Answer:
a = 3xi - 4yj b = -6xj c = -2xi + 2yj d = 5xi + 7yj
a ; b ; c ; d vectors
i and j unit vectors
Step-by-step explanation:
See attached file
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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The error that Loren made is C. She should have solved 149 = StartFraction 19 Over 9 EndFraction (10) + b for b.
<h3>What is an equation?</h3>
It should be noted that an equation is a statement that shows that two mathematical expressions are equal.
In this case, for Loren to find the slope, this will be:
m = y2 - y1/x2 - x1
= (149 - 130)/(10 - 1)
= 19/9
In this case, the error that Loren made is that she should have solved 149 = StartFraction 19 Over 9 EndFraction (10) + b for b.
Learn more about equations on:
brainly.com/question/13763238
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Answer:
x = 45
Step-by-step explanation:
x and (90 - x) are alternate exterior angles and are congruent , then
x = 90 - x ( add x to both sides )
2x = 90 ( divide both sides by 2 )
x = 45
Step-by-step explanation:
Hi there,
The sum of two numbers is 8.
x + y = 8
If three times the first number
is equal to the second number.
3x = y
Replace the y in top equation with 3x
x + 3x = 8
4x = 8
x = 2
Substitute x = 2 in first equation
x + y = 8
2 + y = 8
y = 8 - 2
y = 6
{2,6}
Hope this helps :-)