All categories

3 years ago

Write an algebraic expression that represents 2 less than 18 times a number: answer choices; 1. 18x-2, 2. 2-18x, 3. 2x-18

Mathematics

1 answer:

Jobisdone [24]3 years ago

4 0

A number would be x
18 times this number is 18x
2 less than 18 times a number is 18x-2
1. 18x-2

You might be interested in

Find the maximum and minimum values attained by f(x, y, z) = 5xyz on the unit ball x2 + y2 + z2 ≤ 1.

Allushta [10]

Check for critical points within the unit ball by solving for when the first-order partial derivatives vanish:
$f_x=5yz=0\implies y=0\text{ or }z=0$
$f_y=5xz=0\implies x=0\text{ or }z=0$
$f_z=5xy=0\implies x=0\text{ or }y=0$

Taken together, we find that (0, 0, 0) appears to be the only critical point on $f$ within the ball. At this point, we have $f(0,0,0)=0$ .

Now let's use the method of Lagrange multipliers to look for critical points on the boundary. We have the Lagrangian

$L(x,y,z,\lambda)=5xyz+\lambda(x^2+y^2+z^2-1)$

with partial derivatives (set to 0)

$L_x=5yz+2\lambda x=0$
$L_y=5xz+2\lambda y=0$
$L_z=5xy+2\lambda z=0$
$L_\lambda=x^2+y^2+z^2-1=0$

We then observe that

$xL_x+yL_y+zL_z=0\implies15xyz+2\lambda=0\implies\lambda=-\dfrac{15xyz}2$

So, ignoring the critical point we've already found at (0, 0, 0),

$5yz+2\left(-\dfrac{15xyz}2\right)x=0\implies5yz(1-3x^2)=0\implies x=\pm\dfrac1{\sqrt3}$
$5xz+2\left(-\dfrac{15xyz}2\right)y=0\implies5xz(1-3y^2)=0\implies y=\pm\dfrac1{\sqrt3}$
$5xy+2\left(-\dfrac{15xyz}2\right)z=0\implies5xy(1-3z^2)=0\implies z=\pm\dfrac1{\sqrt3}$

So ultimately, we have 9 critical points - 1 at the origin (0, 0, 0), and 8 at the various combinations of $\left(\pm\dfrac1{\sqrt3},\pm\dfrac1{\sqrt3},\pm\dfrac1{\sqrt3}\right)$ , at which points we get a value of either of $\pm\dfrac5{\sqrt3}$ , with the maximum being the positive value and the minimum being the negative one.

5 0

3 years ago

When a constant force is applied to an object, the acceleration of the object varies inversely with its mass. When a certain con

maria [59]

First:

F=m.a

=4*7

=28N

Second:

F=m.a

28=m.2. (force is constant,so F=28N)

28/2=m

m=14kg.

5 0

2 years ago

Read 2 more answers

If the difference between a number and 21 is divided by2, the result is 4 times the number. What is the number

Ostrovityanka [42]

(n-21)/2=4n is the equation

First, divide what is in the parentheses by 2
0.5n-10.5=4n

Then, multiply the whole equation by 2 so we have all whole numbers
n-21=8n

Move N so that it is with 8n
7n=-21

Divide 21 by 7
n=-3

Solution: The number (n) is equal to -3

6 0

3 years ago

What is the algebraic expression for the difference of 10-u

puteri [66]

I'm pretty sure that you answered it correctly. 10-U

4 0

3 years ago

Read 2 more answers

Write the equation of a line that passes through the points in the table.

lord [1]

Answer: do it have a answer choice if it do then its B,C and e

Step-by-step explanation:

6 0

2 years ago