4 divided by 57 please help

What is the volume of the box pictured below?

SpyIntel [72]

Answer:

The volume of the box is 3/4 cubic meters.

Step-by-step explanation:

We know that volume = length * width * height. We have length, width, and height already, so all we have to do is multiply.

5/6 * 1 1/8 * 4/5. First we convert 1 1/8 from a mixed fraction, to give us 9/8, as 8/8 = 1.

5/6 * 9/8 * 4/5. 5 * 9 = 45, and 6 * 8 = 48. 45/48 reduces to 15/16.

15/16 * 4/5. 15 * 4 = 60, and 16 * 5 = 80. 60/80 reduces to 6/8, which reduces to 3/4.

8 0

3 years ago

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Find the absolute extrema for f(x,y)=4-x^2-y^4+1/2y^2 over the closed disk D:x^2+y^2 is less than or equal to 1

algol [13]

Find the critical points of $f(x,y)$ :

$\dfrac{\partial f}{\partial x}=-2x=0\implies x=0$

$\dfrac{\partial f}{\partial y}=y-4y^3=y(1-4y^2)=0\implies y=0\text{ or }y=\pm\dfrac12$

All three points lie within $D$ , and $f$ takes on values of

$\begin{cases}f(0,0)=4\\f\left(0,-\frac12\right)=\frac{65}{16}\\f\left(0,\frac12\right)=\frac{65}{16}\end{cases}$

Now check for extrema on the boundary of $D$ . Convert to polar coordinates:

$f(x,y)=f(\cos t,\sin t)=g(t)=4-\cos^2-\sin^4t+\dfrac12\sin^2t=3+\dfrac32\sin^2t-\sin^4t$

Find the critical points of $g(t)$ :

$\dfrac{\mathrm dg}{\mathrm dt}=3\sin t\cos t-4\sin^3t\cos t=\sin t\cos t(3-4\sin^2t)=0$

$\implies\sin t=0\text{ or }\cos t=0\text{ or }\sin t=\pm\dfrac{\sqrt3}2$

$\implies t=n\pi\text{ or }t=\dfrac{(2n+1)\pi}2\text{ or }\pm\dfrac\pi3+2n\pi$

where $n$ is any integer. There are some redundant critical points, so we'll just consider $0\le t< 2\pi$ , which gives

$t=0\text{ or }t=\dfrac\pi3\text{ or }t=\dfrac\pi2\text{ or }t=\pi\text{ or }t=\dfrac{3\pi}2\text{ or }t=\dfrac{5\pi}3$

which gives values of

$\begin{cases}g(0)=3\\g\left(\frac\pi3\right)=\frac{57}{16}\\g\left(\frac\pi2\right)=\frac72\\g(\pi)=3\\g\left(\frac{3\pi}2\right)=\frac72\\g\left(\frac{5\pi}3\right)=\frac{57}{16}\end{cases}$

So altogether, $f(x,y)$ has an absolute maximum of 65/16 at the points (0, -1/2) and (0, 1/2), and an absolute minimum of 3 at (-1, 0).

5 0

2 years ago

Charlie gathers apples, pears, and plums. The numbers of apples and plums are 10-partners. There are the same number of apples a

aalyn [17]

Answer:

The total number of pieces of fruit that Charlie can gather ranges from 11 to 19.

Step-by-step explanation:

1. Let's review the information given to us to answer the question correctly:

Numbers of apples and plums are 10-partners, it means that the sum of apples and plums is 10.

Number of apples and pears are the same.

2. How many pieces of fruit can Charlie gather?

Apples = a

Plums = p

Pears = s

a + p = 10

Possible values of a and p:

1 + 9, 2 + 8, 3 + 7, 4 + 6, 5 + 5, 6 + 4, 7 + 3, 8 + 2, 9 + 1

Possible values of s:

1, 2, 3, 4, 5, 6, 7, 8, or 9

Therefore, the total number of pieces of fruit that Charlie can gather ranges from 11 to 19.

7 0

3 years ago

3(5 +4) + 4 – 2 •4= HELPPPP

Y_Kistochka [10]

Answer:

23

Step-by-step explanation: hope this helps

6 0

2 years ago

-5x + (-2) = -2x + 4. Find x

joja [24]

Answer:

x= -2

Step-by-step explanation:

7 0

3 years ago

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