trigonometric ratio tan relates opposite to adjacent. Also, let the blue dotted side be y.
<u>Note:</u> the exact value of tan 60 is 
Thus, we can write 
Approximate value (rounded to nearest tenth): 
b.
Considering the triangle to the right, the side "opposite" to the angle given (53 degrees) is 41.6 (just found in part (a)) and the side "hypotenuse" (side opposite to 90 degree angle) is x. The trigonometric ratio sine relates opposite and hypotenuse.
Thus we can write and solve:
