A clock has a minute hand that is 6 in. Long. How far has the tip of the minute hand traveled between 10:25 a. m and 11:00a. m? Round your answer to the nearest tenth of an inch.

1.83 inches

Step-by-step explanation:

Given:

Length of minute hand = 6 inches

To find: Distance traveled by the minute hand between 10:25 a.m and 11:00 a.m

Solution:

Let denotes arc length, denotes radius and denotes central angle subtended by the arc

So,

Angle subtended by an arc in 1 minute

So, angle subtended by an arc in 35 minutes

Here, = Length of minute hand = 6 inches

So,

inches

m∠a is 90°

m∠b is 40°

ratios represent a pattern or relationship that can be scaled.

equivalent ratios are pairs of ratios that represent the same relationship between quantities, and can be generated by multiplying or dividing both quantities in the ratio by the same factor.

in this lesson, students will use double number lines and ratio reasoning to solve ratio problems. by partitioning double number lines into proportionate intervals, students will build an understanding of equivalent ratio relationships as those that are generated by multiplying or dividing two related quantities by the same number. this lesson will build upon students' prior understanding of multiplicative comparisons, number line reasoning and equivalent fractions (while highlighting the difference between equivalent fractions and equivalent ratios); and will build toward future work in this unit on building ratio tables, and work in future grades in proportionality, scaling, and expressing and graphing linear functions.

step-by-step explanation:

ratios represent a pattern or relationship that can be scaled.

equivalent ratios are pairs of ratios that represent the same relationship between quantities, and can be generated by multiplying or dividing both quantities in the ratio by the same factor.

in this lesson, students will use double number lines and ratio reasoning to solve ratio problems. by partitioning double number lines into proportionate intervals, students will build an understanding of equivalent ratio relationships as those that are generated by multiplying or dividing two related quantities by the same number. this lesson will build upon students' prior understanding of multiplicative comparisons, number line reasoning and equivalent fractions (while highlighting the difference between equivalent fractions and equivalent ratios); and will build toward future work in this unit on building ratio tables, and work in future grades in proportionality, scaling, and expressing and graphing linear functions.