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3 years ago

How many solutions does the system have

Mathematics

2 answers:

Delicious77 [7]3 years ago

4 0

Answer:

There are infinate solutions.

Step-by-step explanation:

Plug (3x-8) in for y

5(3x-8)=15x-40

Simplify

15x-40=15x-40

zimovet [89]3 years ago

4 0

<h3>Answer: Infinitely many solutions</h3>

Explanation:

If we multiply both sides of the second equation by 5, then we go from y = 3x-8 to 5y = 15x-40. This is exactly identical to the first equation of the system.

Therefore, the two equations are equivalent just in slightly different forms. The two equations graph the same line which leads to infinitely many solutions.

The solutions are of the form (x, 3x-8) where x is any real number.

Since there are infinitely many solutions, we consider this system to be dependent.

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3 years ago

Evaluate the surface integral. s x ds, s is the part of the plane 18x + 9y + z = 18 that lies in the first octant.

IceJOKER [234]

In the first octant, the given plane forms a triangle with vertices corresponding to the plane's intercepts along each axis.

$(x,0,0)\implies 18x+9\cdot0+0=18\implies x=1$
$(0,y,0)\implies 18\cdot0+9y+0=18\implies y=2$
$(0,0,z)\implies 18\cdot0+9\cdot0+z=18\implies z=18$

Now that we know the vertices of the surface $\mathcal S$ , we can parameterize it by

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where $0\le u\le1$ and $0\le v\le1$ . The surface element is

$\mathrm dS=\|\mathbf s_u\times\mathbf s_v\|\,\mathrm du\,\mathrm dv=2\sqrt{406}(1-v)\,\mathrm du\,\mathrm dv$

With respect to our parameterization, we have $x(u,v)=(1-u)(1-v)$ , so the surface integral is

$\displaystyle\iint_{\mathcal S}x\,\mathrm dS=2\sqrt{406}\int_{u=0}^{u=1}\int_{v=0}^{v=1}(1-u)(1-v)^2\,\mathrm dv\,\mathrm du=\frac{\sqrt{406}}3$

5 0

3 years ago

(111²) how to solve it

ivolga24 [154]

Answer:

12,321

Step-by-step explanation:

111 to the second power (basically 111 x 111) is 12,321. Multiply 111 by 111 since the exponent is 2. I hope this helps!

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3 years ago

This circle is centered at the origin, and the length of its radius is 4. What is

kolezko [41]

I had the same problem

4 0

3 years ago

How do I find the value of z?

Shalnov [3]

Hello!

The answer is z = 16..

Solve it like this..

#1) Regroup terms

-3 = -7+z/4 ---> -3 = z/4 - 7

#2) Add 7 to both sides.

-3 = z/4 - 7 ---> -3 + 7 = z/4

#3) Do the addition.

-3 + 7 = z/4 ---> 4 = z/4

#4) Multiply both sides by 4.

4 = z/4 ---> 4 * 4 = z.

#5) Do the multiplication.

4 * 4 = z ---> 16 = z

Hope this helps! ☺♥

3 0

3 years ago

How many solutions does the system have​

How many solutions does the system have