Which two ratios show a proportional relationship?

Use number line f to answer the questions.

Andre45 [30]

Answer:

r u in school

Step-by-step explanation:

6 0

3 years ago

Read 2 more answers

Find an equivalent ratio for the ratio 6 to 7. 42 53 13 14 54 36 49

sesenic [268]

Hi there!

Finding the equivalen ratio means to find a equivalent numbers that’s equivalent to 6 and 7 which also means a number that 6 and 7 all goes into...

6,12,18,24,30,36,42

7,14,21,28,35,42

Final Result: 42

3 0

3 years ago

Hailey is 2 years younger than her sister. If Hailey is h years old, which equation represents the age of her sister, s?

butalik [34]

Answer:

S=H+2

Step-by-step explanation:

OK, so hailey is the variable H. And she is 2 years younger than her sister.

What is the age of her sister?

So we know it has to be, hailey's age + something? = age of her sister.

what is that +something? it's the number "2 years younger" so hailey's age; which is h, plus 2 is equal to her sister's age.

H+2=S

OK, why do we need to add 2? instead of minus two? Because hailey is 2 years younger than her sister, so you want hailey's age. If you were to minus 2, you'd be thinking that hailey is OLDER than her sister. Because if you want to her sister's age, you would have to SUBTRACT 2 because you are OLDER than her. So if you are younger than the sister, you would add to get your sister's age.

6 0

3 years ago

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What is the equation of a horizontal line that has a y-intercept of 3.5?

beks73 [17]

First, recall that the equation of a line is

y = mx+b

where

m = slope
b = y-int

The key to this question is the details :

Horizontal line ---> This tells you that your slope is 0

y-int = 3.5 -----> In the equation above, b=3.5

Therefore,

y = 0x + 3.5
y = 0 + 3.5
y = 3.5

4 0

3 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.

5 0

3 years ago