Find the next 3 terms 3/4, 1/2, 1/4, 0

Larios filled her a 5 gallon jug with water. How many times can she fill her to 2- quart canteen with water from the jug?

marusya05 [52]

Answer:

10 times

Step-by-step explanation:

5 gallons = 20 quarts

20 quarts / 2 quarts = 10

4 0

3 years ago

What is the square root of -1?

Alchen [17]

Answer: √−1=i.

Step-by-step explanation: When we say that the square root of a negative number "doesn't exist", we mean that there is no real number solution. However, if we consider complex numbers, we then get a solution to √−1=i.

4 0

3 years ago

Read 2 more answers

Write out the first four terms of the series to show how the series starts. Then find the sum of the series or show that it dive

Nostrana [21]

Answer:

The first four terms of the series are

$(9+3),(\frac97+\frac35),(\frac9{7^2}+\frac3{5^2}),(\frac9{7^3}+\frac3{5^3})$

$\sum_{n=0}^\infty \frac9{7^n}+\frac{3}{5^n}$ = 14.25

Step-by-step explanation:

We know that

Sum of convergent series is also a convergent series.

We know that,

$\sum_{k=0}^\infty a(r)^k$

If the common ratio of a sequence |r| <1 then it is a convergent series.

The sum of the series is $\sum_{k=0}^\infty a(r)^k=\frac{a}{1-r}$

Given series,

$\sum_{n=0}^\infty \frac9{7^n}+\frac{3}{5^n}$

$=(9+3)+(\frac97+\frac35)+(\frac9{7^2}+\frac3{5^2})+(\frac9{7^3}+\frac3{5^3})+.......$

The first four terms of the series are

$(9+3),(\frac97+\frac35),(\frac9{7^2}+\frac3{5^2}),(\frac9{7^3}+\frac3{5^3})$

Let

$S_n=\sum_{n=0}^\infty \frac{9}{7^n}$ and $t_n=\sum_{n=0}^\infty \frac{3}{5^n}$

Now for $S_n$ ,

$S_n=9+\frac97+\frac{9}{7^2}+\frac9{7^3}+.......$

$=\sum_{n=0}^\infty9(\frac 17)^n$

It is a geometric series.

The common ratio of $S_n$ is $\frac17$

The sum of the series

$S_n=\sum_{n=0}^\infty \frac{9}{7^n}$

$=\frac{9}{1-\frac17}$

$=\frac{9}{\frac67}$

$=\frac{9\times 7}{6}$

=10.5

Now for $t_n$

$t_n= 3+\frac35+\frac{3}{5^2}+\frac3{5^3}+.......$

$=\sum_{n=0}^\infty3(\frac 15)^n$

It is a geometric series.

The common ratio of $t_n$ is $\frac15$

The sum of the series

$t_n=\sum_{n=0}^\infty \frac{3}{5^n}$

$=\frac{3}{1-\frac15}$

$=\frac{3}{\frac45}$

$=\frac{3\times 5}{4}$

=3.75

The sum of the series is $\sum_{n=0}^\infty \frac9{7^n}+\frac{3}{5^n}$

= $S_n+t_n$

=10.5+3.75

=14.25

4 0

3 years ago

Math 2 Homework Mod 2.1 (Day 2) Absolute Value Functions

Semenov [28]

The descriptions of the transformations are:

Vertex: (-6, 0)
Stretch factor: 2
Domain: set of all real numbers
Range: set of real numbers greater than or equal to 0

<h3>How to describe transformations, graph, and state domain & range using any notation?</h3>

The function is given as:

f(x) = -2|x + 6|

The above function is an absolute value function, and an absolute value function is represented as:

f(x) = a|x - h| + k

Where

Vertex = (h, k)

Scale factor = a

So, we have:

a = -2

(h, k) = (-6, 0)

There is no restriction to the input values.

So, the domain is the set of all real numbers

The y value in (h, k) = (-6, 0) is 0

i.e.

y = 0

Because the factor is negative (-2), then the vertex is a minimum

So, the range is all set of real numbers greater than or equal to 0

Hence, the descriptions of the transformations are:

Vertex: (-6, 0)
Stretch factor: 2
Domain: set of all real numbers
Range: set of real numbers greater than or equal to 0

Read more about absolute value function at

brainly.com/question/3381225

#SPJ1

4 0

1 year ago

Exercice 2: Un remorqueur tire un bateau à la vitesse de 10 noeuds. La tension du câble est de 2500N, Le câble est parallèle à l

Elza [17]

Répondre:

1 285 watts

Explication étape par étape:

La puissance est exprimée selon la formule;

power = travail effectué / temps

Puissance = Force * (distance / temps)

Depuis Vitesse = distance / temps

Puissance = Force * vitesse

Donné

Force = 2500N

Vitesse (en m / s) = 0,514 m / s

Obligatoire

Puissance

Remplacez la formule donnée;

Puissance = 2500 * 0,514

Puissance = 1,285Watts

Par conséquent, la puissance correspondante requise est de 1285 watts

5 0

3 years ago