What is the domain of the function = x+6-7? x2-7 X2-6 x26 Ox27

Work out the formula of the nth term in the following quadratic sequence: 19, 15, 9, 1...

Butoxors [25]

In a quadratic sequence we'll get a linear first difference and a constant second difference. Let's verify that.

n 1 2 3 4

f(n) 19 15 9 1

1st diff -4 -6 -8

2nd diff 2 2

We see that we got a constant second difference. We could just extend that and work back up to get more values.

n 1 2 3 4 5 6 7

f(n) 19 15 9 1 -9 -21 -35

1st diff -4 -6 -8 -10 -12 -14

2nd diff 2 2 2 2 2

That's just an aside; we're after the general formula. We have

f(1)=19, f(2)=15, f(3)=9

In general we can assume

f(n) = an² + bn + c

We get three equations in three unknowns,

19 = a(1²)+b(1)+c = a+b+c

15 = a(2²) + b(2) + c = 4a + 2b + c

9 = a(3²) + b(3) + c = 9a + 3b + c

That's a 3x3 linear system; it's easy to solve directly. Subtracting pairs,

4 = -3a - b

6 = -5a - b

Subtracting those,

-2 = 2a

a = -1

b = -3a -4 = -1

c = 19-a-b = 21

Answer: f(n) = -n² - n + 21

Check:

f(1) = -1 - 1 + 21 = 19, good

f(2) = -4 - 2 + 21 = 15, good

f(3) = -9 - 3 + 21 = 9, good

f(4) = -16 - 4 + 21 = 1, good

Let's check our extended table, how about

f(7)= -49 - 7 + 21 = -35, good

6 0

3 years ago

In the order of operations, the absolute value sign is considered to be at which level?

morpeh [17]

Answer:

Note that with embedded parentheses (parentheses within parenthesis), you always perform operations inside out; do the math on the inside before the outside. Note that if you have an absolute value | | sign which means take the positive value only of a number inside.

7 0

1 year ago

Read 2 more answers

How would I do the steps to solve this?

allsm [11]

Answer:

The maximum revenue is 16000 dollars (at p = 40)

Step-by-step explanation:

One way to find the maximum value is derivatives. The first derivative is used to find where the slope of function will be zero.

Given function is:

$R(p) = -10p^2+800p$

Taking derivative wrt p

$\frac{d}{dp} (R(p) = \frac{d}{dp} (-10p^2+800p)\\R'(p) = -10 \frac{d}{dp} (p^2) +800 \ frac{d}{dp}(p)\\R'(p) = -10 (2p) +800(1)\\R'(p) = -20p+800\\$

Now putting R'(p) = 0

$-20p+800 = 0\\-20p = -800\\\frac{-20p}{-20} = \frac{-800}{-20}\\p = 40$

As p is is positive and the second derivative is -20, the function will have maximum value at p = 40

Putting p=40 in function

$R(40) = -10(40)^2 +800(40)\\= -10(1600) + 32000\\=-16000+32000\\=16000$

The maximum revenue is 16000 dollars (at p = 40)

3 0

2 years ago

How many number of terms does 5p^2-2p+3r have?

Helga [31]

Answer:

3 terms

Step-by-step explanation:

5 $p^{2}$ - 2p + 3r

It has 3 terms

They are as follows:

5 $p^{2}$

-2p

and 3r

Hope this helps

plz mark as brainliest!!!!!

7 0

3 years ago

Could someone please answer #35 for me

katrin2010 [14]

Answer:

408

Step-by-step explanation:

Volume = length times width times height

So in this situation we can see that 17 is the length, 8 is the width, and 6 is the height

Knowing this information we can continue

If you think of a regular cube, you can split it diagonally and then it would be 2 triangles

So we can split the width, in halve which would be 4 and then apply the formula 4*6*17 and when you solve that you get 408 Now we have to split that in halve because remember it is a triangle and a triangle is halve of a square. Halve of 408 is 204.

If we repeat that prosses for the other side we will also get 204. Now we add 204+204 to get our answer 408.

Sorry is this was a little confusing but that's the best I can explain it.

Hope that helped and have a great day!

Step-by-step explanation:

4 0

3 years ago