Math Problem Statement
Solution
Let's break down and analyze the mathematical problems from your image:
1. Problem 18:
This involves basic operations with scientific notation. The two subproblems are:
- (a)
- (b)
Both require the use of rules for multiplying and dividing numbers in scientific notation.
2. Problem 19:
Again, this asks to simplify expressions involving powers of 10:
- (a)
- (b)
These also require multiplying or dividing the numbers and combining powers of 10.
3. Problem 22:
Here, the task involves writing two movie box office values in both decimal and scientific notation formats.
The movies and box office values provided are:
- "Wonder 2" with $250.7 million
- "Secret Life of Pets" with $368.4 million
For this, the decimal values will need to be converted into scientific notation (e.g., ).
4. Problem 23:
This involves geometry, specifically a right triangle:
- Given: The dimensions of a giant rectangular prism are given. The height and the prism's base diagonal need to be calculated using the Pythagorean Theorem.
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Math Problem Analysis
Mathematical Concepts
Scientific Notation
Operations with Powers of 10
Pythagorean Theorem
Geometry
Formulas
Multiplication of Scientific Notation: (a × 10^m) × (b × 10^n) = (a × b) × 10^(m+n)
Division of Scientific Notation: (a × 10^m) ÷ (b × 10^n) = (a ÷ b) × 10^(m-n)
Pythagorean Theorem: a^2 + b^2 = c^2
Theorems
Pythagorean Theorem
Suitable Grade Level
Grades 8-10
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