4. A runner 1600 meters in 4 minutes. What was his rate of speed? *

Answers

Answer 1

400 meters per minute

400m/s

Related Questions

Which represent geometric sequences? A marathon runner runs half of a race, then runs half the distance left to the finish line, then runs half the distance that still remains, and so on. The first movie rental costs $2, and each additional rental costs $1. 10, 1, 0.1, 0.01, … –4, 20, –100, 500, … –1, 5, 11, 17, 23, …

Answers

Answer:

Step-by-step explanation:

1). Let the length of a marathon race = x miles

Marathon runner runs this race in the sequence formed as,

[tex]\frac{x}{2},\frac{x}{4},\frac{x}{8}.........[/tex]

Common ratio = [tex]\frac{\frac{x}{4}}{\frac{x}{2}}[/tex]

= [tex]\frac{x}{4}\times \frac{2}{x}[/tex]

= [tex]\frac{1}{2}[/tex]

Therefore, it's a geometric sequence.

2). First movie rental cost = $2

Followed by each additional movie rental cost = $1

Therefore, rental of movies will be in the form of a linear equation,

y = 2x + 1

where x = number of movies

And y = Rental of movies

It's not a geometric sequence.

3). 10, 1, 0.1, 0.01.......

Ratio in 2nd and 1st term = [tex]\frac{1}{10}=0.1[/tex]

Ratio in 3rd and 2nd term = [tex]\frac{0.1}{1}=0.1[/tex]

Therefore, ratio in each term is common.

Sequence formed will be a geometric sequence.

4). [tex]\sum_{k=1}^{7}4(0.2)^{k-1}[/tex]

Expression represents a common ratio of 0.2,

Therefore, expression given will represent a geometric sequence.

5). -4, 20, -100, 500, ...........

Ratio of 2nd and 1st term = [tex]\frac{20}{-4}[/tex] = -5

Ratio of 3rd and 2nd term = [tex]\frac{-100}{20}[/tex]

= -5

There is a common ratio = -5

Therefore, it's a geometric sequence.

6). -1, 5, 11, 17.........

Ratio of 2nd and 1st term = [tex]\frac{5}{-1}=-5[/tex]

Ratio of 3rd and 2nd term = [tex]\frac{11}{5}=2.2[/tex]

-5 ≠ 2.2

Therefore, sequence is not a geometric sequence.

7). -500, 100, -20, 4........

Ratio of 2nd and 1st term = [tex]\frac{100}{-500}=-\frac{1}{5}[/tex]

Ratio of 3rd and 2nd term = [tex]\frac{-20}{100}=-\frac{1}{5}[/tex]

Answer:

I agree with person above

Step-by-step explanation:

how many natural number n is the function 5n^2-9/2n+6 also a natural number?

Answers

The function (5n² - 9) / (n + 3) is a natural number for n = 3 and n = 15.

A function is given which is (5n² - 9) / (2n + 6).

We have to find the value of natural number n for which the given function is also natural number.

What do you mean by natural numbers ?

Natural numbers are known as the counting numbers which starts from 1 and end at infinity and also includes the whole numbers excluding 0.

As per the question ;

(5n² - 9) / (2n + 6) is a natural number for the value of n which is also a natural number.

Let's assume ;

(5n² - 9) / (2n + 6) = k

(5n² - 9) / (n + 3) = 2k

So , we can say that (5n² - 9) / (n + 3) is an even number.

We know that ;

Dividend ÷ Divisor = Quotient

If we divide (5n² - 9) by (n + 3) we will get ;

Quotient = 5n - 15

and

Remainder = 36

We can write it as ;

(5n² - 9) ÷ (n + 3) = (5n - 15) + {36 / (n+ 3)}

Here ;

36 / (n+ 3) is a natural number and n is a natural number.

Assume ;

n = 1 , 3 , 6 , 9 , 15 , 33

Let's check ;

for n = 1 ;