Notice that the condition <em>x</em> ≠ 2<em>πk</em> for (presumably) integer <em>k</em> means cos(<em>x</em>) ≠ ±1, and in particular cos(<em>x</em>) ≠ 1 so that we could divide both sides by (1 - cos(<em>x</em>)) safely. Doing so lets us separate the variables:
(1 - cos(<em>x</em>)) <em>y'</em> - <em>y</em> sin(<em>x</em>) = 0
==> (1 - cos(<em>x</em>)) <em>y'</em> = <em>y</em> sin(<em>x</em>)
==> <em>y'</em>/<em>y</em> = sin(<em>x</em>)/(1 - cos(<em>x</em>))
==> d<em>y</em>/<em>y</em> = sin(<em>x</em>)/(1 - cos(<em>x</em>)) d<em>x</em>
Integrate both sides and solve for <em>y</em>. On the right, substitute <em>u</em> = 1 - cos(<em>x</em>) and d<em>u</em> = sin(<em>x</em>) d<em>x</em>.
∫ d<em>y</em>/<em>y</em> = ∫ sin(<em>x</em>)/(1 - cos(<em>x</em>)) d<em>x</em>
∫ d<em>y</em>/<em>y</em> = ∫ d<em>u</em>/<em>u</em>
ln|<em>y</em>| = ln|<em>u</em>| + <em>C</em>
exp(ln|<em>y</em>|) = exp(ln|<em>u</em>| + <em>C </em>)
exp(ln|<em>y</em>|) = exp(ln|<em>u</em>|) exp(<em>C </em>)
<em>y</em> = <em>Cu</em>
<em>y</em> = <em>C</em> (1 - cos(<em>x</em>))
Answer:
(5/3 x - k)/c =b
Step-by-step explanation:
x = 3 / 5 (cb+k)
Multiply each side by 5/3
5/3x =5/3* 3 / 5 (cb+k)
5/3x = (cb+k)
Subtract k
5/3 x - k = cb +k-k
5/3 x - k = cb
Divide by c
(5/3 x - k)/c = cb/c
(5/3 x - k)/c =b
2-4=2
(-2)+4=2
2+4=6
Why is this a question
Answer:
0.234
Step-by-step explanation:
Given that:
Proportion, (p) ; Islanders beat rangers = 5/6 = 0.8333
Probability that islander win exactly 5 out of 7 games
1 - p = 0.1667
Usingbthe binomial distribution formula :
P(x =x) = nCx * p^n * (1 - p)^(n - r)
P(x = 5) = 7C5 * 0.833^5 * 0.1667^2
P(x = 5) = 21 * 0.833^5 * 0.1667^2
P(x = 5) = 0.23405369484362783281917
P(x = 5) = 0.234
Answer: The speed when walking = 3.2 miles per hour
The speed when skateboarding=2(3.2)=6.4 miles per hour
Step-by-step explanation:
Let x be the walking speed then his speed on skateboard be 2x.
Time taken in skateboarding = 1:30-2:15= 45 minutes=3/4 hour
Distance traveled by skating is given by :-
Time taken for walking = 2:15-3:00=45 minutes=3/4 hour
Distance traveled by walking is given by :-
Distance between house and beach = 7.2 miles
Hence, The speed when walking = 3.2 miles per hour
The speed when skateboarding=2(3.2)=6.4 miles per hour