Answer:
is b
Step-by-step explanation:
Answer:
7/897 or .0078
Step-by-step explanation:
897/7
<em>897 cannot fit into 7 so move the decimal place over 3 times.</em>
897/7000
<em>897 can go into 7,000 7 times</em>
.7
897/7000
-6279
________
721
<em>Then since 897 cannot go into 721 you drop down a zero and make it 7,210.</em>
.7
897/70000
-6279
________
7210
<em>897 can go into 7,210 8 times.</em>
.0078 is your final answer.
<em />
1) Make an equation:
![4x + x = 40](https://tex.z-dn.net/?f=4x%20%2B%20x%20%3D%2040)
Where x represents the unknown amount (the number of shells)
2) Solve for x
![5x = 40](https://tex.z-dn.net/?f=5x%20%3D%2040)
Combine the x's
![x = 8](https://tex.z-dn.net/?f=x%20%3D%208)
Divide 40 by 5 to get X alone
3) Answer:
Manny collected 32 seashells, while Cameron only collected 8
Answer:
x=10
Step-by-step explanation:
2x-6=x+4
We subtract x from both sides, to cancel it out from the right side
2x-x = x and x-x = 0
x-6=0+4
x-6=4
add 6 to both sides, since 6+-6 = 0 (to isolate x on the left side)
-6+6 = 0
4+6 = 10
x=10
Answer:
a) ![f (x,y,z)= xy^2\sin(z)](https://tex.z-dn.net/?f=f%20%28x%2Cy%2Cz%29%3D%20xy%5E2%5Csin%28z%29)
b) ![\int_C F \cdot dr =0](https://tex.z-dn.net/?f=%5Cint_C%20F%20%5Ccdot%20dr%20%3D0)
Step-by-step explanation:
Recall that given a function f(x,y,z) then
. To find f, we will assume it exists and then we will find its form by integration.
First assume that F =
. This implies that
if we integrate with respect to x we get that
for some function g(y,z). If we take the derivative of this equation with respect to y, we get
This must be equal to the second component of F. Then
![2xy\sin(z) + \frac{\partial g}{\partial y}=2xy\sin(z)](https://tex.z-dn.net/?f=2xy%5Csin%28z%29%20%2B%20%5Cfrac%7B%5Cpartial%20g%7D%7B%5Cpartial%20y%7D%3D2xy%5Csin%28z%29)
This implies that
, which means that g depends on z only. So ![f(x,y,z) = xy^2\sin(z) + g(z)](https://tex.z-dn.net/?f=%20f%28x%2Cy%2Cz%29%20%3D%20xy%5E2%5Csin%28z%29%20%2B%20g%28z%29)
Taking the derivative with respect to z and making it equal to the third component of F, we get
which implies that
which means that g(z) = K, where K is a constant. So
![f (x,y,z)= xy^2\sin(z)](https://tex.z-dn.net/?f=f%20%28x%2Cy%2Cz%29%3D%20xy%5E2%5Csin%28z%29)
b) To evaluate
we can evaluate it by using f. We can calculate the value of f at the initial and final point of C and the subtract them as follows.
![\int_C F \cdot dr = f(r(\pi))-f(r(0))](https://tex.z-dn.net/?f=%5Cint_C%20F%20%5Ccdot%20dr%20%3D%20f%28r%28%5Cpi%29%29-f%28r%280%29%29)
Recall that
so
Also
so
So ![\int_C F \cdot dr =0](https://tex.z-dn.net/?f=%5Cint_C%20F%20%5Ccdot%20dr%20%3D0)