Math Problem Statement

The user submitted an image containing several math problems related to operations with scientific notation and geometric calculations.

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) 1.6×105÷4×1021.6 \times 10^5 \div 4 \times 10^2
  • (b) 8.8×108×3.3×1048.8 \times 10^8 \times 3.3 \times 10^{-4}

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) 4×107÷8×1034 \times 10^7 \div 8 \times 10^3
  • (b) 2.1×108×6×1092.1 \times 10^{-8} \times 6 \times 10^9

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., 2.507×1082.507 \times 10^8).

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