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-Dominant- [34]

3 years ago

7

To make a 30-pound mixture of two candies to sell for $2 per pound. How many pounds of each candy should be used If red licorice

bits sell for $1.90 per pound and lemon drops sell for $2.20 per pound,

1 answer:

ivann1987 [24]3 years ago

8 0

20 pounds red licorice and 10 pounds lemon drops.

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Use green's theorem to compute the area inside the ellipse x252+y2172=1. use the fact that the area can be written as ∬ddxdy=12∫

Pavel [41]

The area of the ellipse $E$ is given by

$\displaystyle\iint_E\mathrm dA=\iint_E\mathrm dx\,\mathrm dy$

To use Green's theorem, which says

$\displaystyle\int_{\partial E}L\,\mathrm dx+M\,\mathrm dy=\iint_E\left(\frac{\partial M}{\partial x}-\frac{\partial L}{\partial y}\right)\,\mathrm dx\,\mathrm dy$

( $\partial E$ denotes the boundary of $E$ ), we want to find $M(x,y)$ and $L(x,y)$ such that

$\dfrac{\partial M}{\partial x}-\dfrac{\partial L}{\partial y}=1$

and then we would simply compute the line integral. As the hint suggests, we can pick

$\begin{cases}M(x,y)=\dfrac x2\\\\L(x,y)=-\dfrac y2\end{cases}\implies\begin{cases}\dfrac{\partial M}{\partial x}=\dfrac12\\\\\dfrac{\partial L}{\partial y}=-\dfrac12\end{cases}\implies\dfrac{\partial M}{\partial x}-\dfrac{\partial L}{\partial y}=1$

The line integral is then

$\displaystyle\frac12\int_{\partial E}-y\,\mathrm dx+x\,\mathrm dy$

We parameterize the boundary by

$\begin{cases}x(t)=5\cos t\\y(t)=17\sin t\end{cases}$

with $0\le t\le2\pi$ . Then the integral is

$\displaystyle\frac12\int_0^{2\pi}(-17\sin t(-5\sin t)+5\cos t(17\cos t))\,\mathrm dt$

$=\displaystyle\frac{85}2\int_0^{2\pi}\sin^2t+\cos^2t\,\mathrm dt=\frac{85}2\int_0^{2\pi}\mathrm dt=85\pi$

###

Notice that $x^{2/3}+y^{2/3}=4^{2/3}$ kind of resembles the equation for a circle with radius 4, $x^2+y^2=4^2$ . We can change coordinates to what you might call "pseudo-polar":

$\begin{cases}x(t)=4\cos^3t\\y(t)=4\sin^3t\end{cases}$

which gives

$x(t)^{2/3}+y(t)^{2/3}=(4\cos^3t)^{2/3}+(4\sin^3t)^{2/3}=4^{2/3}(\cos^2t+\sin^2t)=4^{2/3}$

as needed. Then with $0\le t\le2\pi$ , we compute the area via Green's theorem using the same setup as before:

$\displaystyle\iint_E\mathrm dx\,\mathrm dy=\frac12\int_0^{2\pi}(-4\sin^3t(12\cos^2t(-\sin t))+4\cos^3t(12\sin^2t\cos t))\,\mathrm dt$

$=\displaystyle24\int_0^{2\pi}(\sin^4t\cos^2t+\cos^4t\sin^2t)\,\mathrm dt$

$=\displaystyle24\int_0^{2\pi}\sin^2t\cos^2t\,\mathrm dt$

$=\displaystyle6\int_0^{2\pi}(1-\cos2t)(1+\cos2t)\,\mathrm dt$

$=\displaystyle6\int_0^{2\pi}(1-\cos^22t)\,\mathrm dt$

$=\displaystyle3\int_0^{2\pi}(1-\cos4t)\,\mathrm dt=6\pi$

3 0

3 years ago

Find the radian measure of an angle of -280°

Bingel [31]

To convert an angle from degrees to radians, multiply by π/180°.

Your angle is
(-280°)*(π/180°) = -14π/9

The appropriate choice is ...
B) (-14π/9)

4 0

3 years ago

A classroom has 12 girls for every 4 boys. What is the ratio of boys to total students?

guapka [62]

Step-by-step explanation:

4:16

No it's ok no need to thank me, it's my duty to help someone like you

6 0

2 years ago

Read 2 more answers

6. A hospital needs a supply of an expensive medicine. Company A has the most

Anton [14]

We are required to find the total milligrams if medicine the hospital can get from the three companies.

The total quantity of medicine the hospital can get from the three companies is 2.75 milligrams

There are there companies:

Company A

Company B

Company C

Company A = 1.3 milligrams

Company A is 0.9 milligrams more than Company C's

A = 0.9 + C

1.3 = 0.9 + C

1.3 - 0.9 = C

0.4 = C

C = 0.4 milligrams

Company A is also twice the difference between the weight of

Company B's supply and Company C's

A = 2(B - C)

1.3 = 2(B - 0.4)

1.3 = 2B - 0.8

1.3 + 0.8 = 2B

2.1 = 2B

Divide both sides by 2

B = 2.1/2

B = 1.05 milligrams

Therefore,

A + B + C

= 1.3 + 1.05 + 0.4

= 2.75 milligrams

Read more:

brainly.com/question/24562139

4 0

2 years ago

Read 2 more answers

76 div 4<br><br> a)15<br><br> b) 8<br><br> c) 19<br><br> d) 0<br><br> Explain

Sunny_sXe [5.5K]

Answer:

C. 19.

Step-by-step explanation:

Let's find the answer.

Step 1: divide the first number of 76, which is 7, by 4 and find the integer part.

7/4=1.75, so the integer part is 1.

Step 2: subtract from 7 the (integer part times 4)

7-(1*4)=3

Step 3: put toether the result (3) and the second number of 76, which is 6, so the result is 36.

Step 4: find how many times we need to add 4s to reach 36, so:

4+4+4+4+4+4+4+4+4=36 which means that:

36/4=9

Step 5: put together the two resulted numbers calculated in step 1, which is 1, and step 4, which is 9:

1 and 9 giving 19, so the answer is:

76/4=19.

In conclusion the answer is C. 19.

6 0

3 years ago