Step-by-step explanation:
We must ask a question that your answer corresponds to each of the topics in the statement, therefore we will review each one:
5. Distances members of the track team jogged last week
How far did you run last week?
6. Numbers of letters in name of street you live on
How many letters are there in the name of your street?
7. Cost of a restaurant dinner
How much did you pay for dinner?
8. Numbers of cars of different colors in a parking lot
What color is your car?
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
Answer:
5
Step-by-step explanation:
We start by seeing how many families we have in total, which is 20. We then must subtract the number of families with girls only, the number of families with both boys and girls, and the number of families with no children. 20 - 7 is 13, then 13 - 8 is 5, and 5 - 0 is 5.
Therefore
(4y+6) +y = 46
We can combine the like terms:
5y + 6 = 46
Subtract 6 on both sides:
5y+6-6=46-6
Therefore 5y =40
Divide by 5 on both sides
5y/5 = 40/5
Therefore
y= 8
We found y but to find the value x we use y.
X= 4y+6
Therefore
x= (4*8)+ 6
Therefore
x= 32 + 6
x= 38.