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3 years ago

Find an explicit formula for g(n)

Mathematics

1 answer:

Elina [12.6K]3 years ago

6 0

Answer:

g(n) = 2n + 49

Step-by-step explanation:

The explicit formula for an arithmetic sequence is

g(n) = a₁ + (n - 1)d

where a₁ is the first term and d the common difference

Given the recursive formula

g(n) = g(n - 1) + 2 ← with d = 2 and a₁ = 51, then

g(n) = 51 + 2(n - 1) = 51 + 2n - 2 = 2n + 49 ← explicit formula

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An angle measures 18.6° less than the measure of its complementary angle. What is the measure of each angle?

weeeeeb [17]

Answer:

X = 35.7 Y=54.3

Step-by-step explanation:

Let the 2 angles be called X and Y were X is the smaller angle

we know that both angles are complementary therefore
X+Y=90

X = Y - 18.6 ( Given )

Y - 18.6 + Y = 90 ( substitution)

2Y = 90 + 18.6

Y = 108.6/2

Y=54.3

X= Y-18.6= 54.3-18.6 = 35.7

Check : X + Y = 35.7+54.3=90

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2 years ago

Long Division: (3x^4-8x^3-x^2+9x+5) / (x-2) pleaseee answer this

Drupady [299]

3x⁴ = 3x³ • x, and

3x³ (x - 2) = 3x⁴ - 6x³

Subtract this from the numerator to get a remainder of

(3x⁴ - 8x³ - x² + 9x + 5) - (3x⁴ - 6x³) = -2x³ - x² + 9x + 5

-2x³ = -2x² • x, and

-2x² (x - 2) = -2x³ + 4x²

Subtract this from the previous remainder to get a new remainder of

(-2x³ - x² + 9x + 5) - (-2x³ + 4x²) = -5x² + 9x + 5

-5x² = -5x • x, and

-5x (x - 2) = -5x² + 10x

Subtract this from the last remainder to get a new one of

(-5x² + 9x + 5) - (-5x² + 10x) = -x + 5

-x = -1 • x, and

-1 (x - 2) = -x + 2

This gives a new remainder of

(-x + 5) - (-x + 2) = 3

3 does not divide x, so we're done.

So, we have

(3x⁴ - 8x³ - x² + 9x + 5) / (x - 2) = 3x³ - 2x² - 5x - 1 + 3/(x - 2)

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3 years ago

A local citizen wants to fence a rectangular community gardenn. The length of the garden should be at least 110ft,and the distan

Arte-miy333 [17]

The question is incorrect
the correct question is
A local citizen wants to fence a rectangular community garden. The length of the garden should be at least 110 ft,and the distance around should be no more than 380 ft. Write a system of inequality that model the possible dimensions of he garden. Graph the system to show all possible solutions

let
x---------------> the length of the garden
y---------------> the wide of the garden

we know that
x>=110
2x+2y <=380---------------> x+y <= 190

Part A) Write a system of inequality that model the possible dimensions of he garden

the answer part A) is
x>=110
x+y <= 190

Part B) Graph the system to show all possible solutions

using a graph tool
see the attached figure
the solution is the triangle show in the figure

the possible solutions of y (wide) would be between 0 and 80 ft
the possible solutions of x (length) would be between 110 ft and 190 ft

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3 years ago

Hacksaw’s Boats of St. Lucia takes tourists on a daily whale/dolphinwatch cruise. Their brochure claims an 80% chance of siting

Fittoniya [83]

Answer:

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Step-by-step explanation:

Consider the provided information.

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The provided claims can be written as: 80% or 0.80

Let say first day you see a dolphin or a whale and same happen on the next day.

Thus, the probability is:

0.80 × 0.80 = 0.64

Probability of see them on both days is 0.64

Hence, the probability you see a dolphin or a whale on both days is 0.64

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3 years ago

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KonstantinChe [14]

Answer:

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Step-by-step explanation:

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2 years ago