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Mathematics

2 answers:

sammy [17]2 years ago

8 0

Answer:

the first one i believe

Step-by-step explanation:

Helen [10]2 years ago

8 0

Answer:

Step-by-step explanation:

SKAUSHBD GCVTFJKIEJF period

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Lazar drives to work every day and passes two independently operated traffic lights. The probability that both lights are green

Natalija [7]

Conditional probability is a measure of probability of an event given that another event has occurred.
P ( A\ B ) = P ( A ∩ B ) / P ( B ) - the conditional probability of A given B
P ( A ∩ B ) = 0.41; P ( B ) = 0.59
P ( A \ B ) = 0.41 / 0.59 = 0.6949152 ≈ 0.69
Answer: B ) 0.69

7 0

2 years ago

Read 2 more answers

The harmonic motion of a particle is given by f(t) = 2 cos(3t) + 3 sin(2t), 0 ≤ t ≤ 8. (a) When is the position function decreas

iren [92.7K]

For the last part, you have to find where $f'(t)$ attains its maximum over $0\le t\le8$ . We have

$f'(t)=-6\sin3t+6\cos2t$

so that

$f''(t)=-18\cos3t-12\sin2t$

with critical points at $t$ such that

$-18\cos3t-12\sin2t=0$

$3\cos3t+2\sin2t=0$

$3(\cos^3t-3\cos t\sin^2t)+4\sin t\cos t=0$

$\cos t(3\cos^2t-9\sin^2t+4\sin t)=0$

$\cos t(12\sin^2t-4\sin t-3)=0$

So either

$\cos t=0\implies t=\dfrac{(2n+1)\pi}2$

$12\sin^2t-4\sin t-3=0\implies\sin t=\dfrac{1\pm\sqrt{10}}6\implies t=\sin^{-1}\dfrac{1\pm\sqrt{10}}6+2n\pi$

where $n$ is any integer. We get 8 solutions over the given interval with $n=0,1,2$ from the first set of solutions, $n=0,1$ from the set of solutions where $\sin t=\dfrac{1+\sqrt{10}}6$ , and $n=1$ from the set of solutions where $\sin t=\dfrac{1-\sqrt{10}}6$ . They are approximately