Topic 6 Online Assessment

Mathematics

1 answer:

spin [16.1K]3 years ago

7 0

Answer:

ok but where is the question

Step-by-step explanation:

You might be interested in

The population of a country grows exponentially at a rate of 1% per year. If the population was 35.7 million in the year 2010, t

Lady_Fox [76]

Answer:

37.52 million

Step-by-step explanation:

using,

A = A'(1+R/100)ⁿ............................. equation 1

Where A = population size in 2015, A' = Initial population, R = rate in percentage, n = number of times between 2010 and 2015.

Given: A' =35.7 million, R = 1%, n = 5.

Substitute these values into equation 1

A = 35.7(1+0.01)⁵

A = 37.52 million.

Hence the size of the population of the country in the year 2015 is 37.52 million

7 0

3 years ago

Find the roots of h(t) = (139kt)^2 − 69t + 80

Sonbull [250]

Answer:

The positive value of $k$ will result in exactly one real root is approximately 0.028.

Step-by-step explanation:

Let $h(t) = 19321\cdot k^{2}\cdot t^{2}-69\cdot t +80$ , roots are those values of $t$ so that $h(t) = 0$ . That is:

$19321\cdot k^{2}\cdot t^{2}-69\cdot t + 80=0$ (1)

Roots are determined analytically by the Quadratic Formula:

$t = \frac{69\pm \sqrt{4761-6182720\cdot k^{2} }}{38642}$

$t = \frac{69}{38642} \pm \sqrt{\frac{4761}{1493204164}-\frac{80\cdot k^{2}}{19321} }$

The smaller root is $t = \frac{69}{38642} - \sqrt{\frac{4761}{1493204164}-\frac{80\cdot k^{2}}{19321} }$ , and the larger root is $t = \frac{69}{38642} + \sqrt{\frac{4761}{1493204164}-\frac{80\cdot k^{2}}{19321} }$ .

$h(t) = 19321\cdot k^{2}\cdot t^{2}-69\cdot t +80$ has one real root when $\frac{4761}{1493204164}-\frac{80\cdot k^{2}}{19321} = 0$ . Then, we solve the discriminant for $k$ :