2 years ago

Solve the following system of equations 3x+2y=1 Y=x-2

Mathematics

1 answer:

OlgaM077 [116]2 years ago

4 0

Answer:

X=1

Y=-1

Step-by-step explanation:

Y=X-2

3X+2(X-2)=1

3X+2X-4=1

5X-4+1

5X=1+4

5X=5

X=1(5/5)

Y=X-2

Y=1-2

Y=-1

You might be interested in

What are the coordinates of

JulsSmile [24]

Answer:

Step-by-step explanation:

6 0

3 years ago

Find the volume V of the solid obtained by rotating the region bounded by the given curves about the specified line.

Elza [17]

Answer:

$\frac{\pi}{18}(e^{10} - e^8) \approx 3324$

Step-by-step explanation:

We begin by solving for x in term of y

$y = ln(3x)$

$e^y = 3x$

$x = \frac{e^y}{3}$

We can use the disk method to calculate the volume of rotation around the y axis

$V = \int\limits^5_4 {\pi r^2} \, dy$

Where $r = x = \frac{e^y}{3}$

$V = \int\limits^5_4 {\pi \left(\frac{e^y}{3}\right)^2} \, dy\\V = \frac{\pi}{9}\int\limits^5_4 {e^{2y}} \, dy\\\\V = \frac{\pi}{9}\left[\frac{e^{2y}}{2}\right]^5_4\\V = \frac{\pi}{9}(e^{10}/2 - e^8/2) = \frac{\pi}{18}(e^{10} - e^8)\\ V = \frac{\pi}{18}19045.5 \approx 3324$