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3 years ago

B(n)=1 (-2)^n-1 What is the 4th term in the sequence

Mathematics

1 answer:

zzz [600]3 years ago

5 0

Answer:

The fourth term of the sequence B(4) =-8

The sequence is 1,-2,4,-8...

Step-by-step explanation:

Explanation:-

Given that the sequence

B(n) = 1(-2)ⁿ⁻¹

Put n=1

B(1) = 1(-2)¹⁻¹ = 2⁰ =1

Put n=2

B(2) = 1(-2)²⁻¹ = (-2)¹ =-2

Put n=3

B(3) =1(-2)³⁻¹ = (-2)² =4

Put n=4

B(4) = 1(-2)⁴⁻¹ =(-2)³ =-8

The sequence

1,-2,4,-8...

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Delvig [45]

Part 1: Circumference of circle = $105.20$ inches & Area of circle = $880.97 inches^{2}$

Part 2: Area of circle = $3.14 ft^{2}$

Part 3: Area of square not covered by circle = $29.69inches^{2}$ .

Step-by-step explanation:

Part 1:

We have radius of circle as $16\frac{3}{4} = 16.75 inches$ . Let's find area & circumference of circle:

Circumference of circle = $2\pi r$

⇒ Circumference of circle = $2\pi r$

⇒ Circumference of circle = $2\pi r$ = $2(3.14)(16.75)$

⇒ Circumference of circle = $105.20$ inches

Area of circle = $\pi r^{2}$

⇒ Area of circle= $\pi r^{2}$

⇒Area of circle = $\pi r^{2}$ = $(3.14)(16.75)^{2}$

⇒ Area of circle = $880.97 inches^{2}$

Part 2:

Circumference of circle = $2\pi r$ = $6.28ft$

⇒ $2\pi r = 6.28$

⇒ $r = \frac{6.28}{2\pi } = \frac{6.28}{2(3.14)} = 1 ft$

Area of circle = $\pi r^{2}$

⇒Area of circle = $\pi r^{2}$ = $(3.14)(1)^{2}$

⇒ Area of circle = $3.14 ft^{2}$

Part 3:

Perimeter of square = $4a$ , a is side of square.

⇒ $4a = 47$

⇒ $a = \frac{47}{4}$

⇒ a = $11.75 inch$

Since radius of circle inscribed in square is half of side of square i.e.

$radius = \frac{a}{2}\\ radius = r = \frac{11.75}{2}$

$r = 5.875inch$

Now, Area of square not covered by circle = Area of square - area of circle

⇒ $a^{2} - \pi r^{2}$

⇒ $11.75^{2} - 3.14(5.875)^{2}$

⇒ $29.69inches^{2}$

∴ Area of square not covered by circle = $29.69inches^{2}$ .

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3 years ago

Why is -1 3/10 as an improper fraction -13/10? Wouldn’t it be -7/10 because -1 * 10 + 3 is -7/10?

kobusy [5.1K]

Answer:

-13/10

Step-by-step explanation:

It wont be -7/10 because to change a mixed number to an improper fraction, we multiply the whole number by the denominator and then add this product with the numerator.

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2 years ago

A person's resting heart rate is typically between 60 and 100 beats per minute.Noah looks at his watch,and counts 8 heartbeats i

fgiga [73]

He has a heart rate of 48 which is not typical.
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3 years ago

If f(x) = 3x+2 and g(x) = x^2 what is g( f(x))

irakobra [83]

Answer:

$9x^{2}+12x+4$

Step-by-step explanation:

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4 years ago

Find the length of YXZ. A.s=3 B.s=60 C.s=75 D.s=236

Damm [24]

R = 15

The circumference of circle: $C=2\pi r$

subtitute: $C=2\pi\cdot15=30\pi$

$1\ rad=\dfrac{180^o}{\pi}\to5\ rad=5\cdot\dfrac{180^o}{\pi}=\dfrac{900^o}{\pi}$

$\dfrac{5\ rad}{360^o}=\dfrac{\frac{900^o}{\pi}}{360^o}=\dfrac{900^o}{\pi}\cdot\dfrac{1}{360^o}=\dfrac{5}{2\pi}$

$s=\dfrac{5}{2\pi}C\to s=\dfrac{5}{2\pi}\cdot30\pi=75$

Answer: C. s = 75

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3 years ago