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3 years ago

Which of these are arithmetic sequences?

Mathematics

1 answer:

evablogger [386]3 years ago

5 0

A sequence of numbers is said to arithmetic if any couple of adjacent terms differ by the same number. That number is said to be the common difference of the sequence. Let's see what the differences are for each sequence:

First sequence

Difference between the first two terms:

$1 - (-3) = 4$

Difference between the third and second terms:

$5 - 1 = 4$

Difference between the fourth and third terms:

$9-5 = 4$

The difference is constant, so this sequence is an arithmetic sequence.

Second sequence

Difference between the first two terms:

$2 - 1 = 1$

Difference between the third and second terms:

$4-2 = 2$

The difference is not constant, so this sequence is not an arithmetic sequence.

Third sequence

Difference between the first two terms:

$-12 - 4 = -16$

Difference between the third and second terms:

$36 - (-12) = 36+12 = 48$

The difference is not constant, so this sequence is not an arithmetic sequence.

Fourth sequence

Difference between the first two terms:

$14 - 7 = 7$

Difference between the third and second terms:

$21 - 14 = 7$

Difference between the fourth and third terms:

$28 - 21 = 7$

The difference is constant, so this sequence is an arithmetic sequence.

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The decreasing population, p, of owls in a national park is being monitored by ecologists and is modeled by the equation p=−0.

n200080 [17]

By solving a quadratic equation, it can be verified that

The owl population will disappear after 329.12 years

What is a quadratic equation?

At first it is important to know about equation

Equation shows the equality between two algebraic expressions by connecting the two algebraic expressions by an equal to sign.

A two degree equation is known as quadratic equation.

Here, a quadratic equation needs to be solved

The decreasing population, p, of owls in a national park is being monitored by ecologists and is modeled by the equation p= $-0. 4t^2+128t+1,200$

For population to disappear, p =0

$-0. 4t^2+128t+1,200 = 0\\0.4t^2 -128t - 1200 = 0\\4t^2 - 1280t - 12000 = 0\\4(t^2 - 320 t - 3000) = 0\\t^2 - 320t -3000 = 0\\t = \frac{-(-320)\pm \sqrt{(-320)^2 - 4 \times 1 \times (-3000)}}{2 \times 1}\\t = \frac{320 \pm 338.23}{2}\\t = \frac{320 + 338.23}{2} \ or \ t = \frac{320 - 338.23}{2}\\t = 329.115 \ or \ t = -9.115$

But t = -9.115 is not possible as time cannot be negative

So, the owl population will disappear after 329.12 years

To learn more about quadratic equation, refer to the link-

brainly.com/question/1214333

#SPJ4

7 0

1 year ago

What is 3/2=9/10k im having troble lots rly

tigry1 [53]

Answer:

k= 5 over 3 =1.667

Step-by-step explanation:

Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :

(3)/(2)-((9)/(10)*k)=0

simplify 9/10

3 9

— - (—— • k) = 0

2 10

simplify 3/2

3 9k

— - —— = 0

2 10

Find the Least Common Multiple

The left denominator is : 2

The right denominator is : 10

Least Common Multiple:

Calculate multipliers for the two fractions

Denote the Least Common Multiple by L.C.M

Denote the Left Multiplier by Left_M

Denote the Right Multiplier by Right_M

Denote the Left Deniminator by L_Deno

Denote the Right Multiplier by R_Deno

Left_M = L.C.M / L_Deno = 5

Right_M = L.C.M / R_Deno = 1

Rewrite the two fractions into equivalent fractions

Two fractions are called equivalent if they have the same numeric value.

For example : 1/2 and 2/4 are equivalent, y/(y+1)2 and (y2+y)/(y+1)3 are equivalent as well.

To calculate equivalent fraction , multiply the Numerator of each fraction, by its respective Multiplier.

L. Mult. • L. Num. 3 • 5

—————————————————— = —————

L.C.M 10

R. Mult. • R. Num. 9k

—————————————————— = ——

L.C.M 10

Adding up the two equivalent fractions

Add the two equivalent fractions which now have a common denominator

Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:

3 • 5 - (9k) 15 - 9k

———————————— = ———————

10 10

Pull out like factors :

15 - 9k = -3 • (3k - 5)

-3 • (3k - 5)

————————————— = 0

When a fraction equals zero ...

Where a fraction equals zero, its numerator, the part which is above the fraction line, must equal zero.

Now,to get rid of the denominator, Tiger multiplys both sides of the equation by the denominator.

Here's how:

-3•(3k-5)

————————— • 10 = 0 • 10

Now, on the left hand side, the 10 cancels out the denominator, while, on the right hand side, zero times anything is still zero.

The equation now takes the shape :

-3 • (3k-5) = 0

Solve : -3 = 0

This equation has no solution.

A a non-zero constant never equals zero.

Solve : 3k-5 = 0

Add 5 to both sides of the equation :

3k = 5

Divide both sides of the equation by 3:

k = 5/3 = 1.667

one solution was found

k = 5/3 = 1.667

hope it helps sry its so long

7 0

3 years ago

A mountain bike has a diameter of 26 inches. To the nearest foot how far does the tire travel when it makes 32 revolutions?

Tcecarenko [31]

Hello!

You have to find the circumference

You use the equation

$2 \pi r$

r is radius which is half the diameter

This gives us 81.68

Multiply this by 32

81.68 * 32 = 2613.76

This is 217.8133333 feet

The answer is 217.8133 feet

Hope this helps!

8 0

2 years ago

Can u guys help me please with 5,6,7,8

iogann1982 [59]

An explanation for this is that a straight line has a angle degree value of 180. Therefore if you draw the line that creates a 139 degree angle, the rest of the line would have an angle measurement of what is left of the 180 degrees. So to get x you would start with the 180 degree straight line value and subtract the 139 degrees of the line that divides it. so equation is:
180 - 139 = x
And and you get 41 degrees.
(To word this another way the two angles of x and 139 have to add up to the straight line of 180 degrees. Therefore another equation could be:
139 + x = 180
which is basically the same equation but might be easier explanation for some to understand.)

questions 7 and 8 are the same but instead of straight line with 180 degrees, you start with right angle with 90 degrees. Therefore x and the 18 degree angle have to add up to 90 degrees making an equation of:
x + 18 = 90
Or
x = 90 - 18
answer would be
x = 7w

4 0

3 years ago

A drinking container is shaped like a cone and must hold at least 10 ounces of fluid. The radius of the top of the container is

Aleks04 [339]

9514 1404 393

Answer:

C. h ≥ 1.9 in

Step-by-step explanation:

As the final step, divide both sides of the inequality by 5.3:

(5.3h)/5.3 ≥ 10/5.3

h ≥ 1.9

6 0

2 years ago