Solution 1
Inspecting a 7th-degree polynomial of 'n' by taking its derivatives
From the given conditions,
2n7+n6+2n4+2n3+2n2
=(n+1)7+(n+1)5+(n+1)4+2(n+1)3+(n+1)2+2(n+1)+1.
2n7+n6+2n4+2n3+2n2
=n7+7n6+21n5+35n4+35n3+21n2+7n+1
+n5+5n4+10n3+10n2+5n+1
+n4+4n3+6n2+4n+1
+2(n3+3n2+3n+1)
+(n2+2n+1)+2(n+1)+1.
n7-6n6-22n5-39n4-49n3-42n2-26n-9=0 .....[1].
Let A(n)=n7-6n6-22n5-39n4-49n3-42n2-26n-9.
For n>2, A(n)<n7-6n6-22n5.
Since A(n)=0,
0<n7-6n6-22n5.
0<n5(n-3+√31)(n-3-√31).
Since n>2, n>3+√31, which means n≥9 .....[2].
Now, to differentiate A(n),
A'(n)=7n6-36n5-110n4-156n3-147n2-84n-26.
A''(n)=42n5-180n4-440n3-468n2-294n-84.
A'''(n)=210n4-720n3-1320n2-936n-294.
A(4)(n)=840n3-2160n2-2640n-936.
A(5)(n)
=2520n2-4320n-2640
=2520{(n-6/7)2-262/147}.
If A(5)(n)=0, n=6/7±√(262/147).
Therefore, A(5)(n)>0 for n≥3.
Although n≥9 according to [2], I try inspecting A(n) for n≥10.
When n≥10, A(4)(n) increases monotonously.
A(4)(10)=840000-216000-26400-936>0.
Therefore, A(4)(n)>0 for n≥10.
And when n≥10, A'''(n) increases monotonously.
A'''(10)=2100000-720000-132000-9360-294>0.
Therefore, A'''(n)>0 for n≥10.
And when n≥10, A''(n) increases monotonously.
A''(10)=4200000-1800000-440000-46800-2940-84>0.
Therefore, A''(n)>0 for n≥10.
And when n≥10, A'(n) increases monotonously.
A'(10)
=7000000-3600000-1100000-156000-14700-840-26>0.
Therefore, A'(n)>0 for n≥10.
And when n≥10, A(n) increases monotonously.
A(10)
=107-6000000-2200000-390000-49000-4200-260-9>0.
Therefore, A(n)>0 for n≥10 .....[3].
From [2] and [3], A(n)=0 only when 9≤n<10.
In consequence, n=9.
Answer: 5n+14-11n-2
Step-by-step explanation:
Point (-3,4) is rotated 180° about the origin in a
counterclockwise direction. What are the coordinates of its
image?
Answer:
( 4 , -3)
Step-by-step explanation:
Rate me branliest please :)
Which of the following could be the equation for a parabola that opens down
with vertex (-11, -28)?
A. x=-5(y + 28)2 - 11
B. y= -5(x +11)2 - 28
C. X= 5(y +11)2 - 28
D. y = 5(x+28)2 - 11
Answer:
B.
Step-by-step explanation:
the negative 5 means that the parabola will open down. the positive 11 in the parentheses is graphed as a negative 11 and the negative 28 stays the same.
PLD HELP ME I WILL FAIL PLSx
Answer:
96.4
Step-by-step explanation:
can someone help me with this I really don't understand
Answer:
No
Step-by-step explanation:
Because the constant of proportionality is not equivalent to 20,13.
Can I have brainliest?
Find the solution to the equation shown below.
–3.4(x – 2) = 9.8 – 4x
Answer:
X= 5
Explanation (Steps):
Step 1: Simplify both sides of the equation.
−3.4(x−2)=9.8−4x
(−3.4)(x)+(−3.4)(−2)=9.8+−4x(Distribute)
−3.4x+6.8=9.8+−4x
−3.4x+6.8=−4x+9.8
Step 2: Add 4x to both sides.
−3.4x+6.8+4x=−4x+9.8+4x
0.6x+6.8=9.8
Step 3: Subtract 6.8 from both sides.
0.6x+6.8−6.8=9.8−6.8
0.6x=3
Step 4: Divide both sides by 0.6.
0.6x0.6=3/0.6
x=5
find the product of 16 and 24
Answer:
384 16 times 24 is equal to 384
Step-by-step explanation:
You just have to multiply them. 16 times 24 is 384.
If a hexagon represents 1 whole what does 1 triangle represent?
Answer:
If the hexagon represents 1 whole, then a triangle must represent , because 6 triangles make 1 hexagon. We can use the triangle to represent the in the problem. Twelve triangles make 2 hexagons, which means there are 12 groups of in 2.
Answer:If the hexagon represents 1 whole, then a triangle must represent , because 6 triangles make 1 hexagon. We can use the triangle to represent the in the problem. Twelve triangles make 2 hexagons, which means there are 12 groups of in 2.
