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nalin [4]
3 years ago
13

A hyperbola centered at the origin has a vertex at (3, 0) and a focus of the hyperbola is located at (9, 0). What are the equati

ons of the directrices?
x = ±
Mathematics
2 answers:
Alborosie3 years ago
8 0
The answer is 1.,.....

frez [133]3 years ago
7 0
It's 1 i agree with the other person because i just took the assignment and got it correct.
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Graph the function y = 2x3 – x2 – 4x + 5. To the nearest tenth, over which interval is the function decreasing?
daser333 [38]
As you progress in math, it will become increasingly important that you know how to express exponentiation properly.

y = 2x3 – x2 – 4x + 5  should be written    <span>y = 2^x3 – x^2 – 4^x + 5.  The 
" ^ " symbol denotes exponentiation.

I see you're apparently in middle school.  Is that so?  If so, are you taking calculus already?  If so, nice!

Case 1:  You do not yet know calculus and have not differentiated or found critical values.  Sketch the function          </span>y = 2x^3 – x^2 – 4^x + 5, including the y-intercept at (0,5).  Can you identify the intervals on which the graph appears to be increasing and those on which it appears to be decreasing?

Case 2:  You do know differentiation, critical values and the first derivative test.  Differentiate  y = 2x^3 – x^2 – 4^x + 5 and set the derivative = to 0:

dy/dx = 6x^2 - 2x - 4 = 0.  Reduce this by dividing all terms by 2:

dy/dx = 3x^2 - x - 2 = 0    I used synthetic div. to determine that one root is x = 2/3.  Try it yourself.  This leaves the coefficients of the other factor, (3x+3); this other factor is x = 3/(-3) = -1.  Again, you should check this.

Now we have 2 roots:  -1 and 2/3

Draw a number line.  Locate the origin (0,0).  Plot the points (-1, 0) and (2/3, 0).  This subdivides the number line into 3 subintervals:

(-infinity, -1), (-1, 2/3) and (2/3, infinity).

Choose a test number from each interval and subst. it for x in the derivative formula above.  If the derivative comes out +, the function is increasing on that interval; if -, the function is decreasing.

Ask all the questions you want, if this explanation is not sufficiently clear.

4 0
3 years ago
Read 2 more answers
12. Write the first five terms of two different sequences that have 10 as the
kodGreya [7K]

Answer:

a)  The arithmetic sequence with common difference 2 that has 8 as the first term.

b) The arithmetic sequence of common difference -5 and first term 15.

Step-by-step explanation:

Let's use for example the arithmetic sequence with common difference 2 that has 8 as the first term. Then the first two terms of this sequence are:

8, and (8+2) = 10 Therefore the second term is 10.

Another arithmetic sequence of common difference -5 and first term 15. The firs two terms of this sequence are:

15, and  (15 - 5)  = 10. Therefore again a 10 as second term.

6 0
3 years ago
Find the slope of the tangent to the graph of the given function at the indicated point. HINT [Recall that the slope of the tang
Mrac [35]

f'(x)

=  8{x}^{7}

slope

8 {( - 8)}^{7}  =  -  {8}^{8}

6 0
3 years ago
What is X in 24x - 52 = -4 ( 1 + 6x )? <br> Please help.
fomenos
I believe x equals one
3 0
3 years ago
Susan can buy 6 flower seed packets for $2. If all the seed packets cost the same amount of money, how many packets can Susan bu
antiseptic1488 [7]

Answer:She can buy 30 packets

Step-by-step explanation:

6 flower seeds  $2

12 flower seeds $4

18 flower seeds $6

24 flower seeds $8

30 flower seeds $10

8 0
3 years ago
Read 2 more answers
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