What makes an equation true?

Derive the equation of motion of the spring-mass system given below. Please show and MARK your derivation step by step. Missing

Arte-miy333 [17]

Answer:

Ö + θ ( (k/m) + (g/l)) = 0

Step-by-step explanation:

Use the FBD attached:

Apply Newtons 2 nd Law in tangential direction:

Sum ( Ft ) = m*a

Sum of all tangential forces is:

m*g*sin(θ) + k*l*sin(θ)*cos(θ) = - m*l*Ö

Using small angle approximations:

sin (θ) = θ

cos (θ) = 1

Ö = angular acceleration.

m*g*θ + k*l*θ = -m*l*Ö

Ö + θ ( (k/m) + (g/l)) = 0

5 0

3 years ago

What types of problems can be solved using the greatest common factor what type of problems can be solved using the least common

Tanzania [10]

There could be problems like there is a light which would flicker in every 7 seconds and there is another one which would flicker in every 8 seconds. So, how many times would they flicker until they would flicker at the same time?

6 0

3 years ago

A corporation must appoint a president, chief executive officer (CEO), chief operating officer (COO), and chief financial off

Yakvenalex [24]

Answer:

a) The officers can be appointed in 24024 different ways.

b) The committee can be appointed in 1001 different ways.

c) 1.1% probability of randomly selecting the committee members and getting the three youngest of the qualified candidates

Step-by-step explanation:

The order in which the officers are appointed is important(the first is the president, second the CEO and so on...). So the permutations formula will be used.

Otherwise, in the committee there are no roles, so the order is not important. So the combinations formula will be used.

Permutations formula:

The number of possible permutations of x elements from a set of n elements is given by the following formula:

$P_{(n,x)} = \frac{n!}{(n-x)!}$

Combinations formula:

$C_{n,x}$ is the number of different combinations of x objects from a set of n elements, given by the following formula.

$C_{n,x} = \frac{n!}{x!(n-x)!}$

A. How many different ways can the officers be appointed?

4 from a set of 14, with roles. So a permutation.

$P_{(14,4)} = \frac{14!}{(14-4)!} = 24024$

The officers can be appointed in 24024 different ways.

B. How many different ways can the committee be appointed?

4 from a set of 14, without roles. So combination

$C_{14,4} = \frac{14!}{4!(14-4)!} = 1001$

The committee can be appointed in 1001 different ways.

C. What is the probability of randomly selecting the committee members and getting the three youngest of the qualified candidates?

A probability is the number of desired outcomes divided by the number of total outcomes.

Desired outcomes.

The three youngest(1 combination), and one of the other 14-3 = 11. So $D = 1*11 = 11$

Total outcomes:

From B., 1001, so $T = 1001$

Probability:

$p = \frac{D}{T} = \frac{11}{1001} = 0.011$

1.1% probability of randomly selecting the committee members and getting the three youngest of the qualified candidates

8 0

3 years ago

a local businesses bought a square ploy of land. the sides of the lot measure 32 feet on each side. he decides to split the lot

san4es73 [151]

Answer:

Approximate length of the diagonal fencing needed is 45.25 cm.

Step-by-step explanation:

Here, each side of the square shaped land = 32 ft

Now, the diagonal fencing is made in side the plot so that the land is divided into two right triangles.

In the triangle:

Base side of the triangle = 32 cm

Perpendicular length of the triangle = 32 cm

Let us assume the hypotenuse of the triangle = k cm

⇒The length of the diagonal in the square = k cm

by PYTHAGORAS THEOREM in a right angled triangle:

$(Base)^{2} + (Perpendicular)^{2} = (Hypotenuse)^{2}$

⇒ $(32)^2 + (32)^2 =k^2\\or, k^2 = 1024 + 1024 = 2048\\\implies k = \sqrt{2048} = 45.25$

or, k = 45.25 cm

Hence,the approximate length of the diagonal fencing needed to fence the square land is 45.25 cm.

6 0

3 years ago

I really need help :( anybody ??

marissa [1.9K]

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Hey!!

Answer:{2,4,5}

Explanation:

<h2>Range</h2>

Let R be relation from A to B.The set of second components or the set of elements of B are called range.

Hope it helps..

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3 0

3 years ago