A factory has three machines that all manufacture the same engine part. From long historical records the company has determined
1 answer:
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Answer:
Step-by-step explanation:
We can use the Polynomial Remainder Theorem. It states that if we divide a polynomial P(x) by a <em>binomial</em> in the form (x - a), then our remainder will be P(a).
We are dividing:
So, a polynomial by a binomial factor.
Our factor is (x + k) or (x - (-k)). Using the form (x - a), our a = -k.
We want our remainder to be 3. So, P(a)=P(-k)=3.
Therefore:
Simplify:
Solve for <em>k</em>. Subtract 3 from both sides:
Factor:
Zero Product Property:
Solve:
So, either of the two expressions:
Will yield 3 as the remainder.
Answer:
The answer is <em>1</em>.
Step-by-step explanation:
Given the expression:
To find:
The expression without absolute value.
Solution:
First of all, let us learn about the absolute value function:
i.e. value is x if x is positive
value is -x if x is negative
Here the given expression contains two absolute value functions:
and
Using the definition of absolute value function as per above definition.
Now, it is given that z < 5 that means z will also be lesser than 6 i.e. z < 6
So, given expression will be equivalent to :
So, the expression is equivalent to <em>1</em>.
See attachment for the graph of the hyperbola 12x^2 - 3y^2 - 108 = 0
<h3>How to graph the hyperbola?</h3>The equation of the hyperbola is given as:
12x^2 - 3y^2 - 108 = 0
Start by calculating the transverse axis
So, we have:
<u>Transverse axis</u>
The vertices of the given hyperbola are (0, 0)
This means that
(h, k) = 0
Where
a = 3 and b = 6
The transverse axis is calculated as:
y = ±b/a(x - h) + k
So, we have:
y = ±6/3(x - 0) + 0
Evaluate the difference and sum
y = ±6/3x
Evaluate the quotient
y = ±2x
This means that the transverse axes are y = 2x and y =-2x
<u>The vertices</u>
In the above section, we have:
The vertices of the given hyperbola are (0, 0)
This means that
(h, k) = 0
<u>The co-vertices</u>
In the above section, we have:
The vertices of the given hyperbola are (0, 0)
This means that
(h, k) = 0
And
a = 3 and b = 6
The co-vertices are
(h - a, k) and (h + a, k)
So, we have:
(0 - 3, 0) and (0 + 3, 0)
Evaluate
(-3,0) and (3, 0)
See attachment for the graph of the hyperbola
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