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2 years ago

Which recursive formula can be used to generate the sequence below, where f(1) = 6 and n ≥ 1?

Mathematics

2 answers:

Liono4ka [1.6K]2 years ago

8 0

Answer:

optian 2

Step-by-step explanation:

Trava [24]2 years ago

4 0

f (n + 1) = f(n) – 5 is the recursive formula can be used to generate the sequence below, where f(1) = 6 and n ≥ 1

<h3>Solution:</h3>

Given that,

f(1) = 6 and n ≥ 1

Given sequence is 6, 1, -4, -9, -14

Let us first analyse the logic used in this sequence

6 - 5 = 1

1 - 5 = -4

-4 - 5 = -9

-9 - 5 = -14

Thus the next terms in sequence are obtained by subtracting 5 from previous term

Thus a recursive formula can be formed as:

f (n + 1) = f(n) – 5

Where "n" is the nth term

Let us check our recursive formula:

f(1+ 1) = f(1) - 5

f(2) = f(1) - 5

f(2) = 6 - 5 = 1

Thus we have got f(2) = 1 which is correct as per given sequence

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In the figure, the ratio of the perimeter of rectangle ABDE to the perimeter of triangle BCD is . The area of polygon ABCDE is s

Gekata [30.6K]

Step 1

Find the perimeter of rectangle ABDE

we know that

the perimeter of rectangle is equal to

$P=2b+2h$

In this problem

$b=ED=2\ units$

$h=AE=6\ units$

substitute

$P=2*2+2*6=16\ units$

Step 2

Find the perimeter of triangle BCD

we know that

the perimeter of triangle is equal to

$P=BD+DC+BC$

In this problem we have

$BD=AE=6\ units$

$DC=BC$

Applying the Pythagoras theorem

$DC^{2}=4^{2}+3^{2}$

$DC^{2}=25$

$DC=5\ units$

substitute

$P=6+5+5=16\ units$

Find the ratio of the perimeter of rectangle ABDE to the perimeter of triangle BCD

we have

the perimeter of rectangle is equal to

$P=16\ units$

the perimeter of the triangle is

$P=16\ units$

the ratio is equal to

$\frac{16}{16} =1$

therefore

the answer Part 1) is the option B

$1$

Step 3

Find the area of polygon ABCDE

we know that

The area of polygon is equal to the sum of the area of rectangle plus the area of triangle

Area of rectangle is equal to

$A=AE*BD=6*2=12\ units^{2}$

Area of the triangle is equal to

$A=\frac{1}{2}AEh$

the height h of the triangle is equal to $4\ units$

substitute

$A=\frac{1}{2}(6)(4)=12\ units^{2}$

The area of polygon is

$12\ units^{2}+12\ units^{2}=24\ units^{2}$

therefore

the answer part 2) is the option C

$24\ units^{2}$

7 0

2 years ago

Read 2 more answers

If cos Θ = square root 2 over 2 and 3 pi over 2 < Θ < 2π, what are the values of sin Θ and tan Θ?

KIM [24]

Answer:

The answer is

$sin(\theta)=-\frac{\sqrt{2}}{2}$

$tan(\theta)=-1$

Step-by-step explanation:

we know that

$tan(\theta)=\frac{sin(\theta)}{cos(\theta)}$

$sin^{2}(\theta)+cos^{2}(\theta)=1$

In this problem we have

$cos(\theta)=\frac{\sqrt{2}}{2}$

$\frac{3\pi}{2}$

The angle $\theta$ belong to the third or fourth quadrant

The value of $sin(\theta)$ is negative

Step 1

Find the value of $sin(\theta)$

Remember

$sin^{2}(\theta)+cos^{2}(\theta)=1$

we have

$cos(\theta)=\frac{\sqrt{2}}{2}$

substitute

$sin^{2}(\theta)+(\frac{\sqrt{2}}{2})^{2}=1$

$sin^{2}(\theta)=1-\frac{1}{2}$

$sin^{2}(\theta)=\frac{1}{2}$

$sin(\theta)=-\frac{\sqrt{2}}{2}$ ------> remember that the value is negative

Step 2

Find the value of $tan(\theta)$

$tan(\theta)=\frac{sin(\theta)}{cos(\theta)}$

we have

$sin(\theta)=-\frac{\sqrt{2}}{2}$

$cos(\theta)=\frac{\sqrt{2}}{2}$

substitute

$tan(\theta)=\frac{-\frac{\sqrt{2}}{2}}{\frac{\sqrt{2}}{2}}$

$tan(\theta)=-1$

8 0

2 years ago

Read 2 more answers

A metal disc of 12cm in diameter and 5cm thick is melted down and cast into a cylindrical bar of diameter 5cm .How long is the b

Trava [24]

Answer:

d bar

Step-by-step explanation:

3 0

2 years ago

A social media platform states that a social media post from a marketing agency has 7 hashtags, on average. A digital marketing

dimaraw [331]

Answer:

a. The average number of hashtags used in a social media post from a marketing agency is different than 7 hashtags.

Step-by-step explanation:

A social media platform states that a social media post from a marketing agency has 7 hashtags, on average.

This means that at the null hypothesis, we test if the mean is 7, that is:

$H_0: \mu = 7$

A digital marketing specialist studying social media advertising believes the average number of hashtags used in a post from a marketing agency is different than the number stated by the social media platform.

Keyword is different, so at the null hypothesis, we test if the mean is different of 7, that is:

$H_1: \mu \neq 7$

Thus, the correct answer is given by option a.

4 0

2 years ago

Given the polynomial 21x 4 + 3y - 6x 2 + 34

padilas [110]

The given polynomial is 21x⁴ + 3y - 6x² + 34

We want to subtract a polynomial, f(x) so that
21x⁴ + 3y - 6x² + 34 - f(x) = 29x² - 7

Therefore
-f(x) = 29x² - 7 - (21x⁴ + 3y - 6x² + 34)
= -21x⁴ + 35x² - 3y - 41

Answer: 21x⁴ - 35x² + 3y + 41

5 0

2 years ago