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alexandr1967 [171]
3 years ago
15

What is the sum of the geometric series 2+6+18+...+486?

Mathematics
1 answer:
marin [14]3 years ago
6 0

Answer:

728

Step-by-step explanation:

2+6+18+...+486

a=2

r=6/2=3

a_{n}=ar^{n-1}\\486=2(3)^{n-1}\\3^{n-1}=486/2=243=3^5\\n-1=5\\n=5+1=6\\S_{6}=2\frac{3^6-1}{3-1} \\=2\frac{729-1}{2}\\=728

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An otter is swimming at - 4.2yo relative to the surface of the water. It dives 6.0 yds desper. After thedive, what is the otter'
k0ka [10]

Answer:

Where to look: Any waterway you’re near! River otters are happy in fresh, brackish and salt water. They’re often seen in coastal areas near the mouths of rivers and creeks. They’re often seen in marshes and wetlands. They’re a little harder to see in vegetated rivers but keep looking, especially when boating. They’re often found in lakes…look where the fish are. In-crowd hint: Check out our otter spotter map to see where they’re often reported!

 

When to look: River otters are most often seen at dusk and dawn, but can be seen at any hour of the day or night.

 

What do I look for? Look for large ripples on the surface of the water, lots of bubbles and a 3 to 4 foot-long animal with a long thick tail. The tail is about a third of the body length of the otter. Otters are dark and sleek in the water. Otters have a large black hairless nose (rhinarium).

 

How do otters swim and move? In the water, river otters do not swim on their backs like sea otters. They can swim along with just their heads showing, they can dive and roll and they often stay underwater for up to 15 or 20 seconds. They also “periscope,” meaning raise their necks far out of the water to see farther. When swimming, they usually carry their bodies just under the surface. They’re very elusive and can “disappear,” into the water, brush, rocks or under overhanging vegetation.

 

On land, river otters are agile, can run quickly and climb trees. They’re small and narrow-bodied, with longer back legs than forelegs, so they move with a humping gait. They’re often seen running across beaches, or along paths near water.

 

There’s a superb Otter/Beaver/Muskrat article with photos and descriptions here.  

SEA OTTER (Enhydra lutris)

In California, sea otters are most often seen around Monterey Bay and Elkhorn Slough. Occasionally we see them in the SF Bay Area. Sea otters are twice the size of river otters, and are never far from the ocean. They have enormous back flippers, and often swim on their backs with their big flippers sticking out of the water. Their tails are short and not as muscular as river otters. They are clumsy on land.

This video by Tom Reynolds shows sea otters first, then river otters. The differences will become obvious!

MUSKRAT (Ondatra zibethicus)

Muskrats are rodents, about 18 inches long, with a thin tail. Like beavers, they swim straight across the water, with their backs at or slightly above water level, without diving and rolling, until it’s time to submerge.

Typical muskrat swimming; note the thin long tail.

Here’s a nice muskrat video.

BEAVER (Castor canadensis)

Beavers are rodents with large orange teeth. They have a very distinctive large, flat tail which slaps the water when they’re startled. Beavers are burly animals, and weigh about twice as much as river otters. Their fur is clumpy when wet. Like muskrats, their bodies are usually at or slightly above water level when they swim.

Here’s a gorgeous beaver, look at that tail!

Here’s our friend Heidi of Worth A Dam in a wonderful video showing the difference between otters and beavers.

HARBOR SEAL (Phoca vitulina)

Harbor seals are seen in the ocean, bays and marshes. They’re quite fat-looking, because they carry a large layer of fat on their bodies to keep them warm in cold waters. Harbor seals have very large heads and big dark eyes. They startle easily, and dive under water with an enormous splash if you surprise them while kayaking. They’re grayish, with mottled fur, sometimes paler gray toward white.

Here’s a fascinating video of a river otter protecting its prey from a curious harbor seal. Many thanks to the Sonoma County Water Agency for sharing with us!

