5x + 2y = 7<br> 7x + 6y = -3<br> Please solve using elimination method.

It is known that the graph of the function y= x goes through the point A(4, −.5). Find k and plot its graph.

matrenka [14]

I will need to see a picture. I feel like I’m missing information.

5 0

3 years ago

A rumor spreads through a small town. Let y ( t ) be the fraction of the population that has heard the rumor at time t and assum

Ivan

Answer:

Differential equation

$\frac{dy}{dt} =ky(1-y)$

Solution

$y=\frac{1}{1+4e^{-0.327t}}$

Value of constant k=0.327 days^(-1)

The rumor reaches 80% at 8.48 days.

Step-by-step explanation:

We know

y(t): proportion of people that heard the rumor

y'(t)=ky(1-y), rate of spread of the rumor

Differential equation

$\frac{dy}{dt} =ky(1-y)$

Solving the differential equation

$\frac{dy}{y(1-y)}=k\cdot dt \\\\\int \frac{dx}{y(1-y)} =k \int dt \\\\-ln(1-\frac{1}{y} )+C_0=kt\\\\1-\frac{1}{y} =Ce^{-kt}\\\\\frac{1}{y} =1-Ce^{-kt}\\\\y=\frac{1}{1-Ce^{-kt}}$

Initial conditions:

$y(0)=0.2\\y(3)=0.4\\\\y(0)=0.2=\frac{1}{1-Ce^0}\\\\1-C=1/0.2\\\\C=1-1/0.2= -4\\\\\\y(3)=0.4=\frac{1}{1+4e^{-3k}} \\\\1+4e^{-3k}=1/0.4\\\\e^{-3k}=(2.5-1)/4=0.375\\\\k=ln(0.375)/(-3)=0.327\\\\\\y=\frac{1}{1+4e^{-0.327t}}$

Value of constant k=0.327 days^(-1)

At what time the rumor reaches 80%?

$y(t)=0.8=\frac{1}{1+4e^{-0.327t}} \\\\1+4e^{-0.327t}=1/0.8=1.25\\\\e^{-0.327t}=(1.25-1)/4=0.0625\\\\t=ln(0.0625)/(-0.327)=8.48$

The rumor reaches 80% at 8.48 days.

8 0

3 years ago

Help 20 ptssss asap !

ELEN [110]

Answer:

Assuming you want an equation, y = -4/3x - 1

Step-by-step explanation:

Formula is y = mx + b

m = slope= -4/3

b = y-intercept = -1

4 0

3 years ago

Can someone help me plz??

Brut [27]

Answer:

96π

Step-by-step explanation:

$v = \frac{1}{3} {r}^{2} h\pi$

V=96π

5 0

3 years ago

Does secondhand smoke increase the risk of a low weight birth? A baby is “low birth weight” if it weighs less than 5.5 pounds at

11111nata11111 [884]

Answer:

H0: p = 0.078

Ha: p ≠ 0.078

Step-by-step explanation:

The researchers say that the rate is about 7.8%, or 0.078 as a decimal. That makes that the null hypothesis because using "is" in math is the same as saying "equals" and the null hypothesis always has the statement of equality in it. The reason there is a not equals to sign in the alternate is for this reason as well. The researchers say it is about that amount, not more or less than that amount. So it makes this a 2 tailed test. If the amount is significantly higher or lower, then we might have to reject the null hypothesis depending on the outcome of the test.

7 0

3 years ago

5x + 2y = 7 7x + 6y = -3 Please solve using elimination method.