Question # 1
Answer:

Step-by-step explanation:
Given the expression

∵ 
∵ 








Therefore,

Question # 2
Answer:

Step-by-step explanation:
Given

∵ 
∵ 










Therefore,

1/3 ln(<em>x</em>) + ln(2) - ln(3) = 3
Recall that
, so
ln(<em>x</em> ¹ʹ³) + ln(2) - ln(3) = 3
Condense the left side by using sum and difference properties of logarithms:


Then
ln(2/3 <em>x</em> ¹ʹ³) = 3
Take the exponential of both sides; that is, write both sides as powers of the constant <em>e</em>. (I'm using exp(<em>x</em>) = <em>e</em> ˣ so I can write it all in one line.)
exp(ln(2/3 <em>x</em> ¹ʹ³)) = exp(3)
Now exp(ln(<em>x</em>)) = <em>x </em>for all <em>x</em>, so this simplifies to
2/3 <em>x</em> ¹ʹ³ = exp(3)
Now solve for <em>x</em>. Multiply both sides by 3/2 :
3/2 × 2/3 <em>x</em> ¹ʹ³ = 3/2 exp(3)
<em>x</em> ¹ʹ³ = 3/2 exp(3)
Raise both sides to the power of 3:
(<em>x</em> ¹ʹ³)³ = (3/2 exp(3))³
<em>x</em> = 3³/2³ exp(3×3)
<em>x</em> = 27/8 exp(9)
which is the same as
<em>x</em> = 27/8 <em>e</em> ⁹
Answer:
The number of fringes at
is given as 20.
Step-by-step explanation:
Question
A Galapagos cactus finch population increases by half every decade. The number of finches is modeled by the expression
,
where d is the number of decades after the population was measured. Evaluate the expression for d = −2
Given :
The number of finches is modeled by the expression :
⇒ 
where
is the number of decades after the population was measured.
To evaluate the expression for d=-2
Solution:
In order to evaluate the given expression to find the number of finches at
, we will plugin
for
in the expression and simplify it.
Plugging in
in the expression:
⇒ 
Using negative exponent property. [
⇒ 
⇒ 
⇒
(Answer)
Thus, the number of fringes at
is given as 20.
This means the number of fringes two decades ago was 20.
Answer:
<u>4 weeks</u>
Step-by-step explanation:
Remaining money (per week) :
- Net income - Expenses
- $400 - $380
- $20
No. of weeks to buy shoes :
- Cost of shoes / Remaining money (per week)
- $70/$20
- 3.5 ≈ <u>4 weeks</u> (nearest whole week)
Answer:
Step-by-step explanation:
must be r and s
because right at in middle of the distance between them is 0