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3 years ago

A company shipped 4i boxes of canned dog food. Each box contains 24 cans. How many cans of dog food did the company ship in all

Mathematics

1 answer:

klio [65]3 years ago

6 0

You multiply 24 by 4 witch leaves you with 96 canned dog food

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Use Stokes' Theorem to evaluate C F · dr where C is oriented counterclockwise as viewed from above. F(x, y, z) = 2yi + xzj + (x

Lady_Fox [76]

By Stokes' theorem, the line integral of $\vec F$ over $C$ is given by the surface integral of the curl of $\vec F$ over $S$ , where $S$ is the region of intersection of the plane $z=y+6$ and the cylinder $x^2+y^2=1$ with $S$ having positive/upward orientation.

Parameterize $S$ by

$\vec s(u,v)=u\cos v\,\vec\imath+u\sin v\,\vec\jmath+(u\sin v+6)\,\vec k$

with $0\le u\le1$ and $0\le v\le2\pi$ .

Take the normal vector to $S$ to be

$\vec s_u\times\vec s_v=-u\,\vec\jmath+u\,\vec k$

The curl of $\vec F$ is

$\nabla\times\vec F(x,y,z)=(1-x)\,\vec\imath-\vec\jmath+(z-2)\,\vec k$

Then the line integral is equivalent to

$\displaystyle\int_C\vec F\cdot\mathrm d\vec r=\iint_S(\nabla\times\vec F)\cdot\mathrm d\vec S$

$=\displaystyle\int_0^{2\pi}\int_0^1\bigg((1-u\cos v)\,\vec\imath-\vec\jmath+(u\sin v+4)\,\vec k\bigg)\cdot\bigg(-u\,\vec\jmath+u\,\vec k\bigg)\,\mathrm du\,\mathrm dv$

$=\displaystyle\int_0^{2\pi}\int_0^1(5u+u^2\sin v)\,\mathrm du\,\mathrm dv=\boxed{5\pi}$

4 0

3 years ago

A cash box of $1 and $5 bills is worth $45. The number of $1 bills is three more than the number of $5 bills. How many of each b

Softa [21]

Answer:

7 $5 bills
10 $1 bills

Step-by-step explanation:

If we take out the extra $3, we can group the bills into one each of $5 and $1, for a value of $6. There will be 7 such groups in the remaining $42.

That means there are 7 bills of the $5 denomination, and 3 more than that (10 bills) of the $1 denomination.

There are 7 $5 bills and 10 $1 bills.

_____

If you want to write an equation, it is usually best to let a variable stand for the most-valuable contributor. Here, we can let x represent then number of $5 bills. Then the value of the cash box is ...

5x +(x+3) = 45

6x = 42 . . . . . . . . subtract 3, collect terms

x = 7 . . . . . . . . . . . there are 7 $5 bills

x+3 = 10 . . . . . . . . there are 10 $1 bills

You may notice that this working parallels the verbal description above. (After we subtract $3, x is the number of $6 groups.)

6 0

3 years ago

Round 12.511 to the nearest TENTHS

netineya [11]

Answer:

Step-by-step explanation:

That would be 12.5 because 12.51 is closer to 12.50 than it is compared to 12.6.

7 0

3 years ago

Need the question answered asap

anygoal [31]

Step-by-step explanation:

First find the area of the rectangle with the variables.

$(x + 5) \times x = {x}^{2} + 5x$

Now the areas are equal, so we have to solve the equation

${x}^{2} + 5x = 36 \\ x + \sqrt{5x} = 6 \\ 3.236x = 6 \\ x = 1.854$

8 0

3 years ago

Help me please with this question

Schach [20]

The answer is B
you have to find the cubic roots of 27 and 729 to find the side lengths of the cubes. The first one has a side length is 3, and the second one has a side length of 9 which s 3x larger.
pls make me brainliest ! ;-)

5 0

3 years ago

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