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2 years ago

Write an explicit formula for each sequence given below.

Mathematics

1 answer:

DerKrebs [107]2 years ago

8 0

Answer:

The first five values are 12, 14, 16, 18 and 20

The recursive formula is as follow

Step-by-step explanation:

Since we need to find the first 5 values we start with n = 1 to n = 5. Note that we don't start from n = 0 as the question states that n ≥ 1.

For the first 5 values we just replace the value of n with 1, 2, 3, 4 and 5 and calculate the answer

The first five values are 12, 14, 16, 18 and 20

A recursive formula is one that

a) Mentions the initial term

b) provides a formula connecting the previous term to the existing term.

Since we know the first term is 12, i.e and we know that the difference between consecutive terms is 2 we can conclude that the recursive formula is made up of the following two formulas

The over all formula is as follow

Step-by-step explanation:

Hope this helps:)

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COME ON ITS 1 QUESTION FOR 50 POINTS!

ale4655 [162]

Answer:

a = 3

b = 2

c = 0

d = -4

Step-by-step explanation:

Form 4 equations and solve simultaneously

28 = a(2)³ + b(2)² + c(2) + d

28 = 8a + 4b + 2c + d (1)

-5 = -a + b - c + d (2)

220 = 64a + 16b + 4c + d (3)

-20 = -8a + 4b - 2c + d (4)

(1) + (4)

28 = 8a + 4b + 2c + d

-20 = -8a + 4b - 2c + d

8 = 8b + 2d

d = 4 - 4b

Equation (2)

c = -a + b + d + 5

c = -a + b + 4 - 4b+ 5

c = -a - 3b + 9

28 = 8a + 4b + 2c + d (1)

28 = 8a + 4b + 2(-a - 3b + 9) + 4 - 4b

28 = 6a - 6b + 22

6a - 6b = 6

a - b = 1

a = b + 1

220 = 64a + 16b + 4c + d (3)

220 = 64(b + 1) + 16b + 4(-b - 1 - 3b + 9) + 4 - 4b

220 = 60b + 100

60b = 120

b = 2

a = 2 + 1

a = 3

c = -3 - 3(2) + 9

c = 0

d = 4 - 4(2)

d = -4

8 0

2 years ago

Read 2 more answers

find the root(s) of f (x) = (x + 5)3(x - 9)2(x + 1). 50 POINTS!!!!!!! -5 with multiplicity 3 5 with multiplicity 3 -9 with multi

Dmitrij [34]

Answer:

The answer to this question can be described as follows:

-5 with multiplicity 3

9 with multiplicity 2

-1 with multiplicity 1

Step-by-step explanation:

Given:

$\Rightarrow f (x) = (x + 5)^3(x - 9)^2(x + 1)$

Solve the above equation:

$\Rightarrow f (x) = (x + 5)(x + 5)(x + 5)(x - 9)(x - 9)(x + 1)\\$

The roots of the polynomial are as follows:

$\Rightarrow (x-x_1)(x-x_2)(x-x_3)......(x-x_n)\\\\\Rightarrow x_1,x_2,x_3.........x_n$

That's why the roots are:

5 with multiplicity 3

9 with multiplicity 2

-1 with multiplicity 1

8 0

2 years ago

Read 2 more answers

Find the measure of the angle formed between the base of the cone and a line segment that represents the slant height

wel

Since there are no figures given, I will give an example.

You are given a silo that is shaped as a closed cylinder with a conical end. The diameter of the silo is 4 ft, the length of the cylindrical part is 6 ft, and the entire length of the silo is 10.5 ft. Suppose that you are asked to find the total volume of grains that can be stored in the silo.

Given:

Cylinder part

D = 4 ft

H = 6 ft

Cone part

H = 10.5 – 6 = 4.5ft

D = 4ft

Required:

Volume of silo

Solution:
V of cylinder = πr²H

V of cylinder = π(4/2)²(6)

V of cylinder = 75.4 ft³

V of cone = πr²H/3

V of cone = π(4/2)²(4.5/3)

V of cone = 18.85 ft³

Total volume = 94.25 ft³

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3 years ago

Solve for x. Each figure is a trapezoid. # 18 has a midsegment. 13)

Vanyuwa [196]

Question 13

${12x+2}=\frac{18+34}{2}\\\\12x+2=26\\\\12x=24\\\\x=\boxed{2}$

Question 14

Base angles of an isosceles trapezoid are congruent, so:

$73x+1=74\\73x=73\\x=\boxed{1}$

3 0

1 year ago

Toby the Tiger makes $25 an hour selling cereal. Write an equation to

gavmur [86]

Answer:

I think it is y=25x

Step-by-step explanation:

Since Tony the Tiger makes $25 an hour, in 2 hours, he would make $50. Both of them, when divided, equal 25, the constant of proportionality.

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2 years ago