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Alex73 [517]
3 years ago
6

I have Ben working on this same question for about 10 minutes. I could really use some help please.

Mathematics
2 answers:
Aleksandr-060686 [28]3 years ago
8 0

Answer:

b

Step-by-step explanation:

a_{1}=4,\\a_{n}=\frac {1}{3} a^{n-1}\\r=\frac{a_{n}}{a_{n-1}} =\frac{1}{3}\\explicit~rule~is\\\\a_{n}=a_{1}r^{n-1}\\a_{n}=4(\frac{1}{3})^{n-1}

Anika [276]3 years ago
7 0

Step-by-step explanation:

Every next term is 1/3 times of the previous term. The first term is 4.

Hence the rule is An = 4 * (1/3)^(n-1).

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A drive has a maximum speed of 10,000 revolutions per minute. If a disc has a diameter of 14 cm​, what is the linear​ speed, in​
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The point 6 cm away from the center travels in a circle of circumference 2π*(6 cm) = 12π cm, so that it covers this distance per revolution, 12π cm/1 rev.

So the disk has a linear speed of

(6000 rev/min) * (12π cm/rev) = 72,000π cm/min

which is equivalent to

(72,000π cm/min) * (1/100,000 km/cm) * (60 min/h)

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If cos Θ = square root 2 over 2 and 3 pi over 2 &lt; Θ &lt; 2π, what are the values of sin Θ and tan Θ?
KIM [24]

Answer:

The answer is

sin(\theta)=-\frac{\sqrt{2}}{2}

tan(\theta)=-1

Step-by-step explanation:

we know that

tan(\theta)=\frac{sin(\theta)}{cos(\theta)}

sin^{2}(\theta)+cos^{2}(\theta)=1

In this problem we have

cos(\theta)=\frac{\sqrt{2}}{2}

\frac{3\pi}{2}

so

The angle \theta belong to the third or fourth quadrant

The value of sin(\theta) is negative

Step 1

Find the value of  sin(\theta)

Remember

sin^{2}(\theta)+cos^{2}(\theta)=1

we have

cos(\theta)=\frac{\sqrt{2}}{2}

substitute

sin^{2}(\theta)+(\frac{\sqrt{2}}{2})^{2}=1

sin^{2}(\theta)=1-\frac{1}{2}

sin^{2}(\theta)=\frac{1}{2}

sin(\theta)=-\frac{\sqrt{2}}{2} ------> remember that the value is negative

Step 2

Find the value of tan(\theta)

tan(\theta)=\frac{sin(\theta)}{cos(\theta)}

we have

sin(\theta)=-\frac{\sqrt{2}}{2}

cos(\theta)=\frac{\sqrt{2}}{2}

substitute

tan(\theta)=\frac{-\frac{\sqrt{2}}{2}}{\frac{\sqrt{2}}{2}}

tan(\theta)=-1

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