17.92
∧ ∧ this is the ones place
this is the tens place
if the ones place is lower then 5 you keep the tens the same. if the ones place is higher then 5 you round the tens place up one. so the answer is 17.90
For 
, on the left we have 
, and on the right,
(where we use the double angle identity: 
)
Suppose the relation holds for 
:
Then for 
, the left side is
So we want to show that
On the left side, we can combine the fractions:
Recall that
so that we can write
(another double angle identity: 
)
Then recall that
which lets us consolidate the numerator to get what we wanted:
and the identity is established.
Answer:
4+√55= 11.42
4-√55= -3.42
Step-by-step explanation:
- w² − 8w − 39 = 0
- w²- 2*4w + 16- 55=0
- (w-4)²=55
- w-4=√55 ⇒ w= 4+√55= 11.42
- w-4=- √55 ⇒ w= 4-√55= -3.42
Answer:
a) (g(x), f(u)) = ( 7*√x , e^u )
b) y ' = 3.5 * e^(7*√x) / √x
Step-by-step explanation:
Given:
- The given function:
y = e^(7*√x)
Find:
- Express the given function as a composite of f(g(x)). Where, u = g(x) and y = f(u).
- Express the derivative of y, y'?
Solution:
- We will assume the exponent of the natural log to be the u. So u is:
u = g(x) = 7*√x
- Then y is a function of u as follows:
y = f(u) = e^u
- The composite function is as follows:
(g(x), f(u)) = ( 7*√x , e^u )
- The derivative of y is such that:
y = f(g(x))
y' = f' (g(x) ) * g'(x)
y' = f'(u) * g'(x)
y' = e^u* 3.5 / √x
- Hence,
y ' = 3.5 * e^(7*√x) / √x
