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3 years ago

10

Find the sum of the first 6 terms of 3 - 6 + 12 + …

1 answer:

Natalka [10]3 years ago

6 0

Answer:

$S_6 = -63$

Step-by-step explanation:

The sequence above is a geometric sequence.

The common ratio (r) = $\frac{-6}{3} = \frac{12}{-6} = -2$

The common ratio < 1, therefore, the formula for the sum of nth terms of the sequence would be: $S_n = \frac{a_1(1 - r^n)}{1 - r}$

a1 = 3

r = -2

n = 6

Plug in the values into the formula

$S_6 = \frac{3(1 - (-2^6)}{1 - (-2)}$

$S_6 = \frac{3(1 - (64)}{1 + 2}$

$S_6 = \frac{3(-63)}{3}$

$S_6 = -63$

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Vladimir [108]

Answer:

$35$

Step-by-step explanation:

One is given the following function ( $y=3x+5$ ). The given problem asks one to find the output of the function when the input is (10). Keep in mind, a general rule for dealing with functions is that, when present, the variable (x) represents the input. Whereas the variable (y) represents the output. Thus, if one were to substitute (10) in place of (x), and simplify: the result one would get is the output. Apply this idea to the given scenario:

$y=3x+5$

$y=3(10)+5$

$y=30+5$

$y=35$

4 0

3 years ago

The distance between Dania and Hollywood is shown on the map. What is the actual distance between Dania and Hollywood?

pishuonlain [190]

Answer:

15 miles

Step-by-step explanation:

If there are 2.5 inches and 1 inch is 6 miles, then just multiply 6 by 2.5 to get 15

6*2.5=15

8 0

3 years ago

First make a substitution and then use integration by parts to evaluate the integral. (Use C for the constant of integration.) x

e-lub [12.9K]

Answer:

$(\frac{x^{2}-25}{2})ln(5+x)-\frac{x^{2}}{4}+\frac{5x}{2}+C$

Step-by-step explanation:

Ok, so we start by setting the integral up. The integral we need to solve is:

$\int x ln(5+x)dx$

so according to the instructions of the problem, we need to start by using some substitution. The substitution will be done as follows:

U=5+x

du=dx

x=U-5

so when substituting the integral will look like this:

$\int (U-5) ln(U)dU$

now we can go ahead and integrate by parts, remember the integration by parts formula looks like this:

$\int (pq')=pq-\int qp'$

so we must define p, q, p' and q':

p=ln U

$p'=\frac{1}{U}dU$

$q=\frac{U^{2}}{2}-5U$

q'=U-5

and now we plug these into the formula:

$\int (U-5)lnUdU=(\frac{U^{2}}{2}-5U)lnU-\int \frac{\frac{U^{2}}{2}-5U}{U}dU$

Which simplifies to:

$\int (U-5)lnUdU=(\frac{U^{2}}{2}-5U)lnU-\int (\frac{U}{2}-5)dU$

Which solves to:

$\int (U-5)lnUdU=(\frac{U^{2}}{2}-5U)lnU-\frac{U^{2}}{4}+5U+C$

so we can substitute U back, so we get:

$\int xln(x+5)dU=(\frac{(x+5)^{2}}{2}-5(x+5))ln(x+5)-\frac{(x+5)^{2}}{4}+5(x+5)+C$

and now we can simplify:

$\int xln(x+5)dU=(\frac{x^{2}}{2}+5x+\frac{25}{2}-25-5x)ln(5+x)-\frac{x^{2}+10x+25}{4}+25+5x+C$

$\int xln(x+5)dU=(\frac{x^{2}-25}{2})ln(5+x)-\frac{x^{2}}{4}-\frac{5x}{2}-\frac{25}{4}+25+5x+C$

$\int xln(x+5)dU=(\frac{x^{2}-25}{2})ln(5+x)-\frac{x^{2}}{4}+\frac{5x}{2}+C$

notice how all the constants were combined into one big constant C.

7 0

3 years ago

I NEED HELP! I WILL MARK BRANLIEST! I need help with 11 & 12

antiseptic1488 [7]

Answer:

The answer is 17 and no

Step-by-step explanation:

#11 The room is a cube so...

cube root the volume 4913

³√4913=17

The length of the room is 17 feet.

#12

Square root 121

√121=11

Since the car is 13 feet the car will not fit in the garage which is 11ft.

6 0

3 years ago

Please help fast HELP

Sveta_85 [38]

Answer:

The letters are really small I can't see it.

Step-by-step explanation:

Sorry

5 0

3 years ago