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nexus9112 [7]
3 years ago
13

The position of the particle moving in space at time t ≥ 0 is r(t) = (2 + 2 cos(t))i − 2 sin(t)j + (3 − t π )k. Find the first t

ime moment t0 such that the velocity vector v(t0) is orthogonal to the vector i − j.
Mathematics
1 answer:
jekas [21]3 years ago
5 0

Answer:

t0 = π/4

Step-by-step explanation:

The velocity v(t) = r'(t) = <-2sint,-2cost>

Since <1,-1>⊥v, <1,-1>•v=0. So,

(1)(-2sint) + (-1)(-2cost) = 0

cost - sint = 0

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Determine the measure of the missing angle in the figure below.
bearhunter [10]

Answer:

Step-by-step explanation:

5 0
3 years ago
1+2-3+4+5-6+7+8-9...+97+98-99
zaharov [31]

Answer:

  1584

Step-by-step explanation:

The sum of this sequence can be found a number of ways. One way is to recast it as the series whose terms are groups of three terms of the given series.

__

<h3>series of partial sums</h3>

The partial sums, taken 3 terms at a time, are

  1+2-3 = 0

  4+5-6 = 3

  7+8-9 = 6

...

  97+98-99 = 96

So the original series is equivalent to ...

  0 +3 +6 +... +96 = 3×1 +3×2 +... +3×32 = 3×(1 +2 +... +32)

That is, the sum is 3 times the sum of the consecutive integers 1..32.

__

<h3>consecutive integers</h3>

The sum of integers 1..n is given by the equation ...

  s(n) = n(n+1)/2

__

<h3>series sum</h3>

Using this to find the sum of our series, we find it to be ...

  series sum = 3 × (32)(33)/2 = 1584

_____

<em>Alternate solution</em>

The given series is the sum of integers 1-99, with 6 times the sum of integers 1-33 subtracted. That is, ...

  1 + 2 - 3 + 4 + 5 - 6 = 1+2+3+4+5+6 -2(3 +6) = 1+2+3+4+5+6 -6(1+2)

Continuing on to ...97 +98 -99 gives the result s(99) -6s(33).

Computed that way, we find the sum to be ...

  (99)(100)/2 -6(33)(34)/2 = 4950 -3366 = 1584

3 0
2 years ago
−3−3/4(c−4)=5/4<br><br>anser for c<br><br>offering brainlyest in the next ten minutes
Anna007 [38]

Answer:

okay so it is −

3

−

1

⋅

3

4

(

−

4

)

=

5

4

−

3

−

3

4

(

−

4

)

=

5

4

Step-by-step explanation:

8 0
2 years ago
What is the radius of (x - 3)2 + (y + 4)2 = 14?
DochEvi [55]
(x-h)^2+(y-k)^2=r^2
r=radius
(x-3)^2+(y+4)^2=14
(x-3)^2+(y+4)^2=(√14)^2
answer is 2nd option
r=√14
6 0
2 years ago
Divide. Do not round your answer. 856.8 ÷ 8
mote1985 [20]

Answer:

your non rounded yo answer is 107.1

3 0
3 years ago
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