You just need to do 12 1/5 ÷ 1 4/5.
To do this, first convert both fractions to improper fractions or topheavy fractions.

12 1/5 -
15 × 5 is 60, 60 + 1 is 61 so 12 1/5 = 61/5

1 4/5 -
1 × 5 is 5 and 5 + 4 is 9. 1 4/5 = 9/5

To divide fractions, you do keep, chang, flip (keep the 1st fraction, change the ÷ to ×, and flip the 2nd fraction)

the question starts as 61/5 ÷ 9/5 and becomes 61/5 × 5/9

multiplication in fractions is literally just numerator × numerator / denominator × denominator.

61 × 5 is 305. 5 × 9 is 45. the fraction is 305/45.

however, we need a whole number. 305/45 converted into a decimal is 6.7777778 (6.7 recurring). obviously you can't put a fraction of a book onto a shelt, so you round it down to the nearest whole number, which is 6.

final answer: 6

4 0

4 years ago

Use the Chain Rule to find the indicated partial derivatives. z = x^4 + xy^3, x = uv^4 + w^3, y = u + ve^w Find : ∂z/∂u , ∂z/∂v

k0ka [10]

I'll use subscript notation for brevity, i.e. $\frac{\partial f}{\partial x}=f_x$ .

By the chain rule,

$z_u=z_xx_u+z_yy_u$

$z_v=z_xx_v+z_yy_v$

$z_w=z_xx_w+z_yy_w$

We have

$z=x^4+xy^3\implies\begin{cases}z_x=4x^3+y^3\\z_y=3xy^2\end{cases}$

and

$\begin{cases}x=uv^4+w^3\\y=u+ve^w\end{cases}\implies\begin{cases}x_u=v^4\\x_v=4uv^3\\x_w=3w^2\\y_u=1\\y_v=e^w\\y_w=ve^w\end{cases}$

When $u=1,v=1,w=0$ , we have

$\begin{cases}x(1,1,0)=1\\y(1,1,0)=2\end{cases}\implies\begin{cases}z_x(1,2)=12\\z_y(1,2)=12\end{cases}$

and the partial derivatives take on values of

$\begin{cases}x_u(1,1,0)=1\\x_v(1,1,0)=4\\x_w(1,1,0)=0\\y_u(1,1,0)=1\\y_v(1,1,0)=1\\y_w(1,1,0)=1\end{cases}$

So we end up with

$\boxed{\begin{cases}z_u(1,1,0)=24\\z_v(1,1,0)=60\\z_w(1,1,0)=12\end{cases}}$

3 0

3 years ago

four balls of wool will make 8 knitted caps.how many balls of wool will malcom need if he wants to make 6 caps?

miss Akunina [59]

We can express this as a ratio. 4 balls :8 caps.

Then simplify. 1 ball: 2 caps.

We have to make caps equal to 6, so multiply by 3. For consistency, we need to multiply the number of balls by 3 too.

3 balls: 6 caps.

So Malcolm needs 3 balls of wool.

8 0

3 years ago