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3 years ago

Can someone please help me?

Mathematics

1 answer:

Lisa [10]3 years ago

7 0

Answer:

Step-by-step explanation:

Using a graphing calculator, the graph shows an almost parabola like shape between 0 and 12

Plus if the width was equal or greater than twelve we would have a 0 or even negative volume which is impossible

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A city has a population of 240,000 people. Suppose that each year the population grows by 7.75%. What will the population be aft

emmasim [6.3K]

Answer:

$\large\boxed{\sf \ \ \ 404,699 \ \ \ }$

Step-by-step explanation:

Hello,

At the beginning the population is 240,000

After 1 year the population will be

240,000*(1+7.75%)=240,000*1.0775

After n years the population will be

$240,000\cdot1.0775^n$

So after 7 years the population will be

$240,000\cdot1.0775^7=404699.058...$

So rounded to the nearest whole number gives 404,699

Hope this helps

7 0

4 years ago

After dans holiday. Dan has 50 new email messages in his inbox . 13 of them are attachements. what proportion of the email messa

dimulka [17.4K]

Answer:

26%

Step-by-step explanation:

Given that Dan has 59 new email messages and 13 have attachment then the proportion that have attachments may be expressed as a ratio of the number with attachments to the total number of emails.

Hence proportion of the email messages have attachments as a percentage

= 13/50 * 100%

= 26%

This means that 26% of the emails received have attachments

6 0

3 years ago

For the triangle shown below, complete the following table.

dem82 [27]

Answer:

Step-by-step explanation:

In the given triangle

With reference angle A

perpendicular (P) = 3

hypotenuse (h) = 5

So sin A = p/h = 3/5

and

With reference angle C

perpendicular (p)= 4

hypotenuse (h) = 5

Sin C = p/h = 4/5

hope it helps :)

3 0

3 years ago

Alex has $20 and Ellen has $12 Alex saving three dollars per day and Ellen is saving five dollars per day after how many days wi

FinnZ [79.3K]

3x+20=5x+12
-3x -3x
20= 2x +12
-12 -12
8=2x
Divide both sides by two
4=x
It will take four days (this is how to solve algebraically)

3 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