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Sliva [168]
3 years ago
10

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:

<h2>12.5</h2>

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
2 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
Read 2 more answers
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