Why are maps incorrectly sized or shaped when we try to put them on a 2d surface?
A. Tilt
B. Distortion
C. Scale
B. Distortion
Simplify this expression using the Quotient Rule of Integer Exponents: 12 to the power of 53 ÷ 7 to the power of 53
To simplify the expression using the Quotient Rule of Integer Exponents, we can subtract the exponents of the bases:
12^53 ÷ 7^53 = (12/7)^53
Which are the correct steps to follow to simplify an exponential expression using the Quotient Rule of Integer Exponents?
A. Check if the bases are the same; if they are, subtract the exponents of the numerator and denominator (leave as-is otherwise); and write the resulting expression in exponential form.
B. Subtract the exponents of the numerator and denominator; and write the resulting expression in exponential form.
Subtract the exponents of the numerator and denominator; and write the resulting expression in exponential form.
C. Check if the bases are the same; if they are, add the exponents of the numerator and denominator (leave as-is otherwise); and write the resulting expression in exponential form.
D. Check if the bases are different; if they are, subtract the exponents of the numerator and denominator; and write the resulting expression in exponential form.
B. Subtract the exponents of the numerator and denominator; and write the resulting expression in exponential form.
explain please
When simplifying an exponential expression using the Quotient Rule of Integer Exponents, we want to simplify the division of two bases with the same exponent.
In this case, we have 12^53 ÷ 7^53.
The Quotient Rule states that when dividing two bases with the same exponent, we can subtract the exponents and write the result with the same base raised to the subtracted exponent.
So, using the Quotient Rule, we subtract the exponents 53 - 53 = 0, and write the resulting expression as (12/7)^0.
Since any number (except zero) raised to the power of 0 is equal to 1, we simplify the expression to be 1.
ok well thank you
You're welcome! If you have any more questions, feel free to ask.
The correct answer is B. Distortion.
When we try to represent the three-dimensional Earth on a two-dimensional surface, such as a map, we encounter various distortions. These distortions occur because it is impossible to perfectly transfer the curved surface of the Earth onto a flat surface without sacrificing some accuracy. There are different types of distortion that can affect the size or shape of maps.
One of the main reasons for this distortion is the challenge of representing a curved surface on a flat plane. Imagine trying to peel and flatten an orange peel – it would be difficult to do so without creating some wrinkles or distortions. Similarly, when we try to flatten the Earth's surface onto a map, distortions occur.
Distortion occurs due to the compromise between preserving either size, shape, distance, or direction on a map. Different map projections, which are mathematical transformations used to represent the Earth, prioritize different properties and minimize distortion in different aspects.
For example, the Mercator projection, commonly used in navigation maps, preserves angles and directions accurately, but greatly distorts the size of objects as you move away from the equator. This is why Greenland appears disproportionately large on Mercator maps. On the other hand, the Peters projection attempts to preserve the size of countries accurately but distorts shapes.
Thus, when maps are created, the challenge lies in finding a balance between different distortions depending on the purpose and the area being mapped.