All categories

3 years ago

Solve for r. (-3,r) and (2,14) m = 5

Mathematics

1 answer:

Jobisdone [24]3 years ago

3 0

Answer:

r = -11

Step-by-step explanation:

14-r ÷ [2-(-3)] = 5

cross-multiply:

14-r = 5*5

14-r = 25

-r = 11

r = -11

You might be interested in

What is the equation of the axis of symmetry

Elena L [17]

I believe it would be x=2 because if you graph x=2 it creates a vertical line through the parabola

8 0

3 years ago

What are the correct steps for solving the equation 9x^2=108? A. X^2= 99

Georgia [21]

Answer:

x=sqrt of 12

Step-by-step explanation:

First, you divide by 9 on both sides:

x^2= 108/9

Then you solve that:

x^2 = 12

Then you find the root of both sides:

sqrt (x^2)= sqrt (12)

and you get:

x= sqrt of 12 which is about 3.46... OR 2√3

5 0

3 years ago

Write down the explicit solution for each of the following: a) x’=t–sin(t); x(0)=1

Kay [80]

Answer:

a) x=(t^2)/2+cos(t), b) x=2+3e^(-2t), c) x=(1/2)sin(2t)

Step-by-step explanation:

Let's solve by separating variables:

$x'=\frac{dx}{dt}$

a) x’=t–sin(t), x(0)=1

$dx=(t-sint)dt$

Apply integral both sides:

$\int {} \, dx=\int {(t-sint)} \, dt\\\\x=\frac{t^2}{2}+cost +k$

where k is a constant due to integration. With x(0)=1, substitute:

$1=0+cos0+k\\\\1=1+k\\k=0$

Finally:

$x=\frac{t^2}{2} +cos(t)$

b) x’+2x=4; x(0)=5

$dx=(4-2x)dt\\\\\frac{dx}{4-2x}=dt \\\\\int {\frac{dx}{4-2x}}= \int {dt}\\$

Completing the integral:

$-\frac{1}{2} \int{\frac{(-2)dx}{4-2x}}= \int {dt}$

Solving the operator:

$-\frac{1}{2}ln(4-2x)=t+k$

Using algebra, it becomes explicit:

$x=2+ke^{-2t}$

With x(0)=5, substitute:

$5=2+ke^{-2(0)}=2+k(1)\\\\k=3$

Finally:

$x=2+3e^{-2t}$

c) x’’+4x=0; x(0)=0; x’(0)=1

Let $x=e^{mt}$ be the solution for the equation, then:

$x'=me^{mt}\\x''=m^{2}e^{mt}$

Substituting these equations in c)

$m^{2}e^{mt}+4(e^{mt})=0\\\\m^{2}+4=0\\\\m^{2}=-4\\\\m=2i$

This becomes the solution m=α±βi where α=0 and β=2

$x=e^{\alpha t}[Asin\beta t+Bcos\beta t]\\\\x=e^{0}[Asin((2)t)+Bcos((2)t)]\\\\x=Asin((2)t)+Bcos((2)t)$

Where A and B are constants. With x(0)=0; x’(0)=1:

$x=Asin(2t)+Bcos(2t)\\\\x'=2Acos(2t)-2Bsin(2t)\\\\0=Asin(2(0))+Bcos(2(0))\\\\0=0+B(1)\\\\B=0\\\\1=2Acos(2(0))\\\\1=2A\\\\A=\frac{1}{2}$

Finally:

$x=\frac{1}{2} sin(2t)$

7 0

4 years ago

Simplify (3n – 2m)2 = ?

Tcecarenko [31]

(3n-2m) (3n-2m)

(you multiply the first number (3n) by the first number in the 2nd bracket (3n) and then by the second number in the 2nd bracket (-2m)), and you do the same for -2m

9n2 - 6mn -6nm +4m2

9n2 -12mn + 4m2

8 0

4 years ago

Read 2 more answers

Which expression correctly shows x^6+2x^3+1 factored completely over the integers?

ira [324]

Answer:

Option D, (x + 1)^2(x^2 - x + 1)^2

Step-by-step explanation:

Step 1: Factor

x^6 + 2x^3 + 1

(x + 1)^2(x^2 - x + 1)^2

Answer: Option D, (x + 1)^2(x^2 - x + 1)^2

8 0

4 years ago

Read 2 more answers