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2 years ago

Consider the parametric equations

Mathematics

1 answer:

MArishka [77]2 years ago

5 0

Answer:(a)x^2+2y^2=2

(b)In the attached diagram

Step-by-step explanation:Step 1: Multiply both equations by t

xt=t(cost -sint)\\ty\sqrt{2} =t(cost +sint)

Step 1: Multiply both equations by t

xt=t(cost -sint)\\ty\sqrt{2} =t(cost +sint)

Step 2:We square both equations

(xt)^2=t^2(cost -sint)^2\\(ty)^2(\sqrt{2})^2 =t^2(cost +sint)^2

Step 3: Adding the two equations

(xt)^2+(ty)^2(\sqrt{2})^2=t^2(cost -sint)^2+t^2(cost +sint)^2\\t^2(x^2+2y^2)=t^2((cost -sint)^2+(cost +sint)^2)\\x^2+2y^2=(cost -sint)^2+(cost +sint)^2\\(cost -sint)^2+(cost +sint)^2=2\\x^2+2y^2=2 hopes this helps

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Convert the complex number z = 4 - 10i from rectangular form to polar form.

mrs_skeptik [129]

ANSWER

$r = 2 \sqrt{29} ( \cos(292 \degree) + \sin(292 \degree))$

EXPLANATION

The polar form of a complex number ,

$z = x + yi$

is given by:

$z = r( \cos( \theta) + i \sin( \theta) )$

where

$r = \sqrt{ {x}^{2} + {y}^{2} }$

The given complex number is:

$z = 4 - 10i$

$r = \sqrt{ {4}^{2} + {( - 10)}^{2} }$

$r = \sqrt{16 + 100}$

$r = \sqrt{116} = 2 \sqrt{29}$

And

$\theta= \tan^{ - 1}(\frac{ y}{x} )$

$\theta= \tan^{ - 1}(\frac{ - 10}{4} )$

$\theta= 292 \degree$

Hence the polar form is :

$r = 2 \sqrt{29} ( \cos(292 \degree) + \sin(292 \degree))$

6 0

2 years ago

A line contains the points (−26, −37)(−26, −37) and (−32, −61)(−32, −61) . What is the slope of the line in simplified form?

Rus_ich [418]

Slope = (y2 - y1)/(x2 - x1) = (-61 - (-37))/(-32 - (-26)) = (-61 + 37)/(-32 + 26) = -24/-6 = 4

Therefore, slope = 4

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2 years ago

5#The distribution of scores on a standardized aptitude test is approximately normal with a mean of 480 and a standard deviation

kirza4 [7]

We want to find the value that makes

$P(X\ge x)=0.2$

To find it we must look at the standard normal table, using the complementary cumulative table we find that

$P(Z\ge z)=0.20045\Leftrightarrow z=0.84$

Then, using the z-score we can find the minimum score needed, remember that

$z=\frac{x-\mu}{\sigma}$

Where

σ = standard deviation

μ = mean

And in our example, x = minimum score needed, therefore

$\begin{gathered} 0.84=\frac{x-480}{105} \\ \\ x=0.84\cdot105+480 \\ \\ x=568.2 \end{gathered}$

Rounding to the nearest integer the minimum score needed is 568, if you get 568 you are at the top 20.1%.

7 0

1 year ago

Determine the solution set of x2 - 80 = 0

meriva

   x² - 80 = 0
Add 80
to each side: x² = 80

Square root
each side: x    = √80

Look it up: x = + 8.944... (rounded)
   and
   x = - 8.944... (rounded).
___________________________________

Here's a cleaner solution:

   x² - 80 = 0
Add 80
to each side: x² = 80

Square root
each side: x    = √80

But 80 = 16 · 5

So √80 = √16 · √5

√16 = 4, so    x = 4 √5

8 0

2 years ago

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Please help due today find the slope.

qaws [65]

Answer:

35. 7/4

36. 1/4

37. 1/3

38. 8/5

39. 3/0 or 3

40. 2/3

Step-by-step explanation:

All you have to do is start with the bottom dot and count up and count left or right to were the other dot is. Then u set up your slope which could be a fraction. Rise/Run

5 0

2 years ago

Read 2 more answers