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4 years ago

What is the value of p+q

Mathematics

1 answer:

Korvikt [17]4 years ago

6 0

$ax^2+bx+c=0\\\\x_1,\ x_2-solutions\\\\x_1+x_2=\dfrac{-b}{a}\\--------------------------\\\\4x^2-7x-2=0\\\\a=4,\ b=-7,\ c=-2\\\\p,\ q-solutions\\\\p+q=\dfrac{-(-7)}{4}=\dfrac{7}{4}$

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Which equation represents the line with slope 1/4 that passes through (-4, 8)?

RoseWind [281]

Answer

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Step-by-step explanation:

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3 years ago

During optimal conditions, the rate of change of the population of a certain organism is proportional to the population at time

Lana71 [14]

Answer:

The population is of 500 after 10.22 hours.

Step-by-step explanation:

The rate of change of the population of a certain organism is proportional to the population at time t, in hours.

This means that the population can be modeled by the following differential equation:

$\frac{dP}{dt} = Pr$

In which r is the growth rate.

Solving by separation of variables, then integrating both sides, we have that:

$\frac{dP}{P} = r dt$

$\int \frac{dP}{P} = \int r dt$

$\ln{P} = rt + K$

Applying the exponential to both sides:

$P(t) = Ke^{rt}$

In which K is the initial population.

At time t = 0 hours, the population is 300.

This means that K = 300. So

$P(t) = 300e^{rt}$

At time t = 24 hours, the population is 1000.

This means that P(24) = 1000. We use this to find the growth rate. So

$P(t) = 300e^{rt}$

$1000 = 300e^{24r}$

$e^{24r} = \frac{1000}{300}$

$e^{24r} = \frac{10}{3}$

$\ln{e^{24r}} = \ln{\frac{10}{3}}$

$24r = \ln{\frac{10}{3}}$

$r = \frac{\ln{\frac{10}{3}}}{24}$

$r = 0.05$

$P(t) = 300e^{0.05t}$

At what time t is the population 500?

This is t for which P(t) = 500. So

$P(t) = 300e^{0.05t}$

$500 = 300e^{0.05t}$

$e^{0.05t} = \frac{500}{300}$

$e^{0.05t} = \frac{5}{3}$

$\ln{e^{0.05t}} = \ln{\frac{5}{3}}$

$0.05t = \ln{\frac{5}{3}}$

$t = \frac{\ln{\frac{5}{3}}}{0.05}$

$t = 10.22$

The population is of 500 after 10.22 hours.

7 0

3 years ago

Factor.<br><br> <img src="https://tex.z-dn.net/?f=%2036t%5E%7B2%7D%20" id="TexFormula1" title=" 36t^{2} " alt=" 36t^{2} " align=

HACTEHA [7]

36t² - 1 =
(6t)² - 1² =
(6t-1)(6t+1)

6 0

3 years ago

Read 2 more answers

Question down below. Thank you

Ann [662]

Answer:

N/A.

Step-by-step explanation:

I will not answer your question and I will be flagging it due to you adding a test/exam question.

8 0

3 years ago

At the shorter waterfall, water falls uninterrupted for 1552 feet before entering the river below. The height h above the river

qwelly [4]

Answer:

Step-by-step explanation:

First note that the river is on the ground level. The height of the river at the ground level is 0

Given the the height h above the river in feet of water going over the edge of the waterfall is modeled by h(t)=-16t^2+1552

When h = 0

0 = -16t^2+1552

16t^2 = 1552

t² = 1552/16

t² = 97

t = √97

<em>Hence the time it takes is 9.9secs to the nearest tenth</em>

8 0

3 years ago