-2/3 divided by 5/4 in simplified form, in a fraction

A student worked out at a gym continuously from 70 minutes. The graph shoes the remaining percentage of the workout as a linear

eduard

Answer: the first answer

Step-by-step explanation: sorry i know it would’ve been better if i typed it but i’m running out of charge so it would be you first answer. this is because domain shows the minimum and maximum values x can be and range is the same but for y. the second and third functions aren’t in any format that i’ve learned before and it’s closest to interval notation which can be written as [min,max] with parentheses if it doesn’t touch those values. but yeah i hope this helped and i’m sorry if it is incorrect. good luck!

7 0

4 years ago

Let P(t) be a population at time t. A simple population model supposes the rate of growth of the population is proportional to t

jeka94

Answer:

$(a) \dfrac{dP}{dt} =k P(t)\\(b)P(t)=Ce^{kt}$

(c) $P(10)\approx 272$

(ii) $P(1000)\approx 26.88 \times 10^{44}\\$

Step-by-step explanation:

(a)The rate of growth of the population is proportional to the population, this is written as:

$\dfrac{dP}{dt} \propto P(t)\\$Introducing our proportionality constant, k\\ \dfrac{dP}{dt} =k P(t)$

(b)

$\dfrac{dP(t)}{P(t)} =k dt\\$Take the integral of both sides\\\int \dfrac{dP(t)}{P(t)} =\int k dt\\\ln P(t)=kt+C, $C a constant of integration\\Take the exponential of both sides\\e^{\ln P(t)}=e^{kt+C}\\P(t)=e^{kt}\cdot e^C $, (Since e^C$ is a constant, we then have:)\\P(t)=Ce^{kt}$

(c)

Suppose the net birthrate of the population is .1, and the initial population is 100.

k=0.1

P(0)=100

Substitution into P(t) gives:

$100=Ce^{kX0}$

C=100

Therefore:

$P(t)=100e^{0.1t}$

(i)When t=10

$P(10)=100e^{0.1 \times 10}\\=271.8\\\approx 272$

(ii)When t=1000

$P(1000)=100e^{0.1 \times 1000}\\=26.88 \times 10^{44}\\$

8 0

4 years ago

Evaluate the following.<br> 3x9+ 20 = 4-8

Vinil7 [7]

Step-by-step explanation:

27+20=4-8

47=4-8

47=-4

3 0

4 years ago

Find the eleventh term of the last term of A.P.<br> 27,23,19,.....-65.

myrzilka [38]

The term to term rule is to subtract 4

Term 1 = 27
Term 2 = 27 - 4 = 23
Term 3 = 23 - 4 = 19
Term 4 = 19 - 4 = 15
Term 5 = 15 - 4 = 11
Term 6 = 11 - 4 = 9
Term 7 = 9 - 4 = 5
Term 8 = 5 - 4 = 1
Term 9 = 1 - 4 = -3
Term 10 = -3 - 4 = -7
Term 11 = -7 - 4 = -11

The eleventh term = -11

3 0

4 years ago

Round to the nearest hundredth 5/8

Solnce55 [7]

Eighths and their multiples are common fractions which I recommend memorizing, but to actually solve this, you use the literal meaning of a fraction and divide 5 by 8. See the long-division below (it was surprisingly difficult to type, so I hope it helps!).

To round 0.625 to the nearest hundredth, we go to the second decimal place, which is 5, so we round up to 0.63.

3 0

3 years ago