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Varvara68 [4.7K]
3 years ago
5

Please solve this :)

Mathematics
1 answer:
Karolina [17]3 years ago
8 0

Answer:

1000 is the best answer yet

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How many terms are there in the sequence 1, 8, 28, 56, ..., 1 ?
BabaBlast [244]

Answer:

9 terms

Step-by-step explanation:

Given:  

1, 8, 28, 56, ..., 1

Required

Determine the number of sequence

To determine the number of sequence, we need to understand how the sequence are generated

The sequence are generated using

\left[\begin{array}{c}n&&r\end{array}\right] = \frac{n!}{(n-r)!r!}

Where n = 8 and r = 0,1....8

When r = 0

\left[\begin{array}{c}8&&0\end{array}\right] = \frac{8!}{(8-0)!0!} = \frac{8!}{8!0!} = 1

When r = 1

\left[\begin{array}{c}8&&1\end{array}\right] = \frac{8!}{(8-1)!1!} = \frac{8!}{7!1!} = \frac{8 * 7!}{7! * 1} = \frac{8}{1} = 8

When r = 2

\left[\begin{array}{c}8&&2\end{array}\right] = \frac{8!}{(8-2)!2!} = \frac{8!}{6!2!} = \frac{8 * 7 * 6!}{6! * 2 *1} = \frac{8 * 7}{2 *1} =2 8

When r = 3

\left[\begin{array}{c}8&&3\end{array}\right] = \frac{8!}{(8-3)!3!} = \frac{8!}{5!3!} = \frac{8 * 7 * 6 * 5!}{5! *3* 2 *1} = \frac{8 * 7 * 6}{3 *2 *1} = 56

When r = 4

\left[\begin{array}{c}8&&4\end{array}\right] = \frac{8!}{(8-4)!4!} = \frac{8!}{4!3!} = \frac{8 * 7 * 6 * 5 * 4!}{4! *4*3* 2 *1} = \frac{8 * 7 * 6*5}{4*3 *2 *1} = 70

When r = 5

\left[\begin{array}{c}8&&5\end{array}\right] = \frac{8!}{(8-5)!5!} = \frac{8!}{5!3!} = \frac{8 * 7 * 6 * 5!}{5! *3* 2 *1} = \frac{8 * 7 * 6}{3 *2 *1} = 56

When r = 6

\left[\begin{array}{c}8&&6\end{array}\right] = \frac{8!}{(8-6)!6!} = \frac{8!}{6!2!} = \frac{8 * 7 * 6!}{6! * 2 *1} = \frac{8 * 7}{2 *1} = 28

When r = 7

\left[\begin{array}{c}8&&7\end{array}\right] = \frac{8!}{(8-7)!7!} = \frac{8!}{7!1!} = \frac{8 * 7!}{7! * 1} = \frac{8}{1} = 8

When r = 8

\left[\begin{array}{c}8&&8\end{array}\right] = \frac{8!}{(8-8)!8!} = \frac{8!}{8!0!} = 1

The full sequence is: 1,8,28,56,70,56,28,8,1

And the number of terms is 9

3 0
3 years ago
Factor the trinomial below.<br> x2 + 14x + 48
elixir [45]
IF IT EQUALS 0
1. find two number that multiplied to 48 and adds to 14, which are 6 and 8.

2. substitute the new numbers in with x to get x^2 + 6x + 8x + 48.

3. factor out the x and the 8 to get x(x+6)+8(x+6).

4. x = -6, x = -8

IF IT DOES NOT EQUAL 0
then (x+6)*(x+8) is your answer.
4 0
3 years ago
In order to sign "uncle," one must first make a "U" handshape and then move in two circles, just under the face. True False
Katarina [22]

Its false because it's false lol

4 0
3 years ago
What is the slope of the graph shown below
stiv31 [10]

Answer:

B=-5

Step-by-step explanation:

Slope=rise/run

The line passes in

P1(-1,3)

and

P2(0,-2)

So slope=(3-(-2))/(-1-0)=5/-1=-5

6 0
3 years ago
The path of a skateboarder can be modeled by the equation (x – 3)2 = –8(y – 8), where distance is in feet and air resistance is
yKpoI14uk [10]

The maximum height and horizontal distance is required.

Maximum height 8 feet; horizontal distance 16 feet

The given path is (x-3)^2=-8(y-8)

If the skateboarder jumps at x = 0 she will land at y = 0. However there will be at horizontal displacement.

(x-3)^2=-8(0-8)\\\Rightarrow (x-3)^2=8^2\\\Rightarrow x-3=\pm 8\\\Rightarrow x-3=8\\\Rightarrow x=11

or

x-3=-8\\\Rightarrow x=-5

The distance between -5 and 11 is 11-(-5)=16

Middle point would be \dfrac{16}{2}=8 from -5.

-5+8=3

So, x=3

The maximum height will be

(3-3)^2=-8(y-8)\\\Rightarrow y-8=0\\\Rightarrow y=8

The maximum height is 8 feet and the horizontal distance is 16 feet.

Learn more:

brainly.com/question/25227606

brainly.com/question/13103131

6 0
3 years ago
Read 2 more answers
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