University:
Carleton College
Course:
MATH 111 | lntroduction to Calculus
Academic year:

2024
Views:

468

Pages:

3
Author:

Alecai8y

Question 1 There are 36 inches in a yard. Write an expression for yards in x inches Answer 1 When converting from a smaller unit to a larger unit, we need to divide and when converting from a larger unit to a smaller unit, we need to multiply. If 36 inches = 1 yard, then the number of yards is equal to the number of inches divided by 36 since we are converting from a smaller unit of inches to a larger unit of yards. If x is the number of inches, we would then get as the expression for the number of yards in x inches. Answer 2 To solve the problem, we can use the fact that there are 36 inches in a yard. We need to write an expression that represents the number of yards in terms of a given number of inches, denoted as 'x'. Let's denote the number of yards as 'y'. We can set up a proportion based on the conversion factor: 36 inches 1 yard x inches y yards To find the expression for yards in terms of inches, we need to isolate 'y'. Cross- multiplying the equation gives us: 36 inches y yards = 1 yard-x inches Simplifying the equation further, we have: 36y = x To express 'y' in terms of 'x', we divide both sides of the equation by 36: y = x 36 Therefore, the expression for yards in terms of inches is: y = x 36 Answer 3 Result: x 36 Solution: The proportionality equation can be expressed as: 36 inches x y 1 yard To find the expression for yards in x inches, we need to isolate y on one side of the 1 yard, which is the equation. We can do this by multiplying both sides of the equation by 36 inches' reciprocal of the right-hand side: 1 yard xX- = y 36 inches Simplifying the expression, we get: x y 36 Thus, the expression for yards in x inches is 36 Answer 4 The expression for yards in x inches can be written as follows: y = x 36 In this expression, y represents the number of yards in x inches. We divide x by 36 because there are 36 inches in a yard. Question 2 A bicycle with tires of radius r=15 inches is being ridden by a boy at a constant speed - the tires are making five rotations per second. How many miles will he ride in minutes? (1mi = 5280 ft) Answer First, we find the speed in ft/s: v = wxr S t v = ((protation sec). (2nradian-rotation)) (15€. (11.) 12 t v = 12.5πf S 15 minutes = 900 seconds so the distance traveled is: d= (12.5)(9005) d = 11250nf In miles, d t S 11250πft. (1 i 1m 5280 ft) ≈6.7mi < s Question 3 At top speed, a coyote can run at a speed of 44 miles per hour. If a coyote could maintain its top speed, how far could it run in 15 minutes? (A) 2.93 miles (B) 11 miles C 176 miles (D) 660 miles: Answer It is given that the top speed of a coyote is 44 miles/hour. We have to find the distance cover by the coyote in 15 minutes time. Let us recall the formula. Distance = Speed × Time In our case Time = 15 minute minute and Speed = 44 miles/hour. Let us convert the time into an hour format. We know that 60minute = 1hour This gives us 1minute = 1/60hour 15minute = (1/60) × 15hour = 1/4hour Hence the distance cover by the coyote in 15 minutes time is given by Distance = 44.1/4miles = 11miles Question 4 The set of whole numbers and their opposites • Positive integer • Ratio • Absolute value • Integer Answer Recall the set of whole numbers: 0, 1, 2, 3... The opposites of these are:, -3, -2, -1 By combining, the set of whole numbers and their opposites is: {...,-3,-2,-1,0,1,2,3...} or the set of integers.