Cross multiply and solve for x
Next term in each sequence 1,4,20,120,...
2 answers:
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Answer:
See explanation
Step-by-step explanation:
The range of the cosine function is
Therefore is not defined.
Assuming your question is rather
Then in the second quadrant.
Answer:
B
Step-by-step explanation:
Exponential functions are curves which approach a horizontal asymptote usually at y=0 or the x-axis. This function has been moved up 5 units so its asymptote is at y=5. This means the function never goes below 5 in its y-values.
The x values are not affected and all are in the function. This is the domain. So the domain is (-∞, ∞).
The y values are affected and are y > 5. This is the range and it is written
(5, ∞).
Option B is correct.
Answer:
1/2, 3
Step-by-step explanation:
This is a pretty involved problem, so I'm going to start by laying out two facts that our going to help us get there.
- The Fundamental Theorem of Algebra tells us that any polynomial has <em>as many zeroes as its degree</em>. Our function f(x) has a degree of 4, so we'll have 4 zeroes. Also,
- Complex zeroes come in pairs. Specifically, they come in <em>conjugate pairs</em>. If -2i is a zero, 2i must be a zero, too. The "why" is beyond the scope of this response, but this result is called the "complex conjugate root theorem".
In 2., I mentioned that both -2i and 2i must be zeroes of f(x). This means that both and
are factors of f(x), and furthermore, their product,
, is <em>also</em> a factor. To see what's left after we factor out that product, we can use polynomial long division to find that
I'll go through to steps to factor that second expression below:
Solving both of the expressions when f(x) = 0 gets us our final two zeroes:
So, the remaining zeroes are 1/2 and 3.