All categories

4 years ago

Is 1, 1/2, 0, -1/2 an Arithmetic sequence? If so, what is the common difference?

Mathematics

2 answers:

Schach [20]4 years ago

6 0

Step-by-step explanation:

Yes, it is Arithmetic sequence

Because

1/2 - 1 = 0 - 1/2=-1/2-0= - 1/2

Common Difference d = - 1/2

Natalija [7]4 years ago

6 0

Answer:

-1/2

Step-by-step explanation:

1/2 - 1 = -1/2

0 - 1/2 = -1/2

-1/2 - 0 = -1/2

You might be interested in

How many colchicine tablets, each containing 600 mcg, may be prepared from 30 g of colchicine?

Leto [7]

Answer:

50,000 tablets may be prepared from 30g of colchicine

Step-by-step explanation:

This problem can be solved as a rule of three problem.

In a rule of three problem, the first step is identifying the measures and how they are related, if their relationship is direct of inverse.

When the relationship between the measures is direct, as the value of one measure increases, the value of the other measure is going to increase too.

When the relationship between the measures is inverse, as the value of one measure increases, the value of the other measure will decrease.

Unit conversion problems, like this one, is an example of a direct relationship between measures.

First Step:

The first step is knowing how many g are in a tablet.

Each gram has 1,000,000 mcg. So:

1g - 1,000,000 mcg

xg - 600 mcg

1,000,000x = 600

$x = \frac{600}{1,000,000} = 0.0006$

Each tablet has 0.0006g

Final step:

How many tablets may be prepared from 30g of colchicine?

1 tablet - 0.0006g

x tablets - 30g

0.0006x = 30

$x = \frac{30}{0.0006}$

x = 50,000

50,000 tablets may be prepared from 30g of colchicine

4 0

3 years ago

Scott fills a container with sugar using a bowl. The bowl hold 1/4 cup of sugar. Scott uses 8 full bowls to fill the container.

liraira [26]

Answer:

Container holds 2 cups of Sugar.

Step-by-step explanation:

Given:

Amount of Sugar bowl contains = $\frac{1}{4} \ cup$

Number of bowls container is filled with = 8

We need find the number of cups of sugar container holds.

Solution:

Now number of cups of sugar container holds can be calculated by Multiplying Amount of Sugar bowl contains with Number of bowls container is filled with.

framing in equation form we get;

number of cups of sugar container holds = $\frac{1}{4}\times8 = 2 \ cups$

Hence Container holds 2 cups of Sugar.

7 0

4 years ago

The height (feet) of an object moving vertically is given by s= (-16t^2)+(208t)+(156), where t is in seconds.

OverLord2011 [107]

Answer:

The object's velocity at t = 7 is -16 ft/s

The maximum height is 832 ft and it occurs when $t=\frac{13}{2}$

Step-by-step explanation:

From the information given, the equation of motion of the object is

$s(t)= -16t^2+208t+156$

For any equation of motion s(t), the instantaneous velocity at time t is given by

$v(t)=\frac{ds}{dt}$

(a) To find the object's velocity at t = 7, you must:

$v(t)=\frac{d}{dt}(-16t^2+208t+156)\\\\v(t)=-\frac{d}{dt}\left(16t^2\right)+\frac{d}{dt}\left(208t\right)+\frac{d}{dt}\left(156\right)\\\\v(t)=-32t+208+0\\\\v(t)=-32t+208$

Next, we evaluate when t = 7

$v(7)=-32(7)+208=-224+208\\\\v(7)=-16$

The object's velocity at t = 7 is -16 ft/s

(b) <em>To find the maximum of a function we always use the derivative of the function and we set it equal zero to find the</em><em> critical points.</em>

To find the maximum height and when it occurs, we set the velocity function equal to 0 and solve for t.

$-32t+208=0\\\\-32t+208-208=0-208\\\\-32t=-208\\\\\frac{-32t}{-32}=\frac{-208}{-32}\\\\t=\frac{13}{2}$

Next, we substitute this value into the equation of motion to find the maximum height

$s(\frac{13}{2})= -16(\frac{13}{2})^2+208(\frac{13}{2})+156\\\\s(\frac{13}{2})=-676+1352+156)=832$

The maximum height is 832 ft and it occurs when $t=\frac{13}{2}$

6 0

3 years ago

It costs $300 to join the new Superfit Gym.You then pay $15 each month and $2 each time you work out Carlo thinks he will use th

tankabanditka [31]

Answer:

Step-by-step explanation:

$15 x 12Mths = $180

2 x 20 = $40 carlo gets back

$300 + $180 = $480

$480 - 40 = $440 is what carlo will spend in one year

Saves $40 from getting $2 back every time he works out

5 0

3 years ago

11. An old machine requires three times as many hours to complete a job as

valentinak56 [21]

Answer:

Step-by-step explanation:

$9(r_n+r_o)=1\\ \\ r_n+r_o=\frac{1}{9}\\ \\ r_o=\frac{r_n}{3}\\ \\ r_n+\frac{r_n}{3}=\frac{1}{9}\\ \\ \frac{4r}{3}=\frac{1}{9}\\ \\ 4r=\frac{1}{3}\\ \\ r=\frac{1}{12}\\ \\ \text{So working alone it would take the new machine 12 hours to finish the job.}$

8 0

3 years ago