To round off 87.321756 to 5 significant figures, we look at the 6th significant figure, which is 6.
Since it's greater than 5, we round up the 5th significant figure.
87.321756 becomes 87.322
Let's factor:
x^2 - y^2 = (x + y)(x - y)
x^2 - xy = x(x - y)
The common factor is (x - y).
To convert centimetres (cm) to millimetres (mm):
1 cm = 10 mm
7.5 cm × 10 = 75 mm
To evaluate 2(-7)²:
First, calculate the exponent:
(-7)² = (-7) × (-7) = 49
Now, multiply by 2:
2 × 49 = 98
The formula for the sum of interior angles of a polygon is:
(n - 2) × 180°
For an 8-sided polygon (n = 8):
Sum of interior angles = (8 - 2) × 180°
= 6 × 180°
= 1080°
Since it's a regular polygon, all interior angles are equal:
Measure of each interior angle = 1080°/8
= 135°
Find the least common multiple (LCM) of 10, 11, and 17.
The LCM of 10, 11, and 17 is the smallest number that is a multiple of all three numbers.
Calculate the LCM.
The prime factorization of the numbers is:
10 = 2 × 5
11 = 11
17 = 17
The LCM is the product of the highest powers of all prime factors: LCM = 2 × 5 × 11 × 17 = 1870.
A function f: A → B is into if it doesn't cover the entire codomain B, meaning there are elements in B that aren't mapped to by any element in A.
This happens when the range of f (the set of elements in B that are actually mapped to) is a proper subset of B.
Therefore, f is into if Range f ≠ B.
To find the common factors, let's list the factors of each number:
Factors of 30: 1, 2, 3, 5, 6, 10, 15, 30
Factors of 45: 1, 3, 5, 9, 15, 45
Factors of 54: 1, 2, 3, 6, 9, 18, 27, 54
The common factors are 1 and 3.