Problem 82 - Prealgebra

Question

The newly launched Herschel Telescope has a mirror 11.5 feet in diameter while Hubble’s mirror is 7.9 feet in diameter. How much larger is Herschel’s mirror in diameter than Hubble’s?

Step-by-Step Solution

Answer

Herschel's mirror is 3.6 feet larger in diameter than Hubble's mirror.

Step 1: Understand the Problem

We need to find out the difference in diameters between the Herschel Telescope's mirror and the Hubble's mirror.

Step 2: Identify the Diameters

The diameter of the Herschel Telescope's mirror is 11.5 feet and the diameter of the Hubble's mirror is 7.9 feet.

Step 3: Compute the Difference

Subtract the diameter of Hubble's mirror from the diameter of Herschel's mirror: \[ 11.5 - 7.9 = 3.6 \]

Step 4: Interpret the Result

The result shows that Herschel's mirror is 3.6 feet larger in diameter than Hubble's mirror.

Key Concepts

Diameter Measurement

The diameter is a fundamental measurement in geometry and is key to solving many real-world problems, including those involving circular objects like telescope mirrors. The diameter of a circle is a straight line going from one side of the circle to the other, passing through the center. It is often represented in feet, meters, or other units of measure. To understand the size or capacity of a circular object, measuring the diameter is crucial.

When comparing objects like telescope mirrors, the diameter helps determine features such as the light-gathering ability. A bigger diameter generally means a larger surface area, which allows for more light to be captured in the case of telescopes. Therefore, it's vital to grasp what the diameter reveals about the object's capabilities, not just its size.

Telescope Mirrors

Telescope mirrors are a key component in the functioning of telescopes, helping to gather and focus light. The size of the mirror, measured by its diameter, plays a crucial role in determining the telescope's effectiveness. A larger diameter results in a greater ability to capture light. This often leads to clearer and more detailed observations of astronomical objects.

• Bigger mirrors can observe fainter and more distant objects in space.
• The mirror diameter affects resolution, impacting how sharp and finely detailed the images can be.

The Herschel Telescope, with its 11.5 feet diameter mirror, collects more light compared to Hubble's 7.9 feet mirror, allowing it to potentially see more distant galaxies or finer details within them. Therefore, understanding the importance of mirror diameter can help explain the capabilities and purposes of different telescopes.

Subtraction in Math

Subtraction is a basic arithmetic operation used to determine the difference between numbers. In this case, we use subtraction to find the difference in diameter between two objects. To do this, you subtract the smaller number from the larger one: \[ 11.5 - 7.9 = 3.6 \]

This process reveals that the Herschel Telescope's mirror is 3.6 feet larger than the Hubble's. Subtraction is applicable in scenarios where you're looking to compare or find out how much larger or smaller one quantity is compared to another.

• The minuend (first number) is the value from which you subtract.
• The subtrahend (second number) is the value to be subtracted.
• The difference is the result of the subtraction.

Mastering subtraction is fundamental in math, as it helps in various practical tasks like making comparisons between sizes, quantities, and other measurable attributes.