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3 years ago

What is the image of C for a 90 degree counterclockwise rotation about A?

Mathematics

2 answers:

Andru [333]3 years ago

7 0

Answer:

Option A. (7, 3)

Step-by-step explanation:

When C is rotated 90° counterclockwise about the point A then C' will come parallel to the point A.

Now we can find the coordinates of the image of point C.

Distance between point A and C is 4 units, so x coordinates of C' (image) will be = 3 + 4 = 7

And y coordinates will remain as 3.

So the new image point C' will be (7, 3)

Option A. (7, 3) is the correct option.

Mashcka [7]3 years ago

3 0

counter clockwise would be rotating it up to the right.

C is 4 spaces away from A ,

A is on X3 & Y3 so 4 +3 = 7

so it would be x7 & Y3 so (7,3), the first answer

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Find the solution r(t)r(t) of the differential equation with the given initial condition: r′(t)=⟨sin9t,sin6t,9t⟩,r(0)=⟨4,6,3⟩

klemol [59]

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$\mathbf r(t)=\left\langle\displaystyle\int\sin9t\,\mathrm dt,\int\sin6t\,\mathrm dt,\int9t\,\mathrm dt\right\rangle$

$\displaystyle\int\sin9t\,\mathrm dt=\frac19\cos9t+C_1$

$\displaystyle\int\sin6t\,\mathrm dt=\frac16\cos6t+C_2$

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With the initial condition $\mathbf r(0)=\langle4,6,3\rangle$ , we find

$\dfrac19\cos0+C_1=4\implies C_1=\dfrac{35}9$

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$\dfrac92\cdot0^2+C_3=3\implies C_3=3$

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$\mathbf r(t)=\left\langle\dfrac19\cos9t+\dfrac{35}9,\dfrac16\cos6t+\dfrac{35}6,\dfrac92t^2+3\right\rangle$

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3 years ago

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stich3 [128]

Have you tried asking a teacher for help before this

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I have a stamp collection. 70% of my stamps are Canadian and 30% are international. I have 500 more Canadian stamps than interna

shutvik [7]

Answer: N= 375, C= 875

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{C-500 = N | (equation 1)

0.7 (C+N) = C | (equation 2)

Express the system in standard form:

{-N+C = 500 | (equation 1)

0.7 N-0.3 C = 0 | (equation 2)

Add 0.7 × (equation 1) to equation 2:

{-N+C = 500 | (equation 1)

0 N+0.4 C = 350 | (equation 2)

Divide equation 2 by 0.4:

{-N+C = 500 | (equation 1)

0. N+C = 875. | (equation 2)

Subtract equation 2 from equation 1:

{-N+0 C = -375. | (equation 1)

0 N+C = 875. | (equation 2)

Multiply equation 1 by -1:

{N+0 C = 375. | (equation 1)

0 N+C = 875. | (equation 2)

Collect results:

Answer: | N = 375 and C=875

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