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Nastasia [14]
2 years ago
6

Ricky is at the bakery shop when he sees that 8 pastries cost $160. He need 16 pastries. How much will 16 pastries cost?

Mathematics
2 answers:
aivan3 [116]2 years ago
6 0
They would each cost $320
kumpel [21]2 years ago
5 0
1) When you're finding ratios, the best thing to do is to add the parts together to find what one part is.
2+4= 6. Then divide this by the total- 18/6=3.
Therefore, the ratio of red to brown chairs is 2*3:4*3
Therefore, the amount of red chairs is 12.

2) The best thing to do i to find out how long it takes him to read one book them multiply this by 15.
To do this, simply divide the amount of time by the amount of books that he has read.
30/10= 3
Therefore, Rock can read a book in three minutes. As he is reading 15, you multiply these together.
3*15= 45
Therefore, it will take Rock 45 minutes to read 15 books.

3) The best thing to do is to find out what one pastry costs, and you can do this by dividing the cost by the amount of pastries.
160/8= 20.
Therefore, one pastry costs $20.
As you want to find the cost of 16 pastries, you simply times these together.
20*16= 320
Therefore, 16 pastries cost $320.

Hope this helps :)
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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 <em>C</em> has a positive orientation in both cases

(a) It looks like the region has the curves <em>y</em> = <em>x</em> and <em>y</em> = <em>x</em> ² as its boundary***, so that the interior of <em>C</em> is the set <em>D</em> 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 <em>C</em> into two component curves,

<em>C₁ </em>: <em>x</em> = <em>t</em> and <em>y</em> = <em>t</em> ² with 0 ≤ <em>t</em> ≤ 1

<em>C₂</em> : <em>x</em> = 1 - <em>t</em> and <em>y</em> = 1 - <em>t</em> with 0 ≤ <em>t</em> ≤ 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) <em>C</em> 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 <em>C</em> into 3 components,

<em>C₁</em> : <em>x</em> = <em>t</em> and <em>y</em> = 0 with 0 ≤ <em>t</em> ≤ 1

<em>C₂</em> : <em>x</em> = 1 - <em>t</em> and <em>y</em> = <em>t</em> with 0 ≤ <em>t</em> ≤ 1

<em>C₃</em> : <em>x</em> = 0 and <em>y</em> = 1 - <em>t</em> with 0 ≤ <em>t</em> ≤ 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
Find mFE<br> A) 52°<br> C) 76°<br> B) 93°<br> D) 112°
mixer [17]

Answer:

76 degrees

Step-by-step explanation:

GE = 180 since it is a straight line

GE = GR + FE

180 = 7x+6 +6x-8

Combine like terms

180 = 13x-2

Add 2 to each side

182 = 13x

Divide by 13

182/13 = 13x/13

14 =x

We want FE

FE = 6x-8

FE = 6(14) -8

    =84 -8

    =76

3 0
2 years ago
PLEASE ANSWER QUICK
makvit [3.9K]
For the first equation, I put it in y=mx+b form, so y=-3x-9
the second one is x=4
hope i helped 
3 0
3 years ago
Rana's computer repair service charges $45/h. Bill's computer repair service charges a flat fee of $25 plus $18/h. Each company
Dmitry [639]

Answer

I not sure but what i would say is b. or if not c.

Step-by-step explanation:

8 0
3 years ago
The segments shown below could form a triangle. True B. False​
Vesna [10]
True

It won’t be a Prefect Triangle but it still is one
(sorry my drawing is bad)

3 0
2 years ago
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