Tom is closer to the roller coaster since the distance to the roller coaster (approximately 7.07 units) is smaller than the distance to the water ride (approximately 7.28 units).
To determine whether Tom is closer to the roller coaster or the water ride, we can use the distance formula from the coordinate system. The distance formula between two points (x₁, y₁) and (x₂, y₂) is given by:
Distance = √[(x₂ - x₁)² + (y₂ - y₁)²]
Let's calculate the distances from Tom's position (2, 3) to the roller coaster (7, 8) and the water ride (9, 1):
Distance to the roller coaster = √[(7 - 2)² + (8 - 3)²] = √[5² + 5²] = √(25 + 25) = √50 ≈ 7.07
Distance to the water ride = √[(9 - 2)² + (1 - 3)²] = √[7² + (-2)²] = √(49 + 4) = √53 ≈ 7.28
Tom is closer to the roller coaster since the distance to the roller coaster (approximately 7.07 units) is smaller than the distance to the water ride (approximately 7.28 units).
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Answer:
Water Slide
Step-by-step explanation:
Answer:
3
Step-by-step explanation:
Rewriting this sentence as an algebraic equation, we get:
3^10 = 3^7 * x^3.
Dividing both sides by 3^7 simplifies the problem:
3^3 = x^3
Here this x corresponds to the 3 in 3^3. Thus, the solution is x = 3.
Using exponent rules and logarithms, the given equation can be simplified and solved to find that x equals 3.
The subject of the question falls into the field of Mathematics, specifically exponent rules, which are used in High School level algebra. In the mathematics problem provided ('3 to the 10th power = 3 to the 7th power times x to the 3rd power'), we need to solve for x using the knowledge of exponents.
First, it's helpful to know that when two expressions with the same base (in this case, 3) are set equal to each other, their exponents must also be equal. Since we know that 3 to the 7th power times x to the 3rd power equals 3 to the 10th power, we can break this down further. This leads to the equation 7 + 3log(x) = 10, where 'log' represents the logarithm.
By simplifying the equation, we get 3log(x) = 10-7, so 3log(x) = 3. Therefore, log(x)=3/3, hence log(x)=1. If we apply anti logarithm on both sides, we'll find that x = 3 to the power of 1, so x = 3. In other words, 3 to the 3rd power will equal3 to the 10th power divided by 3 to the 7th power. Hence, the value of x is 3.
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