What factors would best account for the rise in population in 1850

Pratap puri rowed 10 miles down a river in 2 hours, but the return trip took him 2 and one half hours. Find the rate pratap can

N76 [4]

Answer:

Rate of Pratap in still water is 4.5 miles/hour and rate of current is 0.5 miles/hour.

Step-by-step explanation:

Pratap Puri rowed 10 miles down a river in 2 hours, but the return trip took him 2.5 hours.

We know that, $Speed = \frac{Distance}{Time}$

So, the speed of Pratap with the current will be: $(\frac{10}{2})miles/hour = 5$ miles/hour

and the speed of Pratap against the current will be: $(\frac{10}{2.5})miles/hour = 4$ miles/hour.

Suppose, the rate of Pratap in still water is $x$ and the rate of current is $y$ .

So, the equations will be........

$x+y= 5 .............................. (1)\\ \\ x-y=4 .............................. (2)$

Adding equation (1) and (2) , we will get......

$2x=9\\ \\ x=\frac{9}{2}= 4.5$

Now, plugging this $x=4.5$ into equation (1), we will get.....

$4.5+y=5\\ \\ y=5-4.5 =0.5$

Thus, Pratap can row at 4.5 miles per hour in still water and the rate of the current is 0.5 miles/hour.

6 0

3 years ago

Complete the square to make a perfect square trinomial. Then, write the result as a binomial squared. n^2-4n/3

ololo11 [35]

Answer:

(n- 2/3)²

Step-by-step explanation:

Perfect square trinomial is: a²+2ab+b²= (a+b)²

We have:

n² - 4n/3

It can be put as:

n² -2×n×2/3

Here we consider n = a and -2/3 = b, then

b²= (-2/3)²= 4/9

Now we add 4/9 to a given binomial to make it perfect square:

n² - 2×n×3/2 + 4/9= (n- 2/3)²

So, added 4/9 and got a perfect square (n- 2/3)²

7 0

3 years ago

Show why x−3 is a factor of m(x)=x3−x2−5x−3. Justify your answer. You can show this using remainder theorem, long division, synt

Marat540 [252]

The factors of a polynomial function are the zeros of the function

It is true that x - 3 is a factor of m(x) = x^3 - x^2 - 5x - 3

<h3>How to show why the x - 3 is a factor</h3>

The function is given as:

m(x) = x^3 - x^2 - 5x - 3

The factor is given as:

x - 3

Set the factor to 0

x - 3 = 0

Solve for x

x = 3

Substitute 3 for x in the function

m(3) = 3^3 - 3^2 - 5(3) - 3

Evaluate

m(3) =0

Since the value of m(3) is 0, then x - 3 is a factor of m(x) = x^3 - x^2 - 5x - 3