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3 years ago

Question 13 (Essay Worth 8 points)

Mathematics

1 answer:

mixer [17]3 years ago

3 0

9514 1404 393

Answer:

geometric sequence

Step-by-step explanation:

The terms of the sequence have a common ratio of -12/3 = -4, so the sequence is geometric. The general term is ...

an = 3(-4)^(n-1)

so the sum can be written as ...

$\displaystyle\sum_{n=0}^\infty3(-4)^n$

(Note the summation starts at n=0, corresponding to a first term of 3.)

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Explain 12 divided by 15

Keith_Richards [23]

You do --12/15---you see that this can be simplified by the same factor 3-- si you divide by 3 on both numbers thus you get---4/5 as the answer

4 0

3 years ago

Can some help me with this .

PtichkaEL [24]

Answer:

1. 169π ft²

2. 144π in²

3) 25π yd²

Step-by-step explanation:

1) π * 13²

π * 169

units = ft²

169π ft²

2) π * 12²

π * 144

units = in²

144π in²

3)π * 5²

π * 25

units = yd²

25π yd²

If my answer is incorrect, pls correct me!

If you like my answer and explanation, mark me as brainliest!

-Chetan K

7 0

3 years ago

37. Verify Green's theorem in the plane for f (3x2- 8y2) dx + (4y - 6xy) dy, where C is the boundary of the

Nastasia [14]

I'll only look at (37) here, since

• (38) was addressed in 24438105

• (39) was addressed in 24434477

• (40) and (41) were both addressed in 24434541

In both parts, we're considering the line integral

$\displaystyle \int_C (3x^2-8y^2)\,\mathrm dx + (4y-6xy)\,\mathrm dy$

and I assume C has a positive orientation in both cases

(a) It looks like the region has the curves y = x and y = x ² as its boundary***, so that the interior of C is the set D given by

$D = \left\{(x,y) \mid 0\le x\le1 \text{ and }x^2\le y\le x\right\}$

• Compute the line integral directly by splitting up C into two component curves,

C₁ : x = t and y = t ² with 0 ≤ t ≤ 1

C₂ : x = 1 - t and y = 1 - t with 0 ≤ t ≤ 1

Then

$\displaystyle \int_C = \int_{C_1} + \int_{C_2} \\\\ = \int_0^1 \left((3t^2-8t^4)+(4t^2-6t^3)(2t))\right)\,\mathrm dt \\+ \int_0^1 \left((-5(1-t)^2)(-1)+(4(1-t)-6(1-t)^2)(-1)\right)\,\mathrm dt \\\\ = \int_0^1 (7-18t+14t^2+8t^3-20t^4)\,\mathrm dt = \boxed{\frac23}$

*** Obviously this interpretation is incorrect if the solution is supposed to be 3/2, so make the appropriate adjustment when you work this out for yourself.

• Compute the same integral using Green's theorem:

$\displaystyle \int_C (3x^2-8y^2)\,\mathrm dx + (4y-6xy)\,\mathrm dy = \iint_D \frac{\partial(4y-6xy)}{\partial x} - \frac{\partial(3x^2-8y^2)}{\partial y}\,\mathrm dx\,\mathrm dy \\\\ = \int_0^1\int_{x^2}^x 10y\,\mathrm dy\,\mathrm dx = \boxed{\frac23}$

(b) C is the boundary of the region

$D = \left\{(x,y) \mid 0\le x\le 1\text{ and }0\le y\le1-x\right\}$

• Compute the line integral directly, splitting up C into 3 components,

C₁ : x = t and y = 0 with 0 ≤ t ≤ 1

C₂ : x = 1 - t and y = t with 0 ≤ t ≤ 1

C₃ : x = 0 and y = 1 - t with 0 ≤ t ≤ 1

Then

$\displaystyle \int_C = \int_{C_1} + \int_{C_2} + \int_{C_3} \\\\ = \int_0^1 3t^2\,\mathrm dt + \int_0^1 (11t^2+4t-3)\,\mathrm dt + \int_0^1(4t-4)\,\mathrm dt \\\\ = \int_0^1 (14t^2+8t-7)\,\mathrm dt = \boxed{\frac53}$

• Using Green's theorem:

$\displaystyle \int_C (3x^2-8y^2)\,\mathrm dx + (4y-6xy)\,\mathrm dx = \int_0^1\int_0^{1-x}10y\,\mathrm dy\,\mathrm dx = \boxed{\frac53}$

4 0

3 years ago

Ashley puts 45 stamps in an album. She puts the same number of stamps on each page,and 3 stamps on the last page. There are 2 mo

ludmilkaskok [199]

45 pages total
3 on last page
45-3=42
there are 42 on the rest of the pages
on each page, there are 2 more pages in album than then stamps on pages

amount of stamps on pages with equal number of stamps is
A=numberofpgest times number of stamps on pages
number of pages=p
number of stamps per papge=s
a=ps

2 more pages than stamps on pages
p=2+s
total number of stamps per page is s=(45-3)/(p-1)
(what I did is I first got rid of number of stamps on last page, then got rid of the last page)
P=2+s
s=(45-3)/(2+s-1)
s=42/(s+1)
times s+1 both sides
s^2+s=42
minus 42
s^2+s-42=0
factor
(s-6)(s+7)=0
set equal to zero
s-6=0
s=6

s+7=0
s=-7, false, no negative stamps

6 stamps per page

sub
p=2+s
p=2+6
p=8
8 pages

check
last page is 3 so 8-1=7 page left

7*6=42
3+42=45

correct

there are
8 pages in the album
6 stamps per page

6 0

3 years ago

Solve the quadratic equation by factoring. check your solutions in the original equation. (enter your answers as a comma-separat

Scrat [10]

2x²-19x-33=0
(2x-22 )(2x.+3 ) = 0
(x-11)(2x+3)=0
x-11=0 implies x = 11
2x+3=0 implies x = -3/2

3 0

3 years ago