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Amiraneli [1.4K]
3 years ago
13

Find the explicit formula for the given sequence. 4, 24, 144,864, ....

Mathematics
2 answers:
Brums [2.3K]3 years ago
5 0

Answer:

x * 6

Step-by-step explanation:

4 * 6 = 24

24 * 6 = 144

144 * 6 = 864

inna [77]3 years ago
3 0

Answer:

a_{n} = 4(6)^{n-1}

Step-by-step explanation:

Note the terms in the sequence have a common ratio, that is

r = 24÷ 4 = 144÷ 24 = 864 ÷ 144 = 6

This indicates the sequence is geometric with n th term

a_{n} = a(r)^{n-1}

where a is the first term and r the common ratio

Here a = 4 and r = 6, thus

a_{n} = 4(6)^{n-1} ← explicit formula

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alex41 [277]

Answer:

a piston chamber in a steam or internal combustion engine.

4 0
3 years ago
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A line that includes the point (1, 3) has a slope of -7. What is its equation in slope-intercept
Alex787 [66]

Answer:

y = -7x + 10

Step-by-step explanation:

Using a point slope form equation

y - y1 = m( x - x1)

Given

Point = ( 1 , 3)

Slope = -7

Insert the values into

y - y1 = m(x - x1)

x1 = 1

y1 = 3

y - 3 = m( x - 1)

m = -7

y - 3 = -7(x - 1)

Using a slope intercept form equation

y = mx + c

Open the bracket

y - 3 = -7x + 7

y = -7x + 7 + 3

y = -7x + 10

The equation of the line is

y = -7x + 10

6 0
3 years ago
Help thanksSSSSSSSSSS
Setler79 [48]

Answer:

  • \boxed{\sf{x=24}}

Step-by-step explanation:

<u>GIVEN:
</u>

To find the missing number in the proportion, you have to isolate it the term of x from one side of the equation.

\sf{\dfrac{8}{7}=\dfrac{x}{21}  }

First, thing you do is switch sides.

\sf{\dfrac{x}{21}=\dfrac{8}{7}  }

Multiply by 21 from both sides.

\Longrightarrow: \sf{\dfrac{21x}{21}=\dfrac{8*21}{7} }

Solve.

Multiply the numbers from left to right.

Use the order of operations.

PEMDAS stands for:

  • Parentheses
  • Exponents
  • Multiply
  • Divide
  • Add
  • Subtract

\Longrightarrow: \sf{\dfrac{8*21}{7}=\dfrac{168}{7}=24 }

\Longrightarrow: \boxed{\sf{x=24}}

  • <u>Therefore, the final answer is x=24.</u>

I hope this helps. Let me know if you have any questions.

3 0
2 years ago
The fastest a human has ever run is 27 miles per hour. how many miles per minute did the human rn?
Savatey [412]
27 miles per hour

1 hour = 60 minutes

27 miles per 60 minutes

27/60 miles per 1 minute

9/20 miles per minute

6 0
4 years ago
During halftime of a football game a slingshot launches T-shirts at the crowd a T-shirt is launched from a height of 6 feet with
lesantik [10]

Answer:

2.25 seconds

87 feet

[6, 87]

Step-by-step explanation:

The height of a projectile is:

h(t) = -16t² + vt + s

where v is the initial vertical velocity and s is the initial height.

Here, v = 72 and s = 6.

h(t) = -16t² + 72t + 6

This is a downwards parabola.  The maximum is at the vertex.

t = -b / (2a)

t = -72 / (2×-16)

t = 2.25

h(2.25) = 87

It takes 2.25 seconds to reach the maximum height of 87 feet.

The range is from the lowest height (6 feet) to the maximum height (87 feet).  In interval notation:

[6, 87]

5 0
4 years ago
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