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3 years ago

Write an equation of the line that passes me that passes through (2,-5) and is parrallel to the line 2y=3x+10

Mathematics

1 answer:

Otrada [13]3 years ago

7 0

Step-by-step explanation:

parallel means same slope/gradient

2y = 3x + 10

y = 1.5x + 5

let equation be y = 1.5x + b

sub (2, -5)

-5 = 1.5(2) + b

b = -8

therefore y = 1.5x - 8

Topic: Coordinate Geometry

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Solve each of the following equations. Be make sure to check your solutions. Solve for part b only.

Alona [7]

Answer:

or, 3x-5=2.5x+3-x+4

or, 3x-1.5x=7+5

or, 2.5x=12

or, x=4.8 solved.

3 0

3 years ago

The rate of change of the number of mountain lions N(t) in a population is directly proportional to 725 - N(t), where t is the t

wolverine [178]

Answer:

a) The implied differential equation is $\frac{dN}{725 - N} = kdt$

b) The general equation is $N = 725 - C e^{-kt}$

c) The particular equation is $N = 725 - 325 e^{-0.49t}$

d) The population when t = 5, N(5) = 697 = 700( to the nearest 50)

Step-by-step explanation:

The rate of change of N(t) can be written as dN/dt

According to the question, $\frac{dN}{dt} \alpha (725 - N(t))$

$\frac{dN}{dt} = k (725 - N)\\\frac{dN}{725 - N} = kdt$

Integrating both sides of the equation

$\int {\frac{1 }{725 - N}} \, dN = \int {k} \, dt\\- ln (725 - N) = kt + C\\ ln (725 - N) = -(kt + C)\\725 - N = e^{-(kt + C)} \\725 - N = e^{-kt} * e^{-C} \\725 - N = C e^{-kt}\\N = 725 - C e^{-kt}$

When t = 0, N = 400

$400 = 725 - C e^{-k*0}\\400 = 725 - C\\C = 725 - 400\\C = 325$

When t = 3, N = 650

$650 = 725 - (325 * e^{-3k})\\325 * e^{-3k} = 75\\e^{-3k} = 75/325\\e^{-3k} = 0.23\\-3k = ln 0.23\\-3k = -1.47\\k = 1.47/3\\k = 0.49$

The equation for the population becomes:

$N = 725 - 325 e^{-0.49t}$

At t = 5, the population becomes:

$N = 725 - 325 e^{-0.49*5}\\N = 725 - 325 e^{-2.45}\\N = 696.95\\N(5) = 697$

N(5) = 700 ( to the nearest 50)

6 0

3 years ago

How do you solve log x = 4?

antoniya [11.8K]

In order to solve this, We will want to change it into an exponential form. Assuming that since we do not have a number beside log, It will be log base 10.

10^4=x

We can now solve for x.

This means that x= 10,000

4 0

3 years ago

Read 2 more answers

Please help .-.<br> No absurd answers

VARVARA [1.3K]

Answer:

64 ft²

Step-by-step explanation:

10 ft · 10 ft

100 ft²

$A=\frac{bh}{2}$