A summer camp is organizing a hike and needs to buy granola bars for the campers. The granola bars come in small boxes and large
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The height of the <em>water</em> depth is h = 14 + 6 · sin (π · t/6 + π/2), where t is in hours, and the height of the Ferris wheel is h = 21 + 19 · sin (π · t/20 - π/2), where t is in seconds. Please see the image to see the figures.
<h3>How to derive equations for periodical changes in time</h3>
According to the two cases described in the statement, we have clear example of <em>sinusoidal</em> model for the height as a function of time. In this case, we can make use of the following equation:
h = a + A · sin (2π · t/T + B) (1)
Where:
- a - Initial position, in meters.
- A - Amplitude, in meters.
- t - Time, in hours or seconds.
- T - Period, in hours or seconds.
- B - Phase, in radians.
Now we proceed to derive the equations for each case:
Water depth (u = 20 m, l = 8 m, a = 14 m, T = 12 h):
A = (20 m - 8 m)/2
A = 6 m
a = 14 m
Phase
20 = 14 + 6 · sin B
6 = 6 · sin B
sin B = 1
B = π/2
h = 14 + 6 · sin (π · t/6 + π/2), where t is in hours.
Ferris wheel (u = 40 m, l = 2 m, a = 21 m, T = 40 s):
A = (40 m - 2 m)/2
A = 19 m
a = 21 m
Phase
2 = 21 + 19 · sin B
- 19 = 19 · sin B
sin B = - 1
B = - π/2
h = 21 + 19 · sin (π · t/20 - π/2), where t is in seconds.
Lastly, we proceed to graph each case in the figures attached below.
To learn more on sinusoidal models: brainly.com/question/12060967
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[1] (a) 10 times 4 ones = 10 x 4 ones = 40
(b) 10 times 2 tens = 2 tens = 20
(c) 5 times hundred times 10 = 50 hundreds = 50
[2] (a) 10 times as many as 1 hundred is 10 x 100 = 10 hundreds or 1000 x 1 = 1 thousand
(b) 10 times 6 hundreds is 60 hundreds / 6 thousands
(c) 10 times 8 hundreds is 8 thousands.
(d) 40 hundreds is same as 4 thousands.
<h3>What Is Place Value in Math? </h3>Place value is the base of number system. This is that system in which the position of a digit in a number tells/determine its value. The number 41,316 is different from 51,432 because the digits are in different positions.
The place value of 4 in 41,316 is 10 thousands and place value of 4 in 51,432 is 1 hundred.
we can also find the place value by multiplying the required number of 10.
for ones → multiply by 1
for tens → multiply by 10
for hundreds → multiply by 100
for thousands → multiply by 1000
for ten thousands → multiply by 10000
Here we have given
[1]
(a) 10 times 4 ones which is equal to 40 ones = 40
(b) 10 times 2 tens = 2 tens = 20
(c) 5 hundreds times 10 = 50 hundreds = 50
[2]
(a) 10 times as many as 1 hundred is 10 x 100 = 10 hundreds or 1000 x 1 = 1 thousand
(b) 10 times 6 hundreds is 60 hundreds or 6 thousands
(c) 10 times 8 hundreds is 8 thousands.
(d) 40 hundreds is same as 4 thousands.
Hence,
[1] (a) 10 times 4 ones = 10 x 4 ones = 40
(b) 10 times 2 tens = 2 tens = 20
(c) 5 times hundred times 10 = 50 hundreds = 50
[2] (a) 10 times as many as 1 hundred is 10 x 100 = 10 hundreds or 1000 x 1 = 1 thousand
(b) 10 times 6 hundreds is 60 hundreds or 6 thousands
(c) 10 times 8 hundreds is 8 thousands.
(d) 40 hundreds is same as 4 thousands.
Learn more about " Place value and Number system " from here: brainly.com/question/27734142
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Disclaimer: The question given was incomplete on portal. Here is the complete question.
Question: Label the place value charts. Fill in the blanks to make the following equations true. Draw disks in the place value chart to show how you got your answer, using arrows to show any regrouping.
[1] a. 10 times 4 ones = ____ ones = _____
b. 10 times 2 tens = _____ tens = _____
c. 5 hundreds times 10 = _____ hundreds = ____
[2] Complete the following statements using your knowledge of place value:
a. 10 times as many as 1 hundred is _____ hundreds or _____ thousand.
b. 10 times as many as _____ hundreds is 60 hundreds or _____ thousands.
c. _________ as 8 hundreds is 8 thousands.
d. ______ hundreds is the same as 4 thousands.
Use pictures, numbers, or words to explain how you got your answer for Part (d).
