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2 years ago

2x + 4y + z = 3 x − 2y − 3z = 4 x + y − z = −1

1 answer:

ozzi2 years ago

5 0

A) 2x + 4y + z = 3
B) x − 2y − 3z = 4
C) x + y − z = −1

Multiplying B & C by -1

B) -x + 2y + 3z = -4
C) -x - y + z = +1 Then adding to A
A) 2x + 4y + z = 3
5y + 5z = 0
So basically z = -y

A) 2x + 4y -y = 3
B) x − 2y + 3y = 4
C) x + y +y = −1

A) 2x + 3y = 3

Multiplyig B by -2
B) -2x -2y= -8
C) x + 2y = −1 Adding B&C
-x = -9
x = 9


A) 2*9 + 4y + z = 3
A) 4y + z = -15
B) 9 − 2y − 3z = 4
B) − 2y − 3z = -5

A) 4y + z = -15
B) − 2y − 3z = -5
Multiplying A by 3
A) 12y + 3z = -45
B) − 2y − 3z = -5 Then adding A & B
10y = -50
y = -5

C) x + y − z = −1
C) 9 -5 − z = −1
C)5 =z

So x = 9
y= -5
z = 5

Wow!!!!!!!!!!!!

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Evaluate the line integral, where c is the given curve. (x + 9y) dx + x2 dy, c c consists of line segments from (0, 0) to (9, 1)

viktelen [127]

$\displaystyle\int_C(x+9y)\,\mathrm dx+x^2\,\mathrm dy=\int_C\langle x+9y,x^2\rangle\cdot\underbrace{\langle\mathrm dx,\mathrm dy\rangle}_{\mathrm d\mathbf r}$

The first line segment can be parameterized by $\mathbf r_1(t)=\langle0,0\rangle(1-t)+\langle9,1\rangle t=\langle9t,t\rangle$ with $0\le t\le1$ . Denote this first segment by $C_1$ . Then

$\displaystyle\int_{C_1}\langle x+9y,x^2\rangle\cdot\mathbf dr_1=\int_{t=0}^{t=1}\langle9t+9t,81t^2\rangle\cdot\langle9,1\rangle\,\mathrm dt$
$=\displaystyle\int_0^1(162t+81t^2)\,\mathrm dt$
$=108$

The second line segment ( $C_2$ ) can be described by $\mathbf r_2(t)=\langle9,1\rangle(1-t)+\langle10,0\rangle t=\langle9+t,1-t\rangle$ , again with $0\le t\le1$ . Then

$\displaystyle\int_{C_2}\langle x+9y,x^2\rangle\cdot\mathrm d\mathbf r_2=\int_{t=0}^{t=1}\langle9+t+9-9t,(9+t)^2\rangle\cdot\langle1,-1\rangle\,\mathrm dt$
$=\displaystyle\int_0^1(18-8t-(9+t)^2)\,\mathrm dt$
$=-\dfrac{229}3$

Finally,

$\displaystyle\int_C(x+9y)\,\mathrm dx+x^2\,\mathrm dy=108-\dfrac{229}3=\dfrac{95}3$

5 0

3 years ago

Help me please Solve for r d=rt

Vika [28.1K]

Watch closely. I'll try to go slow.
Stop me if I go too fast, or if I do anything that you don't understand.

Ready ?

You said d = r t

Divide each side by ' t ' : d / t = r

5 0

3 years ago

The line passes through (9,8) and is perpendicular to x-2y=-16

pickupchik [31]

The equation of line perpendicular to x-2y=-16 passing through (9,8) is: y=-2x+26

Step-by-step explanation:

Given

$x-2y=-16\\Adding\ 2y\ on\ both\ sides\\x=2y-16\\Adding\ 16\ on\ both\ sides\\x+16=2y-16+16\\x+16=2y\\2y=x+16\\Dividing\ both\ sides\ by\ 2\\\frac{2y}{2}=\frac{x+16}{2}\\y=\frac{x}{2}+\frac{16}{2}\\y=\frac{1}{2}x+8\\$

The equation is in slope-intercept form, the coefficient of x will be the slope of given line. The slope is: 1/2

As the product of slopes of two perpendicular lines is -1.

$\frac{1}{2}*m=-1\\m=-1*\frac{2}{1}\\m=-2$

Slope intercept form is:

$y=mx+b$

Putting the value of slope

y=-2x+b

To find the value of b, putting (9,8) in the equation

$8=-2(9)+b\\8=-18+b\\b=8+18\\b=26$

Putting the values of b and m

$y=-2x+26$

Hence,

The equation of line perpendicular to x-2y=-16 passing through (9,8) is: y=-2x+26

Keywords: Equation of line, Slope-intercept form

Learn more about equation of line at:

#LearnwithBrainly

4 0

3 years ago

Choose the equation that models the following statement: The current, I amps, produced by a battery is inversely proportional to

Anika [276]

By definition we have to:
V = I * R
Where,
V: Voltage.
I: Current.
R: Resistance.
The current, I amps, produced by a battery is inversely proportional to the resistance, R ohms. Clearing I have:
I = V / R
rewriting:
I = V * (1 / R)
answer:
The equation that models the statement is:
I = V * (1 / R)

7 0

3 years ago

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A machine wheel spins at a rate of 500 revolutions per minute. If the wheel has a diameter of 80 centimeters, what is the angula

solmaris [256]

Answer: 3,140 radians per minute.

Step-by-step explanation:

We know that the wheel does 500 revolutions per minute.

This is called the frequency of the wheel, and this is written as:

f = 500 rev/min = 500 RPM

The angular speed (or Angular velocity) is written as

ω = 2*pi*f

And this quantity is in radians/unit of time.

where pi = 3.14

then:

ω = 2*3.14*500 (rev/min)*(rad/rev) = 3,140 rad/min

This means that the angular velocity (or angular speed) is 3,140 radians per minute.

8 0

2 years ago

Read 2 more answers