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3 years ago

Find the sum of the infinite series 1/3+4/9+16/27+64/81+.... if it exists.

1 answer:

6 0

9/27, 12/27, 16/27

So this is a geometric sequence as each term is 4/3 the previous term.

Since the common ration is greater than one the sum of the series diverges, it does not exist. (The sum just keeps getting larger and larger)

For a geometric series to have a sum r^2<1

So that the normal sum....

s(n)=a(1-r^n)/(1-r) becomes if r^2<1

s=a/(1-r)

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What is the slope of the linear relationship shown in this table of values?

KATRIN_1 [288]

Answer:

Step-by-step explanation:

To find the slope m use any 2 ordered pairs from the table.

Calculate m using the slope formula

m = $\frac{y_{2}-y_{1} }{x_{2}-x_{1} }$

with (x₁, y₁ ) = (- 4, 11) and (x₂, y₂ ) = (2, - 1)

m = $\frac{-1-11}{2+4}$ = $\frac{-12}{6}$ = - 2 → B

4 0

3 years ago

Read 2 more answers

Mr. Sawyer drove his car from his home to New York at the rate of 45 mph and returned over the same road at the rate of 40 mph.

AveGali [126]

Answer: Time taken by him in going = 8 hours

Time taken by him in returning = 9 hours

Step-by-step explanation:

Let the total distance from home to New York is x miles,

$\text{ Since, Time} = \frac{\text{Distance}}{\text{Speed}}$

Also, he drove his car from his home to New York at the rate of 45 mph,

⇒ $\text{ Time taken by him in going } = \frac{x}{45}\text{ hours}$

And, returned over the same road at the rate of 40 mph.

⇒ $\text{ Time taken by him in returning } = \frac{x}{40}\text{ hours}$

According to the question,

Time taken by him in returning - Time taken by him in going = 30 minutes = 1/2 hours, ( 1 hours = 60 minutes )

⇒ $\frac{x}{40}-\frac{x}{45}=\frac{1}{2}$

⇒ $\frac{9x}{360}-\frac{8x}{360}=\frac{1}{2}$

⇒ $\frac{x}{360} = \farc{1}{2}$

⇒ $2x=720$

⇒ $x=360\text{ miles}$

Hence, the total distance from home to New York = x miles = 360 miles

⇒ $\text{ Time taken by him in going } = \frac{x}{45}\text{ hours}$

$=\frac{360}{45}=8\text{ hours}$

⇒ $\text{ Time taken by him in returning } = \frac{x}{40}\text{ hours}$

$=\frac{360}{40}=9\text{ hours}$

3 0

3 years ago

Classify the following polynomials according to the number of terms. Combine any like terms first.

11Alexandr11 [23.1K]

1) Combining like terms, we get x^2 + 5x, which is a binomial.

2) Combining like terms, we get x^3 + 3x^2, which is a binomial.

3) Combining like terms, we get 4x^3 + x^2 - x, which is a trinomial.

4) I can't answer this because there's an asterisk in place of the exponent.

3 0

2 years ago

Consider the graph of the quadratic function y = 3x2 – 3x – 6. What are the solutions of the quadratic equation 0 = 3x2 − 3x − 6

Ilya [14]

Roots of the equation 3x² -3x-6=0 are -1 and 2,
all choices are given wrong
3*2²-3*2-6=0
12-6-6=0
0=0, which is true , so root is 2

3*20²-3*20-6=0
600-60-6=0
534=0 which is wrong, so root is 2, but not 20

4 0

3 years ago

Help!! I don't know what to do with the square root

Karo-lina-s [1.5K]

Answer:

$\sqrt{10}$

Step-by-step explanation:

$g(4) = \sqrt{(4)^2 - (4) - 2} \\\\g(4) = \sqrt{16 - 4 - 2} \\\\g(4) = \sqrt{16 - 6} \\\\g(4) = \sqrt{10}$

You can't simplify this anymore

Hope this helps! : )

7 0

2 years ago