The distance from the bottom of the wheel to a point on the ground can be expressed using the sine function h(t) = a*sin(kt) + b, where b represents the height of the wheel at 4m. The radius a is calculated as 50/2 = 25m. Since it takes 6 minutes for 3 complete rotations, the period can be derived from 2π/k, giving us k = π. Thus, h(t) = 25*sin(π*t) + 4.
Answer:
The mouse's total distance over the course of 3 hours amounts to
of a mile
. The same distance was covered by the mouse each hour. Therefore, to ascertain the distance traveled within a single hour, we need to split the total distance of 3 hours by 3. This yields the distance the mouse managed in one hour.
Thus, the distance covered during one hour becomes =
of a mile
. The mistake made by Matt was that he only adjusted the denominator of the expression by dividing it by 3, which likely led to a miscalculation.
The accurate assessment is: The mouse covers 1/24 of a mile every hour
Response:
Count of bottles = 6
Count of cans = c
Detailed reasoning:
Based on the following information:
Containers for selling water:
17 oz bottle
11 oz can
Let the number of bottles be denoted as b
Count of cans represented as c
b + c = 11 - - - (1)
17b + 11c = 157 - - - (2)
b = 11 - c
Insert into (2)
17(11 - c) + 11c = 157
187 - 17c + 11c = 157
187 - 6c = 157
-6c = 157 - 187
-6c = -30
c = 30/6
c = 5
From; b = 11 - c
b = 11 - 5
b = 6
Thus,
Count of bottles = 6
Count of cans = c
Answer:
The cost difference per mile between the two companies is $0.12.
Step-by-step explanation:
Gabi formulates the equation
to determine after how many miles, denoted as m, the charges of both companies will be equal.
The first company levies
for m miles traveled.
The second company's charge for the same m miles is
.
In these equations, the figures 7.20 and 8.40 signify the initial fees the companies impose.
The values 0.22 and 0.1 represent the respective costs per mile.
As such, the disparity in per-mile charges amounts to
.
An alternative method to tackle this problem is by calculating the per-mile rate for each company:
1. Cost per mile for the first company

2. Cost per mile for the second company

3. The difference:

The minimum number of batches Joyce can produce is one.