Answer:
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<span>(A) Find the approximate length of the plank. Round to the nearest tenth of a foot.
Given that the distance of the ground is 3ft.
In order to get the length of the plank,
we can use the this one.
cos 49 = ground / plank
cos 49 = 3 / plank
plank = cos 49 / 3
plank = 0.10 ft
</span><span>(b) Find the height above the ground where the plank touches the wall. Round to the nearest tenth of a foot.
</span><span>
The remaining angle is equal to
angle = 180 - (90+49)
angle = 41
Finding the height.
tan 41 = height / ground
tan 41 = height / 3
height = tan 41 / 3
height = 0.05 ft.
(A) 0.10 feet
(B) 0.05 feet</span>
Answer:
(a) 5 mayflies
(b) 15 mayflies
(c) 84 flying flies
Step-by-step explanation:
Represent Mayflies with M and the total flying insects with F
The ratio can be represented as:
![M : F = 5 : 14](https://tex.z-dn.net/?f=M%20%3A%20F%20%3D%205%20%3A%2014)
Solving (a):
![F = 14](https://tex.z-dn.net/?f=F%20%3D%2014)
Find M
Substitute 14 for F in ![M : F = 5 : 14](https://tex.z-dn.net/?f=M%20%3A%20F%20%3D%205%20%3A%2014)
![M : 14 = 5 : 14](https://tex.z-dn.net/?f=M%20%3A%2014%20%3D%205%20%3A%2014)
Convert to fraction
![\frac{M}{14} = \frac{5}{14}](https://tex.z-dn.net/?f=%5Cfrac%7BM%7D%7B14%7D%20%3D%20%5Cfrac%7B5%7D%7B14%7D)
Multiply through by 14
![14 * \frac{M}{14} = \frac{5}{14} * 14](https://tex.z-dn.net/?f=14%20%2A%20%5Cfrac%7BM%7D%7B14%7D%20%3D%20%5Cfrac%7B5%7D%7B14%7D%20%2A%2014)
![M = 5](https://tex.z-dn.net/?f=M%20%3D%205)
Solving (b):
![F = 42](https://tex.z-dn.net/?f=F%20%3D%2042)
Find M
Substitute 42 for F in ![M : F = 5 : 14](https://tex.z-dn.net/?f=M%20%3A%20F%20%3D%205%20%3A%2014)
![M : 42 = 5 : 14](https://tex.z-dn.net/?f=M%20%3A%2042%20%3D%205%20%3A%2014)
Convert to fraction
![\frac{M}{42} = \frac{5}{14}](https://tex.z-dn.net/?f=%5Cfrac%7BM%7D%7B42%7D%20%3D%20%5Cfrac%7B5%7D%7B14%7D)
Multiply through by 42
![42 * \frac{M}{42} = \frac{5}{14} * 42](https://tex.z-dn.net/?f=42%20%2A%20%5Cfrac%7BM%7D%7B42%7D%20%3D%20%5Cfrac%7B5%7D%7B14%7D%20%2A%2042)
![M = \frac{5}{14} * 42](https://tex.z-dn.net/?f=M%20%3D%20%5Cfrac%7B5%7D%7B14%7D%20%2A%2042)
![M=5*3](https://tex.z-dn.net/?f=M%3D5%2A3)
![M= 15](https://tex.z-dn.net/?f=M%3D%2015)
Solving (c):
![M = 30](https://tex.z-dn.net/?f=M%20%3D%2030)
Find F
Substitute 30 for M in ![M : F = 5 : 14](https://tex.z-dn.net/?f=M%20%3A%20F%20%3D%205%20%3A%2014)
![30 : F = 5 : 14](https://tex.z-dn.net/?f=30%20%3A%20F%20%3D%205%20%3A%2014)
Convert to fraction
![\frac{F}{30} = \frac{14}{5}](https://tex.z-dn.net/?f=%5Cfrac%7BF%7D%7B30%7D%20%3D%20%5Cfrac%7B14%7D%7B5%7D)
Multiply through by 30
![30 * \frac{F}{30} = \frac{14}{5} * 30](https://tex.z-dn.net/?f=30%20%2A%20%5Cfrac%7BF%7D%7B30%7D%20%3D%20%5Cfrac%7B14%7D%7B5%7D%20%2A%2030)
![F = \frac{14}{5} * 30](https://tex.z-dn.net/?f=F%20%3D%20%5Cfrac%7B14%7D%7B5%7D%20%2A%2030)
![F = 14*6](https://tex.z-dn.net/?f=F%20%3D%2014%2A6)
![F = 84](https://tex.z-dn.net/?f=F%20%3D%2084)
Answer:
$333
Step-by-step explanation:
$9.25 x 6 <em>hours</em> x (2 <em>days in a weekend</em> x 3 <em>weeks</em>) = $333