Answer:
The system has two distinct solutions.
Step-by-step explanation:
The given system of equations are:
and
In order to determine the number of solutions the two equations have, we need to equate the two equations to obtain,
We now group all terms on the left hand side and equate everything to zero.
This is now a quadratic equation in 
with 
.
At this stage we check the number of solutions using the discriminant.
Since the discriminant is greater than zero, the equation will have two distinct roots.
Therefore the system of equations has exactly two distinct solutions.
If you wish to see these solutions, you can continue as follows;
We factor 
to obtain,
When 
Then we have,
When 
Then we have,
See graph
<h3>Answer: Approximately 191 bees</h3>
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Work Shown:
One way to express exponential form is to use
y = a*b^x
where 'a' is the initial value and 'b' is linked to the growth rate.
Since we're told 34 bees are there initially, we know a = 34.
Then after 4 days, we have 48 bees. So we can say,
y = a*b^x
y = 34*b^x
48 = 34*b^4
48/34 = b^4
24/17 = b^4
b^4 = 24/17
b = (24/17)^(1/4)
b = 1.090035
Which is approximate.
The function updates to
y = a*b^x
y = 34*(1.090035)^x
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As a way to check to see if we have the right function, plug in x = 0 and we find:
y = 34*(1.090035)^x
y = 34*(1.090035)^0
y = 34*(1)
y = 34
So there are 34 bees on day 0, ie the starting day.
Plug in x = 4
y = 34*(1.090035)^x
y = 34*(1.090035)^4
y = 34*1.4117629
y = 47.9999386
Due to rounding error we don't land on 48 exactly, but we can round to this value.
We see that after 4 days, there are 48 bees.
So we confirmed the correct exponential function.
------------------------
At this point we can find out how many bees there are expected to be after 20 days.
Plug in x = 20 to get
y = 34*(1.090035)^x
y = 34*(1.090035)^20
y = 190.672374978452
Round to the nearest whole number to get 191.
There are expected to be roughly 191 bees on day 20.
Answer:
r
Step-by-step explanation:
sin is o/h so across from 12 would be the angle r
Answer:
13
Step-by-step explanation:
7 cm +1 cm +2cm +2cm :12cm
