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3 years ago

How do you do these questions?

Mathematics

1 answer:

Doss [256]3 years ago

4 0

Step-by-step explanation:

(a) Fₙ₋₁ > 0, so Fₙ₊₁ > Fₙ. Each term is bigger than the one before it, so the function is increasing, meaning the series will diverge to infinity.

(b) Fₙ₊₁ / Fₙ = (Fₙ + Fₙ₋₁) / Fₙ

Divide.

Fₙ₊₁ / Fₙ = 1 + (Fₙ₋₁ / Fₙ)

Rewrite the second fraction using negative exponent.

Fₙ₊₁ / Fₙ = 1 + (Fₙ / Fₙ₋₁)⁻¹

Take the limit of both sides as n approaches infinity.

lim(n→∞) Fₙ₊₁ / Fₙ = 1 + lim(n→∞) (Fₙ / Fₙ₋₁)⁻¹

Substitute with φ.

φ = 1 + φ⁻¹

Solve.

φ² = φ + 1

φ² − φ − 1 = 0

φ = [ -(-1) ± √((-1)² − 4(1)(-1)) ] / 2(1)

φ = (1 ± √5) / 2

Since the ratio can't be negative:

φ = (1 + √5) / 2

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Ten times the square of a non-zero number is equal to fifty times the number. what is the number?

lys-0071 [83]

10x^2 = 50x.....subtract 50x from both sides
10x^2 - 50x = 0...factor
10x(x - 5) = 0

10x = 0
x = 0 <== this one is eliminated because x cannot be zero

x - 5 = 0
x = 5 <== ur answer

4 0

3 years ago

Select the set of equations that would be used to solve the following absolute value equation:|x-5|=20

-BARSIC- [3]

X-5= 20
x-5= -20

Absolute value makes a negative positive, so when you are solving x-5 could have been 20 originally or -20 originally. Solve for both.

7 0

3 years ago

Read 2 more answers

The cone and the cylinder below have equal surface area. True or false.

WARRIOR [948]

Answer:

False

Step-by-step explanation:

The surface area of the cone is

$V=\pi r^2 +\pi rl$

$SA=\pi r^2 +\pi\times r\times 2r$

$SA=\pi r^2 +2\pi\times r^2$

$SA=3\pi r^2$

The surface area of the cylinder is:

$SA=2\pi r^2 +2\pi rh$

$SA=2\pi r^2 +2\pi\times r\times r$

$SA=4\pi r^2$

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3 years ago

PLEASE HELP WILL GIVE BRAINLIEST Which of the following scale factors will result in an enlargement? A. k < –1 B. –1 < k &

Sergio [31]

Answer: OPTION A.

Step-by-step explanation:

By definition, a dilation can be an enlargement or a reduction of the shape.

An enlargement is when dilation creates a larger image and a reduction is when dilation creates a smaller image.

When, the scale factor is greater than 1, the image is an enlargement and when the scale factor is between 0 and 1, the image is a reduction.

It is important to know that with a negative scale factor the enlargement will will be inverted and it will also be on the other side of the center of dilation.

Knowing this, we can say that the scale factor that will result in an enlargement is:

$k$