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3 years ago

Can someone help me solve this and explain how to solve if possible please?

Mathematics

1 answer:

DIA [1.3K]3 years ago

4 0

The length of road is the range and the time
in days is the domain. Any measure of time, like years, days, minutes will always be the independent variable, D. What does it mean by set of values?

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Determine if the following infinite series converges or diverges

Mandarinka [93]

Using limits, it is found that the infinite sequence converges, as the limit does not go to infinity.

<h3>How do we verify if a sequence converges of diverges?</h3>

Suppose an infinity sequence defined by:

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

Then we have to calculate the following limit:

$\lim_{k \rightarrow \infty} f(k)$

If the <u>limit goes to infinity</u>, the sequence diverges, otherwise it converges.

In this problem, the function that defines the sequence is:

$f(k) = \frac{k^3}{k^4 + 10}$

Hence the limit is:

$\lim_{k \rightarrow \infty} f(k) = \lim_{k \rightarrow \infty} \frac{k^3}{k^4 + 10} = \lim_{k \rightarrow \infty} \frac{k^3}{k^4} = \lim_{k \rightarrow \infty} \frac{1}{k} = \frac{1}{\infty} = 0$

Hence, the infinite sequence converges, as the limit does not go to infinity.

More can be learned about convergent sequences at brainly.com/question/6635869

#SPJ1

6 0

1 year ago

Read 2 more answers

Your take home pay is $1500 and you have 22% withheld in taxes. What is your gross pay?

wlad13 [49]

We have been given that the take home pay is $1500 and 22% is withheld as taxes.

Let us assume that the gross pay is x dollars. Therefore, take home pay must be 78% of x because 22% of the pay is withheld as taxes, so you get to take home only 78% of the gross pay.

Since we have been given that take home pay is $1500 and it is 78% of the total gross pay. Therefore, we can set up an equation:

$78\%\text{ of }x=1500\\\frac{78}{100}x=1500\\0.78x=1500\\x=\frac{1500}{0.78}\\x=\$1923.08$

Therefore, gross pay is $1923.08

5 0

2 years ago

Read 2 more answers

Can someone please help with the last problem

Brut [27]

Answer:

18x +9h

Step-by-step explanation:

Such problems are tedious, but not difficult. The trick is to avoid making mistakes in the algebra.

$\dfrac{f(x+h)-f(x)}{h}=\dfrac{(9(x+h)^2)-(9x^2)}{h}\\\\=\dfrac{9(x^2+2xh+h^2)-9x^2}{h}=\dfrac{18xh+9h^2}{h}=\boxed{18x+9h}$

3 0

2 years ago

A rectangle an an area of 30 square meters anda has dimensionsperimeter of 34 meters. What are the of the rectangle

vazorg [7]

The sides of the rectangle are:
xy = 39
2x + 2y

Solve by simultaneous equation:
ysquared -17y + 30 = 0

Solution:
The sides are equal to 15 and 2

6 0

2 years ago

The number of kilograms of water in a human body varies directly as the mass of the body. An 87-kg person contains 58 kg of wat

katen-ka-za [31]

Answer:

50 kg water.

Step-by-step explanation:

We have been given that the number of kilograms of water in a human body varies directly as the mass of the body.

We know that two directly proportional quantities are in form $y=kx$ , where y varies directly with x and k is constant of variation.

We are told that an 87-kg person contains 58 kg of water. We can represent this information in an equation as:

$58=k\cdot 87$

Let us find the constant of variation as:

$\frac{58}{87}=\frac{k\cdot 87}{87}$

$\frac{29*2}{29*3}=k$

$\frac{2}{3}=k$

The equation $y=\frac{2}{3}x$ represents the relation between water (y) in a human body with respect to mass of the body (x).

To find the amount of water in a 75-kg person, we will substitute $x=75$ in our given equation and solve for y.

$y=\frac{2}{3}(75)$

$y=2(25)$

$y=50$

Therefore, there are 50 kg of water in a 75-kg person.

3 0

3 years ago