Question
Jaya starts driving north for 9 miles, then takes a right turn, and then he drives east for another 40 miles. At the end of driving, what is the distance of a straight line from the starting point?
Answers
GPT-4o mini
To find the straight-line distance from the starting point to the endpoint after Jaya's drive, we can visualize his path as forming a right triangle.
1. **Northward Distance**: Jaya drives north for 9 miles.
2. **Eastward Distance**: After turning right, he drives east for 40 miles.
Now, we can represent this situation as a right triangle where:
- The northward leg of the triangle is 9 miles,
- The eastward leg of the triangle is 40 miles.
We can use the Pythagorean theorem to find the hypotenuse (the straight-line distance from the starting point):
\[
c = \sqrt{a^2 + b^2}
\]
where:
- \( a = 9 \) miles (northward distance),
- \( b = 40 \) miles (eastward distance),
- \( c \) is the distance from the start to the endpoint.
Substituting the values into the formula:
\[
c = \sqrt{9^2 + 40^2}
\]
\[
c = \sqrt{81 + 1600}
\]
\[
c = \sqrt{1681}
\]
\[
c = 41
\]
Therefore, the straight-line distance from the starting point to the endpoint is **41 miles**.
1. **Northward Distance**: Jaya drives north for 9 miles.
2. **Eastward Distance**: After turning right, he drives east for 40 miles.
Now, we can represent this situation as a right triangle where:
- The northward leg of the triangle is 9 miles,
- The eastward leg of the triangle is 40 miles.
We can use the Pythagorean theorem to find the hypotenuse (the straight-line distance from the starting point):
\[
c = \sqrt{a^2 + b^2}
\]
where:
- \( a = 9 \) miles (northward distance),
- \( b = 40 \) miles (eastward distance),
- \( c \) is the distance from the start to the endpoint.
Substituting the values into the formula:
\[
c = \sqrt{9^2 + 40^2}
\]
\[
c = \sqrt{81 + 1600}
\]
\[
c = \sqrt{1681}
\]
\[
c = 41
\]
Therefore, the straight-line distance from the starting point to the endpoint is **41 miles**.
u suree?>
GPT-4o mini
Yes, I am sure. Let's summarize the calculation again clearly:
1. Jaya drives north for 9 miles and east for 40 miles.
2. We can model this as a right triangle, where:
- One leg (northward) is 9 miles,
- The other leg (eastward) is 40 miles.
Using the Pythagorean theorem to find the hypotenuse \(c\):
\[
c = \sqrt{a^2 + b^2}
\]
where \(a = 9\) miles and \(b = 40\) miles. Substituting these values in:
\[
c = \sqrt{9^2 + 40^2} = \sqrt{81 + 1600} = \sqrt{1681} = 41 \text{ miles.}
\]
So the straight-line distance from the starting point to the endpoint is indeed **41 miles**. If you have any further questions or would like clarification on any steps, feel free to ask!
1. Jaya drives north for 9 miles and east for 40 miles.
2. We can model this as a right triangle, where:
- One leg (northward) is 9 miles,
- The other leg (eastward) is 40 miles.
Using the Pythagorean theorem to find the hypotenuse \(c\):
\[
c = \sqrt{a^2 + b^2}
\]
where \(a = 9\) miles and \(b = 40\) miles. Substituting these values in:
\[
c = \sqrt{9^2 + 40^2} = \sqrt{81 + 1600} = \sqrt{1681} = 41 \text{ miles.}
\]
So the straight-line distance from the starting point to the endpoint is indeed **41 miles**. If you have any further questions or would like clarification on any steps, feel free to ask!
how did you make that 1681 into 41?
GPT-4o mini
To simplify \( \sqrt{1681} \) into \( 41 \), we need to find the square root of 1681.
Here's how it works:
1. **Finding the square root**: We need to determine what number, when multiplied by itself (squared), equals 1681.
2. **Calculating**:
- To find \( \sqrt{1681} \), you can use a calculator, but if we do it manually, we can factor or test perfect squares.
3. **Testing perfect squares**:
- We check various numbers:
\[
1^2 = 1, \quad 2^2 = 4, \quad 3^2 = 9, \quad \ldots, \quad 10^2 = 100, \quad 20^2 = 400, \quad 30^2 = 900, \quad 40^2 = 1600, \quad 41^2 = 1681
\]
- When we get to \( 41 \):
\[
41 \times 41 = 1681
\]
4. **Conclusion**: Since \( 41^2 \) equals 1681, we can conclude that:
\[
\sqrt{1681} = 41
\]
Therefore, the straight-line distance from the starting point to the endpoint is indeed \( 41 \) miles. If you have any further questions or need additional clarification, feel free to ask!
Here's how it works:
1. **Finding the square root**: We need to determine what number, when multiplied by itself (squared), equals 1681.
2. **Calculating**:
- To find \( \sqrt{1681} \), you can use a calculator, but if we do it manually, we can factor or test perfect squares.
3. **Testing perfect squares**:
- We check various numbers:
\[
1^2 = 1, \quad 2^2 = 4, \quad 3^2 = 9, \quad \ldots, \quad 10^2 = 100, \quad 20^2 = 400, \quad 30^2 = 900, \quad 40^2 = 1600, \quad 41^2 = 1681
\]
- When we get to \( 41 \):
\[
41 \times 41 = 1681
\]
4. **Conclusion**: Since \( 41^2 \) equals 1681, we can conclude that:
\[
\sqrt{1681} = 41
\]
Therefore, the straight-line distance from the starting point to the endpoint is indeed \( 41 \) miles. If you have any further questions or need additional clarification, feel free to ask!