Step-by-step explanation:

3 0
3 years ago
Identify the quadratic function from the four functions
Alchen [17]

Quadratic Function is a function that takes the equation form of:

\large \boxed{y = a {x}^{2}  + bx + c}

where a ≠ 0. However the form of Quadratic Function above can also be called "standard form" or general form because it is commonly used when defining the function. Quadratic Functions also have other two forms which are intercept form and vertex form.

<u>Vertex</u><u> </u><u>Form</u>

\large \boxed{y = a {(x - h)}^{2}  + k}

<u>Intercept</u><u> </u><u>Form</u>

\large \boxed{y = (ax - b)(bx - c)}

The intercept form can be expressed as y = (x-a)(x-b) depending on the other perspective.

If you look at all four functions, you will notice that only two of functions have the second degree as highest degree while the third function has third degree as highest and fourth function has fourth degree. Recall the definition of Quadratic Function above that the highest degree of Quadratic Function can only be second degree (squared, x² as example). Therefore we can rule out the x³ and -2x⁴ away.

So our only quadratic functions are:

\large{ \begin{cases}y =  -  {x}^{2}  - 4 \\ y =  {(x - 1)}^{2}  - 7 \end{cases}}

As for the f(x) = -x²-4. The equation is in standard form which is y = ax²+bx+c. The second equation is in vertex form which is y = a(x-h)²+k.

Answer

  • The only quadratic functions are f(x) = -x²-4 and f(x) = (x-1)²-7
  • -x²-4 is in standard form.
  • (x-1)²-7 is in vertex form.

Hope this helps and let me know if you have any doubts.

<em>Als</em><em>o</em><em> </em><em>let</em><em> </em><em>me</em><em> </em><em>know</em><em> </em><em>if</em><em> </em><em>you</em><em> </em><em>want</em><em> </em><em>me </em><em>t</em><em>o</em><em> </em><em>convert</em><em> </em><em>the</em><em> </em><em>function</em><em> </em><em>into</em><em> </em><em>other</em><em> </em><em>form</em><em>.</em><em> </em><em>For</em><em> </em><em>ex</em><em>.</em><em> </em><em>convert</em><em> </em><em>the</em><em> </em><em>vertex</em><em> </em><em>form</em><em> </em><em>to</em><em> </em><em>standard</em><em> </em><em>form</em><em>.</em><em> </em>

Happy Learning and Good Luck with your assignment!

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3 years ago
Figure out what the percent is
DaniilM [7]

The percentage of data that is roughly greater than 66, as displayed in the box plot, is 100%.

<h3>How to Determine a Percentage of a Data Represented in a Box Plot?</h3>

In a box plot, we have the following displayed five-number summary which tells what percentage of the data distribution for each part of the data distribution:

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Lower quartile (Q3): This is the value at where the box in the box plot starts at the edge of the box. From this point to the left, all data values that fall within the bracket make up 25% of the data.

Median: this is the middle value at the point where the line divides the box and data below this point make up 50% of the data.

The other five-number summary are the maximum and the minimum values that are represented by the whiskers.

On the box plot given, 66 is at the extreme whisker at the left. This means that the percentage of data that is roughly greater than 66 is 100%.

Learn more about the box plot on:

brainly.com/question/14277132

#SPJ1

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Naily [24]
Wat y'all must don't no what it is. what grade is y'all in but I need help in some of my stuff
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3 years ago
Fifteen more than four times a number is equal to the difference between 191 and four times the number. Find the number.
Semenov [28]

Answer:

The number would be 22.

Step-by-step explanation:

In order to solve for the number, we need to make both statements into numerical statements.

Fifteen more than four times a number = 15 + 4x

difference between 191 and four times the number = 191 - 4x

Now we set them equal to each other.

15 + 4x = 191 - 4x -----> Add 4x to each side

15 + 8x = 191 ------> Subtract 15 from both sides

8x = 176 -------> Divide by 8

x = 22

5 0
3 years ago
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