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3 years ago

What is the angular velocity of a 6–foot pendulum that takes 3 seconds to complete an arc of 14.13 feet? Use 3.14 for π

1 answer:

3 0

1) Calculate the whole arc (complete circumference):

Circumference = 2π*radius

radius = 6 foot

=> Circumference = 2 * 3.14 * 6 foot = 37.68

2) Calculate the time to make a whole round, by making a proportion with the two ratios:

ratio 1 = x / 37.68 =

ratio 2 = 3 / 14.13

ratio 1 = ratio 2 =>

   x 3s
---------- =   -----------
37.68 ft    14.13 ft

=> x = 3 * 37.68 / 14.13 = 8 s

3) Calcuate the angular velocity as the 2π rad (which is the total angle of a circle) divided by the time.

So the angular velocity is 2π rad / 8 s = 2*3.14 foot / 8 s = 0.785 rad / s

Answer: 0.785 rad / s

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-9(x+2)=54 apply the distributive property and simplify

Tomtit [17]

Answer:

x = -8

Step-by-step explanation:

-9 (x+2) = 54

-9x - 18 = 54

-9x = 72

x = -8

Hope this helps :)

Let me know if there are any mistakes!!

8 0

3 years ago

in a history class the girl to boy ratio is 9 to 5 if there are a total of 70 students, how many boys are there

Nikolay [14]

Answer:

Girls: 45

Boys: 25

Step-by-step explanation:

$9 + 5 = 14$

$70 \div 14 = 5$

$9 \times 5 = 45$

$5 \times 5 = 25$

Awnser Check:

$45 + 25 = 70$

8 0

2 years ago

Find the Shaded Area: 10 m 10 m

Greeley [361]

Answer:

100-25pi m

Step-by-step explanation:

Let us subtract the circles area from the square

First, let us find the area of the square:

Base x height =

10m x 10m = 100m

Now, the circle:

pi x radius ^2 =

pi x (10/2)^2 =

pi x 5^2=

25 pi

Therefore, the shaded area is 100-25pi m. You can also simplify it further by plugging in the 3.14... value into pi.

I hope this helps! :)

6 0

3 years ago

Prove that \displaystyle \frac{\cos \theta}{1 + \sin \theta} = \frac{1 - \sin \theta}{\cos \theta}

Bogdan [553]

Answer:

sin^2(θ)+cos^2(θ)=1

Step-by-step explanation:

We know that the statement above is true because of the Pythagorean identity theorem, which states the aforementioned equation. If you solve the equation for 1 you get the same equation.

To do this first multiply both sides by cos(θ), this gives you (cos^2θ)/1+sinθ = 1-sinθ

Then, multiply both sides by sinθ. This equals cos^θ=1-sin^2θ.

Finally, add sin^2θ to both sides. This equals the final answer of cos^2θ+sin^2θ=1. Which is true.

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2 years ago

Please show the steps for this question Divide z4 by z-3

dsp73

Z^4 / z^-3 = z^7 - when you divide numbers written in exponential form, you keep the base and subtract the exponents. z^4 divided by z^-3 = z^ (4- (-3)) = z^7.

8 0

3 years ago