Ask question

Ask question

All categories

3 years ago

12

Rosa saved up her money and bought a model train. Each of the 8 cars on the train was the same length. When Rosa put all the car

s together, the train was 3 feet long. How long was each car?

1 answer:

Natalka [10]3 years ago

3 0

Answer:

4.5 inches long

Step-by-step explanation:

3 feet is equal to 36 inches, so you do 36/8 which equals out to 4.5 inches per car

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

What is the slope for (-11,7),(15,-3)

soldier1979 [14.2K]

-5/13

Formula: Y2-Y1/X2-X1

4 0

3 years ago

Read 2 more answers

7.) Jessica took her parents out to dinner. The total

m_a_m_a [10]

57.29 you do 48.55 times .18 which =8.74 then add the tip with the initial cost 8.74+48.55 =57.29 to get your answer 57.29

3 0

3 years ago

Read 2 more answers

The total weight of 30 bags of flour and 4 bags of sugar is 42.6 kg. If each bag of sugar weighs 0.75 kg, what is the weight of

alina1380 [7]

The answer is: Each bag of flour weighs 1,32 kg.

If we the total weight of the bags is given, and we know both the number of bags of flour and sugar, and we also know the weight of each bag of sugar, then we have to find the unknown, which is X. 30 times X plus 4 times the weight of a bag of sugar would equal 42.6kg. Next step is to put the unknown on one side and the known values on the other side. We have 30 times X equals 42.6 minus 4 times 0.75.
To find X we need to divide the value with 30, or to sum up

30X + 4*0.75 = 42.6
30X + 3 = 42.6
X = (42.6 - 3) / 30
X = 1.32 kg

7 0

3 years ago

Read 2 more answers

What is 16 ÷ 2 x 5 x 3 ÷ 6

aliya0001 [1]

Answer:

20

Step-by-step explanation:

use PEMDAS.

do 5 x 3, the multiply that by 16/2.

you would get 120.

then divide by 6

4 0

3 years ago

Read 2 more answers