What is the value of the expression

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

Sav [38]

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 a and b 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.

8 0

3 years ago

A bouncing ball reaches a height of 54 inches at its first peak, 36 inches at its second peak, and 24 inches at its third peak.

steposvetlana [31]

54, 36, 24 are the 1st 3 element of a geometric progression with 2/3 as a common ratio: PROOF:
the 1st term is 54, (a₁= 54) the 2nd term a₂ = 24, then
(a₂ = a₁.r) or 36 = 54.r → r= 36/54 = 2/3. Same logique for the 3rd term.
So 2/3 is common ratio. We know that :U(n) = a.(r)ⁿ⁻¹. Then if a =54 and r = x (given by the problem), then f(x) = 54.xⁿ⁻¹
n, being the rank of any element of this geometric progression

7 0

3 years ago

Read 2 more answers

1 2 3 4 5 6 7 8 9 10 11

alexandr402 [8]

1) PEMDAS: 12 * 5 + 6 / 6

12 * 5 = 60

60 + 6 / 6

6 / 6 = 1

60 + 1 = 61

61 is the final answer.

2) Absolute Value: |-2 - 4| = -6 HOWEVER, because it is in the absolute value signs, it becomes 6. 6 - 4 = 2

2 in the final answer.

3) 4 + 4 + 2 = 10 Because they are all negatives, we add back the negative sign.

-10 is the final answer.

4) 15x + 1 = 26

Subtract 1 from each side.

15x = 25.

25/15 = 1.6...

x = 1.6...

5) 2x -4 + 3x = - 1

2x + 3x = 5x

5x - 4 = -1

Add 4 to each side

5x = 3

3/5 = 0.6

x = 0.6

6) x-2/3 = x+4/5

I don't remember the steps, but the answer is x = 11

7) Finding the relationship between x:4 and 5:20

20/5 = 4

x = 1

The smaller rectangle has a reduction of 5 times.

8) Mean is found by adding all the number, then dividing by the amount added.

18 + 27 + 15 + 24 + 18 + 26 + 19 + 24 = 171

171/8 = 21.375

Mean = 21.375

Median is found by putting the numbers in increasing order, then finding the middle number, 15, 18, 18, 19, 24, 24, 26, 27. 24 + 19 = 43. 43/2 = 21.5

Median = 21.5

9) Circumference of a circle = 2(pi)(r)

Circumference = 30πin (thats the pi symbol)

If you use the typical pi fill-in (3.14) the its 2 * 3.14 * r then it would = 94.5in.

10) Combing Like Terms: 5x + 7y - 8y^2 + 2x - y

5x + 2x = 7x

7x + 7y - 8y^2 - y

-y + 7y = 6y

Answer: -8y^2 + 7x + 6y

5 0

3 years ago

Find the area of the shape below. * PLSS HELP

Travka [436]

Answer:

92

because the formula for the triangle is 1/2×b×h

and the formula for the rectangle nos l×w and then add those.

6 0

2 years ago

Read 2 more answers

Kyle asked a random group of students what their favorite sport was. The results are below. Boys Girls Basketball 10 8 Football

Ronch [10]

Answer:

The probability that Kyle will pick a girl who likes football is 12.5%.

Step-by-step explanation:

The data provided is as follows:

Boys Girls Total

Basketball 10 8 18

Football 25 7 32

Soccer 9 19 28

Baseball 18 22 40

Total 62 56 118

Compute the probability that Kyle will pick a girl who likes football as follows:

$P(F|G)=\frac{n(G\cap F)}{n(G)}$

$=\frac{7}{56}\\\\=0.125\\\\=12.5\%$

Thus, the probability that Kyle will pick a girl who likes football is 12.5%.

6 0

3 years ago