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stepladder [879]
3 years ago
15

Use the table to determine the degree of the power function.

Mathematics
1 answer:
valkas [14]3 years ago
5 0

9514 1404 393

Answer:

  3

Step-by-step explanation:

The x-values in the table are evenly-spaced, so we can determine the degree of the function by looking at successive differences of the f(x) terms.

f(x): -23, -4, 3, 4, 5, 12, 31

first differences: 19, 7, 1, 1, 7, 19

second differences: -12, -6, 0, 6, 12

third differences: 6, 6, 6, 6

The third differences are constant, so the function values can be matched by a <em>third degree</em> polynomial.

_____

<em>Additional comment</em>

The first differences are found by subtracting the function value from the next one. Likewise, the second differences are found by subtracting each first-difference value from the next one. An so on for the third differences.

The level at which the differences are constant is the degree of the polynomial that will match the function values. (Compare this to what you know about an arithmetic sequence, where first differences are constant and the sequence is described by a linear (degree 1) equation.)

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n August 31 of the current year, the assets and liabilities of Gladstone, Inc. are as follows: Cash $27,900; Supplies, $900; Equ
frez [133]

The amount of stockholders’ equity as of August 31 of the current year is $26400.

<h3>How to calculate the equity?</h3>

The owner's equity will be:

= Cash + Supplies + Equipment - Account payable

= 27900 + 900 + 8500 - 7300

= 26400

Therefore, the amount of stockholders’ equity as of August 31 of the current year is

Learn more about equity on:

brainly.com/question/1957305

#SPJ1

8 0
2 years ago
For brainiest:):):):):):):):)
mars1129 [50]

Answer:

A1) 125

A2) 47.5%

B) 30

Step-by-step explanation:

Remember 'of' in this sentence means times(*). % shows a certain number/100.

a1) 48% 'of' what number is 60?

(let unknown number be x)

48/100 *x=60

Solve the equation, and the answer is x=125

a2) what percentage 'of' 120 is 57?

(let the unknown percentage be x)

(x/100)*120=57

x=47.5%

b) 24 students= 80% of the total number of students

1%=24/80

100% of the total number of students=30

So, there are total of 30 students

8 0
3 years ago
Evaluate the integral. (sec2(t) i t(t2 1)8 j t7 ln(t) k) dt
polet [3.4K]

If you're just integrating a vector-valued function, you just integrate each component:

\displaystyle\int(\sec^2t\,\hat\imath+t(t^2-1)^8\,\hat\jmath+t^7\ln t\,\hat k)\,\mathrm dt

=\displaystyle\left(\int\sec^2t\,\mathrm dt\right)\hat\imath+\left(\int t(t^2-1)^8\,\mathrm dt\right)\hat\jmath+\left(\int t^7\ln t\,\mathrm dt\right)\hat k

The first integral is trivial since (\tan t)'=\sec^2t.

The second can be done by substituting u=t^2-1:

u=t^2-1\implies\mathrm du=2t\,\mathrm dt\implies\displaystyle\frac12\int u^8\,\mathrm du=\frac1{18}(t^2-1)^9+C

The third can be found by integrating by parts:

u=\ln t\implies\mathrm du=\dfrac{\mathrm dt}t

\mathrm dv=t^7\,\mathrm dt\implies v=\dfrac18t^8

\displaystyle\int t^7\ln t\,\mathrm dt=\frac18t^8\ln t-\frac18\int t^7\,\mathrm dt=\frac18t^8\ln t-\frac1{64}t^8+C

8 0
3 years ago
1. The variable y varies inversely with x and y = 6 when x = 3.
Y_Kistochka [10]
Inverse variation means y=k/x, we are given (3,6) so

6=k/3

k=18 so

y=18/x

y=18/27

y=2/3
7 0
3 years ago
Please help with this problem
Maurinko [17]

Answer:

0.01p + 0.05n > 40

0.01p + 0.05n < 20

Step-by-step explanation:

it has to be MORE (greater) than 40

it has to be LESS than 20 coins

hope this helps

not sure if you have to write the second equation, so sorry if it's wrong. :)

7 0
3 years ago
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