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3 years ago

Find the sum of the first 6 terms in the sequence -5 -25 -125 -625

1 answer:

5 0

This is a geometric sequence, so use the formula for the sum of a geometric sequence:
Sum = (a(r^n - 1))/(r - 1)
where a is the first term, -5
r is the common ratio, 5
and n is the number of terms

Thus,
Sum = ((-5)(5^6 - 1))/(5-1) = -19530

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Please answer correctly !!!!!! Will mark brainliest !!!!!!!!!!

AfilCa [17]

Answer:

Sakura spoke for 2 minutes in Hungarian and for 3 minutes in Polish

Step-by-step explanation:

So make the variables.

Hungarian = x

Polish = y

x and y are the amount of time she spent in minutes.

x + y = 5

150x + 270 = 190y

x = 5 - y

750 - 150y + 270 = 190y

1020 = 340y

y = 3

x = 2

4 0

3 years ago

Use Newton’s Method to find the solution to x^3+1=2x+3 use x_1=2 and find x_4 accurate to six decimal places. Hint use x^3-2x-2=

luda_lava [24]

Let $f(x) = x^3 - 2x - 2$ . Then differentiating, we get

$f'(x) = 3x^2 - 2$

We approximate $f(x)$ at $x_1=2$ with the tangent line,

$f(x) \approx f(x_1) + f'(x_1) (x - x_1) = 10x - 18$

The $x$ -intercept for this approximation will be our next approximation for the root,

$10x - 18 = 0 \implies x_2 = \dfrac95$

Repeat this process. Approximate $f(x)$ at $x_2 = \frac95$ .

$f(x) \approx f(x_2) + f'(x_2) (x-x_2) = \dfrac{193}{25}x - \dfrac{1708}{125}$

Then

$\dfrac{193}{25}x - \dfrac{1708}{125} = 0 \implies x_3 = \dfrac{1708}{965}$

Once more. Approximate $f(x)$ at $x_3$ .

$f(x) \approx f(x_3) + f'(x_3) (x - x_3) = \dfrac{6,889,342}{931,225}x - \dfrac{11,762,638,074}{898,632,125}$

Then

$\dfrac{6,889,342}{931,225}x - \dfrac{11,762,638,074}{898,632,125} = 0 \\\\ \implies x_4 = \dfrac{5,881,319,037}{3,324,107,515} \approx 1.769292663 \approx \boxed{1.769293}$

Compare this to the actual root of $f(x)$ , which is approximately <u>1.76929</u>2354, matching up to the first 5 digits after the decimal place.

4 0

2 years ago

Which of the binomials below is a factor of this trinomial?

8_murik_8 [283]

Answer:

C. x - 4

Step-by-step explanation:

The best way to do this is to first take out GCF

6(x² - x - 12)

Then we factor

6(x - 4)(x + 3)

We can now see our answer.

8 0

3 years ago

Read 2 more answers

a fair (6 sided) die is rolled TWO times. What is the probability that the first die is a 2 or the second die is a prime

alexdok [17]

Answer:

The probability that the first die is a 2 or the second die is a prime = 1/12

Step-by-step explanation:

It is given that,a fair (6 sided) die is rolled TWO times.

The sample space for rolling 2 dies

(1, 1), (1, 2) .......... (1,6)

(2,1) ..........................

(6, 1) ..........................(6, 6)

There are total of 6^2 = 36 sample space

<u>To find the probability</u>

The prime numbers from 1 to 6 are 2, 3 and 5

the possible outcomes are(2,1), (2, 3) and (2, 5)

The probability that the first die is a 2 or the second die is a prime = 3/36 = 1/12

4 0

2 years ago

The area of a circle is 100 square miles. What is the diameter?

adell [148]

Answer:

The diameter of a circle with an area of 100 square miles is 20/√π miles.

Step-by-step explanation:

Area =100 = πr^2.

diameter = d = 2r.

100 = πr^2.

100/π = r^2.

√(100/π) = r.

10/√π = r.

d = 2r.

d = 2 * 10/√π.

d = 20/√π

5 0

2 years ago