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3 years ago

Find an explicit rule for the nth term of a geometric sequence where the second and fifth terms are -6 and 162, respectively.

2 answers:

5 0

Hello,

a(2)=-6
a(3)=-6*r
a(4)=-6*r²
a(5)=-6*r^3=162
a(5)/a(2)=r^3=162/(-6)=-27==>r=-3

a(1)=-6/(-3)=2
a(2)=2*(-3)
a(3)=2*(-3)²
a(4)=2*(-3)^3
a(5)=2*(-3)^4

a(n)=2*(-3)^(n-1)

Answer

wlad13 [49]3 years ago

4 0

Answer:

an = 2 • (-3)^n - 1

Step-by-step explanation:

I have taken the test and this is the correct option :)

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What is the second law of exponents

Vlad1618 [11]

Answer:

When we divide powers of the same base, this means that we have to do is subtract the exponents. ... In other words, all we would need is to divide two powers that have the same exponent then the subtraction would lead to zero

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3 years ago

A 22m ladder and a 20m ladder were leaned against a building. The bottom of the longer ladder was 4m farther from the building t

OLga [1]

Answer:

Both ladder reaches 18.1 m up the building ⇒ 3rd answer

Step-by-step explanation:

* Lets study the information to solve the problem

- There are two ladders

- The lengths of them are 22 m and 20 m

- The bottom of the longer was 4 m farther than the bottom of the

shorter from the building

- Both of them reached the same distance up the building

* Lets solve the problem

- Let the distance between the bottom of the shorter ladder to the

building is x

∵ The bottom of the longer ladder is farther by 4

∴ The distance between the bottom of the longer ladder and the

building is x + 4

- Let the ladders reached the distance h up the building

* Now we have two right triangles

# Their hypotenuses are 22 and 20

# Their heights are h

# Their bases are x + 4 , x

- Lets find h in each triangle using the rule of Pythagoras

∵ (hypotenuse)² = (leg 1)² + (leg 2)²

# The longer ladder

∵ hypotenuse = 22

∵ leg 1 = x + 4

∵ leg 2 = h

∴ (22)² = (x + 4)² + h² ⇒ simplify

∴ 484 = (x + 4)² + h² ⇒ subtract (x + 4)² from both sides

∴ h² = 484 - (x + 4)² ⇒ (1)

# The shorter ladder

∵ hypotenuse = 20

∵ leg 1 = x

∵ leg 2 = h

∴ (20)² = (x )² + h² ⇒ simplify

∴ 400 = x² + h² ⇒ subtract x² from both sides

∴ h² = 400 - x² ⇒ (2)

- Equate (1) , (2) to find x

∴ 484 - (x + 4)² = 400 - x² ⇒ Add (x + 4)² and subtract 400 in both sides

∴ 84 = (x + 4)² - x² ⇒ open the bracket

∴ 84 = x² + 2(4)(x) + 4² - x² ⇒ simplify

∴ 84 = 8x + 14 ⇒ subtract 16 from both sides

∴ 68 = 8x ⇒ divide both sides by 8

∴ x = 8.5

- Substitute this value of x in (1) or (2) to find h

∵ h² = 400 - x²

∴ h² = 400 - (8.5)² = 327.75 ⇒ take √ for both sides

∴ h = 18.1

* Both ladder reaches 18.1 m up the building

4 0

3 years ago

A store owner had 225 suits. At the end of a sale he had sold 4/5 of them. How many suits were left?

AleksAgata [21]

The store owner sold 4/5 of the suitces. That means 1/5 of the suitcases are left. Multiple 225 to 1/5

$225* \frac{1}{5} = \frac{225}{1}* \frac{1}{5} = \frac{225*1}{1*5} = \frac{225}{5} =45$

There are 45 suitcases left

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4 years ago

Read 2 more answers

To measure the height of the cloud cover at an airport, a worker shines a spotlight upward at an angle 75° from the horizontal.

DaniilM [7]

The geometry of the problem does not seem well-described here. Assuming the spotlight beam and the observation are in the same vertical plane, there are two possibilities for the height:
.. 446 m . . . . . spotlight is aimed toward observer
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See the attachment for the geometry. Choose the answer corresponding to the geometry of the problem.

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3 years ago

Select the correct answer.

const2013 [10]

Answer:

The third one

Step-by-step explanation:

600-225 (the weight of Terrell and his equipment)

=375

375/25(weight of each box)

=15

the circle is close because it can be exactly 15 or or less.

8 0

3 years ago