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2 years ago

At what points does the helix r(t) = sin t, cos t, t intersect the sphere x2 + y2 + z2 = 65? (round your answers to three decima

l places. if an answer does not exist, enter dne.)

Mathematics

1 answer:

Firdavs [7]2 years ago

7 0

$\mathbf r(t)=\langle x(t),y(t),z(t)\rangle=\langle\sin t,\cos t,t\rangle$

$x^2+y^2+z^2=\sin^2t+\cos^2t+t^2=65$
$\implies t^2=64$
$\implies t=\pm8$

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KATRIN_1 [288]

Answer:

The translation is $1$ unit to the left and $5$ units down

Step-by-step explanation:

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we know that

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That means

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adoni [48]

To solve this problem, we must first convert all of the numbers represented by words into their numeral equivalents so we can simplify. To do this, we must remember that the ones place is the first to the left of the decimal point, and the tens place is one place farther to the left. If we have 4 tens and 3 ones, this is the same as 43 (we put the digit 4 in the tens place and the digit 3 in the ones place). If we replace our words with our new numerical value, we get:

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To solve this, we just multiply these two numbers together, which gives us:

430

Therefore, your answer is 430.

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The sequence of transformations involved is a reflection across the x axis, followed by a reflection across the y = x line

Step-by-step explanation:

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