All categories

3 years ago

What is the explicit formula for this sequence?

Mathematics

1 answer:

Zarrin [17]3 years ago

8 0

Step-by-step explanation:

The above sequence is a geometric sequence

For an nth term in a geometric sequence

$a(n) = a ({r})^{n - 1}$

where

n is the number of terms

a is the first term

r is the common ratio

From the question

a = 5

r = 10/5 = 2

Therefore the explicit formula for this sequence is

$a(n) = 5( {2})^{n - 1}$

Hope this helps you

You might be interested in

The product of a number u and 3 is 6

Airida [17]

Answer:

This equation is u·3=6

To solve this u would equal 2.

Step-by-step explanation:

These word problems are very simple. The key word is <u>product.</u> This means to multiply. The other key word is <u><em>is.</em></u><em> </em>This means equals most of the time.

If you have any questions feel free to ask in the comments. - Mark

4 0

3 years ago

A train travels 150 km in the same time that a plane covers 525 km. If the speed of the plane is 20 km per hr less than 4 times

babunello [35]

Answer:

Step-by-step explanation:

3 0

3 years ago

Two forces with magnitudes of 100 and 50 pounds act on an object at angles of 50° and 160°, respectively. Find the direction and

MatroZZZ [7]

<h2>Hello!</h2>

Since there is no additional information, we can assume that the given angles are respect to the horizontal axis (x), so

The answer is:

Magnitude: 95.14 lbs

Direction: 80° respect to the x-axis

Since there is no additional information about the given angles, we can assume that both angles are respect to the horizontal axis (x), positive direction to x-axis positive directions (right) and above x-axis.

<h2>Calculations:</h2>

100 pounds (lb) force, 50° angle:

$100lbs*cos(50)=64.28lbs\\100lbs*sin(50)=76.60lbs$

50 pounds (lb) force, 160° angle:

$50lbs*cos(160)=-46.98lbs\\50lbs*sin(160)=17.10lbs$

So,

For x-axis forces we have:

64.28lbs (positive direction)

-46.98lbs (negative direction)

Then,

$64.28lbs-46.98lbs=17.3lbs$ (positive direction)

Fox y-axis forces we have:

76.60lbs (positive direction)

17.10 lbs (positive direction)

Then,

$76.60lbs + 17.10 lbs =93.7lbs$ (positive direction)

So, we have the two components values of the acting force:

17.3 lbs for the x-axis and 93.7 lbs for the y-axis.

Therefore,

We have to calculate the angle between both resultant force components:

Let's calll it α

So,

$\alpha=tan^{-1}(\frac{y-axisValue}{x-axisValue})=tan^{-1}(\frac{93.7}{17.3})\\\alpha=79.5=80$

Hence, the angle between both resultant force components is 80 °, meaning that the resultant force direction is positive, above the x-axis.

Now we have to calculate the magnitude of the resultant force since the sum of both resultant force components is equal to the hypotenuse of the formed triangle, we have that:

$sin(\alpha)=\frac{y-axisValue}{ResultantForceMagnitude}=\frac{93.7lbs}{ResultantForceMagnitude}\\\\ResultantForceMagnitude=\frac{93.7lbs}{sin(80)}=95.14lbs$