Step-by-step explanation:
The amount of revenue brought in by states from motor vehicle licenses increased at a relatively constant rate of 499.79 million dollars per year from 1990 to 2000. In 2000, the states brought in 15,099 million dollars in revenue from motor vehicle licenses
Answer:
a. the approximate revenue from licenses in 1990 was $10,101.10 million.
b. The function is x = 10,101.10 + 499.79y
c. The revenue from licenses in 1999 is $14,599.21 million.
Step-by-step explanation:
The amount of revenue brought in by states from motor vehicle licenses increased at a relatively constant rate of 499.79 million dollars per year from 1990 to 2000. In 2000, the states brought in 15,099 million dollars in revenue from motor vehicle licenses.
a: what was the approximate revenue from licenses in 1990?
b: write an equation that gives the revenue as a function of the number of years since 1990.
c: find the revenue from licenses in 1999.
a: what was the approximate revenue from licenses in 1990?
This can be calculated using the following function:
x = a + by ............................... (1)
Where;
x = Amount brought in 2000 = $15,099 million
a = Amount brought in 1990 = ?
b = Amount of relative constant rate of increase = $499.79 million
y = Number of years between 1990 and 2000 = 10
Substituting the values into equation (1) and solve for a, we have:
15,099 = a + (499.79 * 10)
a = 15,099 - 4,997.90
a = $10,101.10 million
Therefore, the approximate revenue from licenses in 1990 was $10,101.10 million.
b: write an equation that gives the revenue as a function of the number of years since 1990.
Using equation (1) in part a above, we substitute the values for a and b to obtain an equation that gives the revenue as a function of the number of years since 1990 as follows:
x = 10,101.10 + 499.79y ....................... (2)
c: find the revenue from licenses in 1999.
Since 1999 is 9th year from 1990, we therefore substitute y = 9 in equation (2) as follows:
x = 499.79 + 10,101.10y
x = 10,101.10 + 499.79(9)
x = 10,101.10 + 4,498.11
x = $14,599.21 million
Therefore, the revenue from licenses in 1999 is $14,599.21 million.
PLEASE HELP!
Find four numbers, the
sum of which is 45, so
that if 2 is added to
the first number, 2 is
subtracted from the
second number, the third
number is multiplied by
2, while the fourth
number is divided by 2,
then the four numbers so
produced are all the
same.
45
Step-by-step explanation:
45 +2=47
47-2=45
45×2=90
90÷2=45
Hue is arranging chairs. She can form 6 rows of a given length with 3 chairs left over, or 8 rows of that
same length if she gets 15 more chairs. Complete the equation and solve it to find how many chairs are inthat row length. In your equation, use the variable x to represent the number of chairs in each row.
Answer:
8r + 15 = x
Step-by-step explanation:
So being that they can form 6 rows but have 3 left over we know that there are more than three chairs in each row. So for example:
6r + 3 = x
or (x = chairs, r = chairs in the row)
8r + 15 = x
can someone here recommend me some music
Answer:
Surfaces, "Sunday Best"
Natalia Lafourcade, "La Malquerida" ...
Lil Mosey, "Blueberry Faygo" ...
Sada Baby, "Slide" ...
Zebra Katz, "In In In" ...
Jessie Reyez feat. ...
Halsey, "You Should Be Sad" ...
The Rolling Stones, "Living in a Ghost Town" ...
Surfin’ by SURAN
Gone by Rosé
Embarrassed by BTS
Candy by BAEKHYUN
This Night (feat. Blue.D & Jhnover) by GroovyRoom
Kate is going on a long distance car trip. She begins with 16 gallons of gas in her car and her car burns 3 gallons of gas each hour. If she ends her road trip with 1 gallon of gas left in the tank, how many hours was she driving
9514 1404 393
Answer:
5 hours
Step-by-step explanation:
Starting with 16 gallons and ending with 1 gallon means that Kate has used 15 gallons of gas. Burning 3 gallons per hour means her travel time was ...
(15 gal)/(3 gal/h) = 5 h
Kate was driving for 5 hours.
Troy needs to complete 45 hours of training. During the fall, Troy completed 12 hours of training, and during the spring he completed twice as many hours as he had during the fall. Which equation can be used to find how many more hours of training (h) Troy needs to complete? Select one:
Answer:
[tex]36 + h = 45[/tex]
[tex]h = 9[/tex]
Step-by-step explanation:
Given
[tex]Total = 45[/tex]
[tex]Fall = 12[/tex]
[tex]Spring = 2 * Fall[/tex]
Required
Determine the equation to find the hours (h) left
The sum of the hours spent during the fall, spring and the hours left must be equal to the total hours.
