Answer:
52 students
Step-by-step explanation:
Let's assume A represents number of students in the library means A=86,
B represents number of student in student union means B = 78
U represents total students surveyed means U = 136
section II represents number of students in library and student union means
II = 34
Now from figure we can see
number of students only in library is represented by section I .
and section I can be written as
I = A - II
I = 86-34 = 52
only in Union represents III
III = B - II
III = 78-34 = 44
not in library or not in union = U - (I + II + III)
= 136 - (52+ 34+ 44)
= 136 - 130 = 6
Answer:
Step-by-step explanation:
We have to take the derivatives for both functions and replace in the differential equation. Hence
for y=e^{-5x}:
![y(x)=e^{-5x}\\y'(x)=-5e^{-5x}\\y''(x)=25e^{-5x}\\](https://tex.z-dn.net/?f=y%28x%29%3De%5E%7B-5x%7D%5C%5Cy%27%28x%29%3D-5e%5E%7B-5x%7D%5C%5Cy%27%27%28x%29%3D25e%5E%7B-5x%7D%5C%5C)
for y=e^{6x}:
![y(x)=e^{6x}\\y'(x)=6e^{6x}\\y''(x)=36e^{6x}\\](https://tex.z-dn.net/?f=y%28x%29%3De%5E%7B6x%7D%5C%5Cy%27%28x%29%3D6e%5E%7B6x%7D%5C%5Cy%27%27%28x%29%3D36e%5E%7B6x%7D%5C%5C)
Now we replace in the differential equation y'' − y' − 30y = 0
for y=e^{-5x}:
![25e^{-5x}+5e^{-5x}-30e^{-5x}=0\\25+5-30=0](https://tex.z-dn.net/?f=25e%5E%7B-5x%7D%2B5e%5E%7B-5x%7D-30e%5E%7B-5x%7D%3D0%5C%5C25%2B5-30%3D0)
for y=e^{6x}:
![36e^{6x}-6e^{6x}-30=0\\36-6+30=0](https://tex.z-dn.net/?f=36e%5E%7B6x%7D-6e%5E%7B6x%7D-30%3D0%5C%5C36-6%2B30%3D0)
Now, to know if both function are linearly independent we calculate the Wronskian
![W(f,g)=fg'-f'g](https://tex.z-dn.net/?f=W%28f%2Cg%29%3Dfg%27-f%27g)
![W(e^{-5x},e^{6x})=(e^{-5x})(6e^{6x})-(-5e^{-5x})(e^{6x})\neq 0](https://tex.z-dn.net/?f=W%28e%5E%7B-5x%7D%2Ce%5E%7B6x%7D%29%3D%28e%5E%7B-5x%7D%29%286e%5E%7B6x%7D%29-%28-5e%5E%7B-5x%7D%29%28e%5E%7B6x%7D%29%5Cneq%200)
I hope this is useful for you
Best regard
A 6-pound bag of cat food is the better buy, because it costs $2.14 per pound and bag costs $12.84.
I got $2.14 by dividing 6 from $12.84.
However, I don’t know if it’s correct, but I hope you get the answer correct.
Answer:
I think the answer is 1 7/9
First, we must determine the circumference of the paddle wheel.
The formula for the circumference of a circle is:
c = 2πr
Where r is the radius of the circle. However, we know d = 2r where d is the diameter of the circle.
Therefore:
c = 2rπ = dπ
Substituting 8ft for d gives a circumference of:
c = 8πft
The time it takes to complete 1 revolution can be found using the formula:
t = d/s
Where:
t is the time it takes: what we are solving for in this problem.
d is the distance traveled: we calculated this as 8πft
s is the speed traveled: from the problem we know this is
6.7ft/sec
Substituting and calculating t gives:
t = 8πft / (6.7ft/sec)
t = 1.2πsec
Two find how long it would take for 100 revolutions we can multiply this time by 100
100 × 1.6πsec ⇒ 122.2πsec
If a number is required for the answer we can use 3.14 as an estimate for π giving:
122.2πsec ⇒ 122.2 × 3.14sec ⇒ 383sec