The mixed number is 4 5/12.
Answer: 15e^5x
Step - by - step
y=3e^5x - 2
By the sum rule, the derivative of 3e^5x - 2 with respect to x is d/dx [ 3e^5x ] + d/dx [-2].
d/dx [ 3e^5x ] + d/dx [ -2 ]
Evalute d/dx [ 3e^5x ]
Since 3 is constant with respect to x , the derivative of 3e^5x with respect to x is
3 d/dx [ e^5x ].
3 d/dx [ e^5x ] + d/dx [ -2 ]
Differentiate using the chain rule, which states that d/dx [ f(g(x))] is f' (g(x)) g' (x) where f(x) = e^x and g(x) = 5x.
To apply the Chain Rule, set u as 5x.
3 ( d/du [ e^u] d/dx [5x] ) + d/dx [ -2]
Differentiate using the Exponential rule which states that d/du [ a^u ] is a^u ln(a) where a=e.
3( e^u d/dx[5x] ) + d/dx [ -2 ]
Replace
3(e^5x d/dx [5x] ) + d/dx [ -2 ]
3(e^5x( 5 d/dx [x] )) + d/dx [ -2 ]
Diffentiate using the Power Rule which states that d/dx [x^n] is nx^n-1 where n=1.
3(e^5x(5*1)) + d/dx [-2]
3 ( e^5x * 5 ) + d/dx [-2]
Multiply 5 by 3
15e^5x + d/dx [-2]
Since -2 is constant with respect to x, the derivative of -2 with respect to x is 0.
15e^5x + 0
15e^5x
In a triangle, the side opposite the largest angle is the longest one. So the answer is 8 inches.
Line 1 and Line 4 are parallel lines
Solution:
General equation of a line:
y = mx + c
where m is the slope and c is the y-intercept of the line.
<u>To find the slope of each line:</u>
Line 1: 
Slope 
Line 2: 
Add 7 on both sides, we get
Slope 
Line 3: 
Slope 
Line 4: 
Subtract x from both sides, we get
Multiply by 
on both sides, we get
Slope 
<em>Two lines are parallel, if their slopes are equal.</em>
From the above slopes,
Therefore Line 1 and Line 4 are parallel lines.
To begin lets say year one the population is 2,000
assume this in percent we can say that 2,000=100%
at the end of this year the population will have grown by 4% meaning that
100%+4% will be the new population =104%
but we know that 100%=2,000 so what about 104%=X?
so (104*2000)/100=2,080
So year 1 the population will have grown by 80 people amounting to 2080 people.
Now do it manually year by year until we reach the 15th year. i will help you up to year 3
2nd year= (2080*104)/100=2163.2
3rd year= (2163*104)/100=2249.728
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