In other word;
[tex]Fall + Spring + h = Total[/tex]
Substitute 2 * Fall for Spring
[tex]Fall + 2 * Fall + h =Total[/tex]
Substitute values for Fall and Total
[tex]12 + 2 * 12 + h = 45[/tex]
[tex]12 + 24 + h = 45[/tex]
[tex]36 + h = 45[/tex]
The above represents the equation,
Solving further for h
[tex]h = 45 - 36[/tex]
[tex]h = 9[/tex]
Hence, there are 9 hours left
The graph shows the results of a race between Peter and Stuart. Both boys begin the race at the same time.
Which statements are true about the race?
Select each correct answer.
Peter runs the race at an approximate rate of 4.6 yd/s .
Stuart runs the race at a faster rate than Peter.
Peter is given a 40 yd head start and wins the race.
Stuart finishes the race 1 s after Peter finishes the race.
Stuart is given a 40 yd head start and loses the race.
Stuart runs a longer race than Peter.
Answer:it would be the 2nd , 3rd, 5th,
one
Step-by-step explanation:
Lucas bought an 8 pack if bottled iced tea. Each bottle contained 14.75 fluid ounces. What was the totals number of fluid ounces in all the bottles?
Answer:
118 fluid ounces in all.
Step-by-step explanation:
The answer 118 because 14.75 multiplied by 8 is 118.
What is the momentum of a 2000-kg car traveling at 20 m/s?
a. O kg m'sec
b. 0.001 kg'm'sec
c. 100 kg m sec
d. 40,000 kg m sec
Answer:
D
Step-by-step explanation:
force = mass × acceleration
Answer: D
Step-by-step explanation:
NEED HELP ASAP!!!!!!!!!!!!!!!!!!
Answer:
I dont. understannnnd
Will give brainliest
Problem 12
Answer:
44 yards
Step-by-step explanation:
Answer:
wouldn't you just do 14 times 8? If so it would be 112 yards (i might be wrong tho..)
Pls help me with this!!
W33D
Step-by-step explanation:
Answer:
B
Step-by-step explanation:
Assuming the dilatation is centred at the origin.
Then multiply each set of coordinates by the scale factor [tex]\frac{1}{3}[/tex] , thus
(- 12, 3 ) → [tex]\frac{1}{3}[/tex](- 12), [tex]\frac{1}{3}[/tex] (3) ) → (- 4, 1 )
(0, 6 ) → ( [tex]\frac{1}{3}[/tex] (0), [tex]\frac{1}{3}[/tex] (6) ) → (0, 2 )
(3, - 3 ) → ( [tex]\frac{1}{3}[/tex] (3), [tex]\frac{1}{3}[/tex] ( - 3 ) ) → (1, - 1 )
Here please help
I will give brainest
Pleaseeeeee helpppppp
Answer:
5,d
6,e
7,b
8,f
9,c
10,a
five ninths plus four sixths have a nice day Owo
Answer:
Shoyo here!
Step-by-step explanation:
1.22222222222
hehe, that's a long number- have a nice day! <3
which triangle is congruent to the triangle with vertices (2,-2), (7,10) and (4,6) ?
Answer:
Ion know what you mean
Step-by-step explanation:
help? i need to due right now
Answer:
200
Step-by-step explanation:
14.
The graph shows the decrease in the value, v, of a commercial
jet over time, t, measure in years.
Which equation best represents the graph?
F v(t) = 5.5t + 110
G v(t) = -5.5t + 110
H v(t) = -110 + 110
J v(t) = 11t + 110
Step-by-step explanation:
hugs did ta don't think she knows what that was you baby girl so ti you but I'm not sure what you mean 4buy64g7gugugguvbb Jo is my first year of my first time doing your opinion how are ilocano or so I will get you a quote please let your opinion how much I love sorry na please ❣️❣️ you ❣️❣️❣️❤️ you
How many times further is 4,500,000,000and 58,000,000
Answer: 4442000000
Step-by-step explanation:
Answer:
I know the answer but ill give you a hint all you do is subtract
Step-by-step explanation:
because it says how farthere
Help me please 12 and f
Answer:
It is not equivalent.
Step-by-step explanation:
You have to expand the brackets :
(x-4)(x+3)
= x(x) + x(3) - 4(x) - 4(3)
= x² + 3x - 4x - 12
= x² - x - 12
Therefore, x² - x - 12 / (x-4)(x+3) is not equivalent to x² - 4x - 12.
Question 1(Multiple Choice Worth 4 points) (04.07A) Two quantities are related, as shown in the table below: x y 2 2 4 5 6 8 8 11 Which equation best represents the relationship? y = 3 over 2x + 2 y = 3 over 2x y = 3 over 2x − 1 y = 3x + 2
Answer:
id say C if not sorry
Step-by-step explanation:
Answer: The answer is C
Step-by-step explanation: Thanks to the person above me I got the question right.
What is the quotient when 22,464 is divided by 72?
Answer:
312
Step-by-step explanation:
help plzz hurry i didnt study and need help
Which expression can be used to determine the slope of the linear function graphed below?
Answer:
Y = 2x-4
Step-by-step explanation:
the anwser is, A
Step-by-step explanation:
-4-0
2-0