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Jlenok [28]
2 years ago
9

Write an explicit formula for the geometric sequence below and use it to find the 9th term. 256, 64, 16, 4, . . .

Mathematics
1 answer:
Nastasia [14]2 years ago
7 0

im doing this problem right now---

ok so a1=256 a2=64 a3=15 a4=4... find a9

the sequence divides by 1/4 every term

an=a1*r^n-1

an=(256)*(1/4)^n-1

replace n with 9

A9=(256)*(1/4)^9-1

A9=(256)*(1/4)^8

=(256)*(1/4)

A9=64^8

1/256 or a9= 0.00390625

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The product of three consecutive integers is 3360. What is the sum of the three integers?
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Step-by-step explanation:

let the integer be x .

three consecutive integers : x, x+1, x+2.

according to the problem,.

Let the first of the 3 consecutive numbers be X.

Therefore the second number is (X + 1)

The third number is therefore (X + 2)

The product of the 3 consecutive numbers is:

( X )( X + 1 )( X + 2 ) = 3360 Equation( 1 )

Expanding Equation ( 1 ) gives

X³ + 3X² + 2X - 3360 = 0 Equation (2)

Solve Equation (2 ) which gives the following values for X

X1 = 14

X2 = - 8.5 + i (12.951834)

X3 = - 8.5 - i (12.951834).

the numbers are 14,15,16.

sum is 14+15+16 = 45.

hope this helps you.

5 0
2 years ago
Whats the vertex at of y-13=2(x+4)^2
Kipish [7]
The vertex form:
y=a(x-h)^2+k
(h,k) - the coordinates of the vertex

y-13=2(x+4)^2 \\
y=2(x+4)^2+13 \\
y=2(x-(-4))^2+13 \\ \\
h=-4 \\ k=13

The coordinates of the vertex are (-4,13).
7 0
2 years ago
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Explain how the following are related: linear relationship, proportional relationship, equivalent ratios, and direct variation
Scilla [17]
With all of the following you are able to make a graph, table, and a equation.
5 0
2 years ago
What is 2.03 written in words and numbers?
Rudiy27
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5 0
3 years ago
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Akira receives a prize at a science fair for having the most informative project. Her trophy is in the shape of a
AlekseyPX

Answer:

45 square inches

Step-by-step explanation:

Akira receives the prize at the science fair for having the most informative project her trophy is in the shape of a square pyramid and is covered in shiny gold foil how much gold foil did it take to cover the trophy including the bottom

Total surface  =  surface area of the base square + area of 4 triangles

Calculate the surface area of the base square

surface area of the square =  s^2

where s= side length

s=3 in

The surface area of the base  =s^2

=3^2

= 9 square inches

The surface area of the side triangles

The area of the triangle = (1/2)* side length* slant height

Side length=3 in

Slant height=6 in

substituting the values,

The area of the triangle =1/2*3*6

= 18/2

= 9 square inches

There are 4 triangles

The area of 4 triangles  =  4 x 9  

= 36 square inches

Therefore,

Total surface  =  surface area of the base square + area of 4 triangles

=  9 + 36

= 45 square inches

6 0
2 years ago
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