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skad [1K]
3 years ago
7

15. If x=a Sin2t (I+Cos2t) and y=b Cos 2t (1-Cos2t) then finddy/dx at =22/7*4​

Mathematics
1 answer:
Sav [38]3 years ago
8 0

By the chain rule,

\dfrac{\mathrm dy}{\mathrm dx}=\dfrac{\mathrm dy}{\mathrm dt}\dfrac{\mathrm dt}{\mathrm dx}\implies\dfrac{\mathrm dy}{\mathrm dx}=\dfrac{\frac{\mathrm dy}{\mathrm dt}}{\frac{\mathrm dx}{\mathrm dt}}

It looks like we're given

\begin{cases}x=a\sin(2t)(1+\cos(2t))\\y=b\cos(2t)(1-\cos(2t))\end{cases}

where <em>a</em> and <em>b</em> are presumably constant.

Recall that

\cos^2t=\dfrac{1+\cos(2t)}2

\sin^2t=\dfrac{1-\cos(2t)}2

so that

\begin{cases}x=2a\sin(2t)\cos^2t\\y=2b\cos(2t)\sin^2t\end{cases}

Then we have

\dfrac{\mathrm dx}{\mathrm dt}=4a\cos(2t)\cos^2t-4a\sin(2t)\cos t\sin t

\dfrac{\mathrm dy}{\mathrm dt}=-4b\sin(2t)\sin^2t+4b\cos(2t)\sin t\cos t

\implies\dfrac{\mathrm dy}{\mathrm dx}=\dfrac{4b\cos(2t)\sin t\cos t-4b\sin(2t)\sin^2}{4a\cos(2t)\cos^2t-4a\sin(2t)\cos t\sin t}

\implies\boxed{\dfrac{\mathrm dy}{\mathrm dx}=\dfrac ba\tan t}

where the last reduction follows from dividing through everything by \cos(2t)\cos^2t and simplifying.

I'm not sure at which point you're supposed to evaluate the derivative (22/7*4, as in 88/7? or something else?), so I'll leave that to you.

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Following are the number of grams of carbohydrates in a sample of 12-ounce espresso beverages offered at Starbucks. 6 , 9, 10, 2
marusya05 [52]

Answer:

x=6, 9, 10, 20, 22, 25, 27, 40 , 48, 59

i= 1,  2 , 3,  4,    5,   6,    7,   8,    9,    10

And as we can see here the position for x=40 is 8, so then we can calculate the percentile for 40 grams like this:

p=\frac{8}{10} *100 = 80

So the  the vale of 40 gr correspond to the 80th percentile of the data since accumulates 80% of the values below.

Step-by-step explanation:

We can define a percentile as "a value on a scale of 100 that indicates the percent of a distribution that is equal to or below it"

For this case we have the following data given:

6 , 9, 10, 20, 22, 25, 27, 40 , 48, 59

And we want to calculate the percentile for the value of 40 grams

Since the dataset is on increasing way there is no problem to calculate this percentile.

We see that we have a total of n =10 observations, and we can rank the position of each observation (i) like this:

x=6, 9, 10, 20, 22, 25, 27, 40 , 48, 59

i= 1,  2 , 3,  4,    5,   6,    7,   8,    9,    10

And as we can see here the position for x=40 is 8, so then we can calculate the percentile for 40 grams like this:

p=\frac{8}{10} *100 = 80

So the  the vale of 40 gr correspond to the 80th percentile of the data since accumulates 80% of the values below.

3 0
3 years ago
Find the solution of the differential equation that satisfies the given initial condition. dy/dx=x/y , y(0)=-1
Charra [1.4K]

Separating variables, we have

\dfrac{dy}{dx} = \dfrac xy \implies y\,dy = x\,dx

Integrate both sides.

\displaystyle \int y\,dy = \int x\,dx

\dfrac12 y^2 = \dfrac12 x^2 + C

Given that y(0)=-1, we find

\dfrac12 (-1)^2 = \dfrac12 0^2 + C \implies C = \dfrac12

Then the particular solution is

\dfrac12 y^2 = \dfrac12 x^2 + \dfrac12

y^2 = x^2 + 1

y = \pm\sqrt{x^2 + 1}

and because y(0)=-1, we take the negative solution to accommodate this initial value.

\boxed{y(x) = -\sqrt{x^2+1}}

7 0
2 years ago
A²-b²-c²-8b²+a²+c² what is the answer
wlad13 [49]
Well this only simplifies to a smaller equation
so the answer would be...

2a²-9b²
4 0
3 years ago
In the line 3y=4x-1 and 9y=x+3 are parallel to each other the value of q is
jonny [76]
Do you mean the value of y? there is no q in these equations.
5 0
3 years ago
Read 2 more answers
Identify the vertical asymptotes of f(x) = 2 over quantity x squared plus 3 x minus 10.
zysi [14]
The function is:
f ( x ) = 2 / ( x² + 3 x - 10 )
x² + 3 x - 10 = x² + 5 x - 2 x - 10 = x ( x + 5 ) - 2 ( x + 5 ) =
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x + 5 = 0 => x = - 5
x - 2 = 0 => x = 2
Answer:
The vertical asymptotes are: x = - 5 and x = 2.
3 0
3 years ago
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