1√3
The exact value of cot(π3) cot ( π 3 ) is 1√3 .
complete question:
A fountain is made up of two semicircles and a quarter circle. The diameter of the semicircles is 10 ft. Find the perimeter of the fountain. Round your answer to the nearest tenth. The picture is represented below.
Answer:
The perimeter of the fountain = 47.1 ft
Step-by-step explanation:
The fountain has 2 semi circle from a smaller circle with the diameter represented as 10 ft and a quarter circle from a bigger circle with the radius equals to 10 ft.
The perimeter is the distance around the fountain.The perimeter is the circumference in circular perspective. Therefore,
perimeter for a full circle = 2πr
Half circle = 2πr/2 = πr
For 2 half circle = πr + πr = 2πr
For 2 half circle = 2πr
r = 10/2 = 5
perimeter for 2 half circle = 2 × 5 × 3.14 = 31.4 ft
Perimeter for the quarter circle
r = 10 ft
Quarter circle perimeter = 1/4 × 2πr = πr/2
Quarter circle perimeter = (3.14 × 10)/2
Quarter circle perimeter = (31.4)/2
Quarter circle perimeter = 15.7 ft
The perimeter of the fountain = 15.7 ft + 31.4 ft = 47.1 ft
Answer:
f(x) = -3x
--->#6
f(x) = |x-1|+3
--->#5
f(x) = √(x+3)
--->#3
1/2x²
--->#1
f(x) = (x+1)²-3
--->#4
4|x|--->#2
Step-by-step explanation:
Recall for transformations:
- Adding a number outside the function moves it up
- Subtracting a number outside the function moves it down
- Adding inside the function moves it to the left
- Subtracting inside the function moves it to the right
- Multiplying to the function by a number less than 1 compresses
- Multiplying to a function by a number greater than 1 stretched it
- Multiplying by a negative flips the graph
f(x) = -3x
This is multiplication by a number greater than 1 and a negative so this stretches and flip. This is #6, a reflection.
f(x) = |x-1|+3
Subtraction inside the function shifts it to the right 1 and addition outside shifts it up 3. This is #5.
f(x) = √(x+3)
Addition inside the function shifts it to the left 3. This is #3
1/2x²
Multiplication by 1/2 which is less than 1 compresses it. This is #1.
f(x) = (x+1)²-3
Addition inside the function shifts the function to the left once. This is #4.
4|x|
Multiplying by 4, a number greater than 1, stretches it. This is #2.
Answer:
1.
Step-by-step explanation:
1. 2x-4=10
2x=14
x=7
2. 3x+3=2x-1
3x-2x=-1-3
x=-4
3. 7x+x=24
8x=24
x=3(
4. 5+x=-18
x=-18-5
x=-23
5. -14=10-6x
6x=10+14
6x=24
x=4
6. 2x-2=x+12
2x-x=12+2
x=14
7. 3x-31=2
3x=2+31
3x=33
x=11
8. 5x-14=16
5x=16+14
5x=30
x=6
9. 2x+8=4(5-x)
2x+8=20-4x
2x+4x=20-8
6x=12
x=2
10. 2x-3=3(1+x)
2x-3=3+3x
2x-3x=3+3
-x=6
