Hey there!

On this problem, we have to combine like terms. A like term in this sense doesn't have to have the same coefficient, but it has to have the same variable.

Our like terms are 2m and 4m, along with 3 and 5.

When we add 2m and 4m we get 6m, and when we add 5 and 3 we get eight.
Notice how 5 and three are like terms because they're both whole numbers and don't have any variables.

Your solution is 6m + 8.

My advice to you is pay attention to your like terms and don't mix them up. A strategy is to underline like terms in the same color.

Hope this helps!

6 0

3 years ago

If C is the line segment from 7 3 to 0 0 find the value of the line integral C 4y2i xj dr

saul85 [17]

Parameterize $C$ by

$\mathbf r(t)=(x(t),y(t))=(1-t)(7,3)+t(0,0)=(7-7t,3-3t)$

where $0\le t\le1$ . Then

$\mathrm d\mathbf r=(-7\,\mathbf i-3\,\mathbf j)\,\mathrm dt$

and the line integral is equivalent to

$\displaystyle\int_C(4y^2\,\mathbf i+x\,\mathbf j)\cdot\mathrm d\mathbf r=\int_0^1(4(3-3t)^2\,\mathbf i+(7-7t)\,\mathbf j)\cdot(-7\,\mathbf i-3\,\mathbf j)\,\mathrm dt$
$\displaystyle=\int_0^1(-252t^2+525t-273)\,\mathrm dt=-\dfrac{189}2$