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2 years ago

What is the solution to the inequality 14y−14≥14?

Mathematics

2 answers:

Mrac [35]2 years ago

7 0

Answer:

$y \geqslant 2$

Step-by-step explanation:

1. Add 14 to both sides.

$14y \geqslant 28$

2. Divide both sides by 14.

$y \geqslant 2$

makkiz [27]2 years ago

6 0

14y > 0 is the answer

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7 log(15/16)+6log(8/3)+5log(2/3)+log(32/25)<br>by logarithm laws<br>

hammer [34]

Answer:

1.5871

Step-by-step explanation:

According to the Question,

we have, 7 log(15/16)+6log(8/3)+5log(2/3)+log(32/25)

The Solution, With Basic Properties of Log.

7*log15-7*log16+6*log8-6*log3+5*log2-5*log3+log32-log25

7*1.176-7*1.204+6*0.903-6*0.477+5*0.3010-5*0.477+1.505-1.3979

on Solving, We get

1.5871

4 0

3 years ago

19. In the expression: 5.3t + (12-3) - 7 + 6.2,

Marat540 [252]

Answer:

D. 4

Step-by-step explanation:

Terms are separated by addition and subtraction signs

8 0

2 years ago

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.

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3 years ago

4. Which property of operations is used to write 15x + 9 as 9 + 15x?

suter [353]

Solution: The commutative property of addition states that when two numbers are being added, their order can be changed without affecting the sum.

8 0

2 years ago

What can you not tell from a box plot?

Galina-37 [17]

I'm not sure what your asking lol but in a box plot you can only see the mean median and mode

3 0

3 years ago