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3 years ago

Point K(–2, 1) is rotated 90° about the origin. What are the coordinates of K′?

Mathematics

1 answer:

yarga [219]3 years ago

4 0

Answer:

The co-ordinates of K¹( -1 , -2 )

Step-by-step explanation:

Explanation:-

Given that the point K( -2,1 )

when rotating a point 90° about the origin

Given point A(x,y) transformation to A¹( - y,x )

Given point K(-2,1) → K¹ ( -(1) , -2)

Final answer:-

The co-ordinates of K¹( -1 , -2 )

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What is X/3=3X-15/4 Please help me thanks

Rufina [12.5K]

X=9x-45/4
4x=36x-45
4x-36x=-45
-32x=-45
x=45/32

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3 years ago

Evaluate the integral using the indicated trigonometric substitution. (use c for the constant of integration.) x^3 / sqrt x^2 +

slava [35]

$\displaystyle\int\frac{x^3}{\sqrt{x^2+49}}\,\mathrm dx$

Taking $x=7\tan\theta$ gives $\mathrm dx=7\sec^2\theta\,\mathrm d\theta$ , so that the integral becomes

$\displaystyle\int\frac{(7\tan\theta)^3}{\sqrt{(7\tan\theta)^2+49}}(7\sec^2\theta)\,\mathrm d\theta$
$=\displaystyle7^4\int\frac{\tan^3\theta\sec^3\theta}{\sqrt{49\tan^2\theta+49}}\,\mathrm d\theta$
$=\displaystyle7^3\int\frac{\tan^3\theta\sec^3\theta}{\sqrt{\tan^2\theta+1}}\,\mathrm d\theta$
$=\displaystyle7^3\int\frac{\tan^3\theta\sec^3\theta}{\sqrt{\sec^2\theta}}\,\mathrm d\theta$
$=\displaystyle7^3\int\frac{\tan^3\theta\sec^3\theta}{|\sec\theta|}\,\mathrm d\theta$

When $\sec\theta>0$ , we have

$=\displaystyle7^3\int\frac{\tan^3\theta\sec^3\theta}{\sec\theta}\,\mathrm d\theta$
$=\displaystyle7^3\int\tan^3\theta\sec^2\theta\,\mathrm d\theta$

and from here we can substitute $u=\tan\theta$ to proceed from here.

Quick note: When we set $x=7\tan\theta$ , we are implicitly enforcing $-\dfrac\pi2$ just so that the substitution can be undone later via $\theta=\tan^{-1}\dfrac x7$ . But note that over this domain, we automatically guarantee that $\sec\theta>0$ , so the absolute value bars can be dropped immediately.

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3 years ago

I got b = 5 but I wanted to make sure from you beautiful ppl <3

GrogVix [38]

Answer:

b=5

Step-by-step explanation:

10 = -2b + 4b

Combine like terms

10 = 2b

Divide each side by 2

10/2 = 2b/2

5 = b

4 0

3 years ago

Read 2 more answers

Paula drinks 1 tenth gallon of milk every morning. How many days will it take Paula to drink 1 gallon of milk,no files just type

elixir [45]

Answer:

10 days

Step-by-step explanation:

Divide 1 gallon by

0.1 gallon per day:

1 gallon

---------------------- = 10 days

0.1 gallon/day

3 0

3 years ago

Find the solution to the system of equations.

VARVARA [1.3K]

Answer:

(2,3)

Step-by-step explanation:

use the equal values method.

set y equal to itself.

y = -2x+7 but also 5x-7

-2x+7=5x-7 ............................. solve the equation

7x=14

x=2

Now substitute the x value into one of the equations given. for example i'll do -2x+7.

-2(2) +7 =y

-4+7=y

3=y

so thats your answer

x=2, y=3

(2,3)

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4 years ago