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2 years ago

Write the following equation in slope-intercept form. State the slope and y-intercept.

Mathematics

1 answer:

posledela2 years ago

3 0

Answer:

y = -2x-7/9

Step-by-step explanation:

Slope-intercept form is y=mx+b where m is the slope and b is the y intercept. Start by solving for y.

-18x-9y=7

-9y=18x+7 (divide through by -9)

y=-2x-7/9

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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 me pls thank you alot!

damaskus [11]

Your answer will be -1/7

4 0

3 years ago

Read 2 more answers

What is the value of x?<br> 3(-9 - 4x) - 4= 8x - 9(x + 12)

Gemiola [76]

Answer:

x=7

Step-by-step explanation:

uhhh yes

5 0

3 years ago

Read 2 more answers

PLEASE HELP ASAP!!! CORRECT ANSWER ONLY PLEASE!!!

bearhunter [10]

No fewer than four female volunteers: x≥ 4.

A comedian needs up to ten volunteers: x+y ≤10.

y≥0

5 0

3 years ago

QUICK HELP ME! seven children in a family like apples, 6 children like bananas, and 5 children like peaches. four children like

il63 [147K]

9514 1404 393

Answer:

Step-by-step explanation:

1 child likes all three

4 like apples and bananas, so 4-1 = 3 like apples and bananas only

3 like apples and peaches, so 3-1 = 2 like apples and peaches only

2 like peaches and bananas, so 2-1 = 1 like peaches and bananas only

7 like apples, but 3+2+1 like one or more other fruits, so 1 likes apples only

6 like bananas, but 3+1+1 like one or more other fruits, so 1 likes bananas only

5 like peaches, but 2+1+1 like one or more other fruits, so 1 likes peaches only

1 + 1 + 1 = 3 like exactly 1 fruit;

3 + 2 + 1 = 6 like exactly 2 fruits;

1 likes exactly 3 fruits.

The total number of children is 3 + 6 + 1 = 10.

Assuming all the referenced children are in the family, there are 10 children in the family.

5 0

3 years ago