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liberstina [14]
3 years ago
8

Find the 8th term of the geometric sequence whose common ratio is 2/3 and whose first term is 7​

Mathematics
1 answer:
motikmotik3 years ago
8 0

Answer:

The 8th term of the sequence is 896/2187.

Step-by-step explanation:

We want to find the 8th term of a geometric sequence whose common ratio is 2/3 and whose first term is 7.

We can write a direct formula. Recall that the direct formula of a geometric sequence is given by:

\displaystyle x_{n} = a\left(r\right)^{n-1}

Where <em>a</em> is the initial term and <em>r</em> is the common ratio.

Substitute:

\displaystyle x_{n} = 7\left(\frac{2}{3}\right)^{n-1}

To find the 8th term, let <em>n</em> = 8. Substitute and evaluate:

\displaystyle \begin{aligned} x_{8} &= 7\left(\frac{2}{3}\right)^{(8) - 1} \\ \\ &= 7\left(\frac{2}{3}\right)^{7} \\ \\ &= 7\left(\frac{128}{2187}\right) \\ \\ &= \frac{896}{2187} = 0.4096...\end{aligned}

In conclusion, the 8th term of the sequence is 896/2187.

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A minigolf ball is on a perfectly horizontal surface, x = 2 m away from the center of the hole. There is a small obstacle in the
nika2105 [10]
<h3>Answer:</h3><h3>Two possible smallest and largest angles are 11.78° and 78.22°.</h3>

Step-by-step explanation:

Minigolf ball will follow a trajectory to get into the hole.

Since range of a trajectory is calculated by the formula,

R=\frac{u^{2}sin2\theta}{g}

Where u = initial speed of the ball

θ = angle between the hole and direction in which the ball has been projected

g = gravitational pull

Now we plug in the values in the formula,

2=\frac{7^{2}sin(2\theta)}{9.8}

sin2θ = \frac{2\times 9.8}{49}

2θ = sin^{-1}(0.4)

2θ = 23.57° or 156.43°

θ = 11.78° or 78.22°

Hence two possible smallest and largest angles are 11.78° and 78.22°.

6 0
3 years ago
What is the slope of the line?<br><br> no slope<br> 1<br> 0<br> -2
morpeh [17]

Answer:

0

Step-by-step explanation:

4 0
3 years ago
I need to know what is <br><img src="https://tex.z-dn.net/?f=%20-%2015%20%5Cdiv%203" id="TexFormula1" title=" - 15 \div 3" alt="
Slav-nsk [51]

The answer is -3 because mathematically -15 divided by 3 equals -3



8 0
3 years ago
If a triangle has side lengths 7, 10, and 12, is it a right triangle??
Vesnalui [34]

Answer:

No. Remember, a right angle must have a 90 degree angle. We can find the lengths with the Pythagorean Theorem.

Step-by-step explanation:

Given the length 7, 10, and 12, we can assume that 12 is the hypotenuse (it is the longest length).

- we can use 7 and 10 interchangeably.

Fill in the equation, a^2 + b^2 = c^2

                 where c = 12, and a or b = 7 or 10.

To indicate if the given lengths would form a right angle, we can only input 7 or 10, not both.

Therefore, 7^2 + b^2 = 12^2 or 10^2 + b^2 = 12^2

7^2 + b^2 = 12^2 ==> 49 + b^2 = 144 ==> <u>b= </u>\sqrt{95<u> ==> </u><u>9.746</u>

b= 9.7, not 10.

10^2 + b^2 = 12^2 ==> 100 + b^2 = 144 ==> <u>b = </u>\sqrt{44<u> ==> </u><u>6.633 </u>

b= 6.6, not 7.

Therefore, the lengths 7, 10, and 12, does NOT make a right triangle.

Hope this helps!

5 0
3 years ago
A cantaloupe weights 56 ounces there are 16 ounces in a pound how many pounds does the cantaloupe weight
Semenov [28]
It would be 3.5 as you start with 56 then take away 16 =40 then another witch is 24 the another 16 Is 8 so you have taken e16 away so far that's 3 pound and because you can take a full 16 off that makes it a half so final awnser is 3.5 56-16=40-16=24-16=8=3 pounds and a half hope I have helped you in any way
5 0
3 years ago
Read 2 more answers
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