Interval notation is used to write a set of real numbers from one value to another value.
On the left, you start with left parenthesis or left bracket.
Then you follow by two numbers separated by a comma.
You then finish with a right parenthesis or right bracket.
To include a number, use a square bracket.
To exclude a number use parenthesis.
To write the set of numbers, you need to list the smallest number in the set followed by the largest number in the set. An interval is always stated with two numbers, from the smallest in the set to the largest in the set. The numbers are always separated by a comma.
Examples:
1) All numbers from 6 to 10, including 6 and 10.
Algebra: 6 <= x <= 10
Interval: [6, 10]
Notice brackets since both 6 and 10 are included in this interval.
2) All number from 5 to 20, including 5 but not including 20.
Algebra 5 <= x < 20
Interval: [5, 20)
Bracket with 5 means include 5. Parenthesis with 20 means 20 is not included.
3) All numbers greater than or equal to 7.
Algebra: x >= 7
Interval: [7, ∞)
The 7 has a bracket because it is included. Infinity always has parenthesis.
With the infinity symbol, always use parenthesis, not square bracket.
4) All numbers less than -5.
Algebra: x < - 5
Interval: (-∞, 5)
Now for your problems.
10.
This is a line. Both the domain and range all all real numbers.
That means the interval is from negative infinity to positive infinity.
(-∞, ∞)
Both the domain and range are that same interval, all real numbers, from negative infinity to positive infinity.
13.
The domain is all real numbers as you can see the x-coordinates extend left forever and right forever. The domain is the same interval as the domain and range of problem 10.
The range is zero and all positive numbers.
You can think of it a all values of y such that y is greater than or equal to zero. Notice that zero is included in the interval.
[0, ∞)
Since zero is included, we use a left bracket, not left parenthesis.
With infinity, we alyways use parentheses, not brackets.
Answer:
b = d/(2ac)
Step-by-step explanation:
10abc - 2d = 3d
Add 2d to each side
10abc - 2d+2d = 3d+2d
10 abc = 5d
Divide each side by 10ac
10 abc/ (10ac) = 5d/10ac
b = d/(2ac)
Answer:
1) 2(t - 7)(t + 1)
2) $32,000
Step-by-step explanation:
v(t) = 2t² - 12t - 14
v(t) = 2(t² - 6t - 7) = 2(t - 7)(t + 1)
x = -b/2a = 6/2 = 3
y = 2(3)² - 12(3) - 14 = -32
(3, -32) means at 3 months, -32 thousand dollars
C = Pi * d where C = circumference, d = diameter, r = radius
C = 2*pi *r
we need to watch the units since they are different
Pool A
C = 2 * pi * r
C = 2 * pi * 12 = 24 * pi in feet
Pool B
C = pi * d
change meters to feet
7.5 m * 3.28 ft/ 1 m = 24.6 ft
C = pi * 24.6 = 24.6* pi in ft
Pool B had a greater circumference
24.6 * pi > 24 pi
Answer:
The width and length of rectangle is 12.728 m
Step-by-step explanation:
Let the length of the rectangle = L
let the width of the rectangle = W
The subjective function is given by;
F(p) = 2(L + W)
F = 2L + 2W
Area of the rectangle is given by;
A = LW
LW = 162 ft²
L = 162 / W
Substitute in the value of L into subjective function;
Take the second derivative of the function, to check if it will given a minimum perimeter
Determine the critical points of the first derivative;
df/dw = 0
L = 162 / 12.728
L = 12.728 m
Therefore, the width and length of rectangle is 12.728 m
