If there is such a scalar function <em>f</em>, then



Integrate both sides of the first equation with respect to <em>x</em> :

Differentiate both sides with respect to <em>y</em> :


Integrate both sides with respect to <em>y</em> :

Plug this into the equation above with <em>f</em> , then differentiate both sides with respect to <em>z</em> :



Integrate both sides with respect to <em>z</em> :

So we end up with

the width of Yun's area model is 7x units or ( x-2 )units .
<u>Step-by-step explanation:</u>
Here we have , Yun was trying to factor 7x^2-14x. He found that the greatest common factor of these terms was 7x and made an area model: What is the width of Yun's area model. Let's find out:
We know that area of rectangle :
⇒
.........(1)
Now , According to question we have
⇒ 
⇒ 
Comparing this equation to equation (1) we get that :
⇒
or , 
Therefore , the width of Yun's area model is 7x units or ( x-2 )units .
<span>The question asks us to determine the values for a and b in the linear equation. Linear equation in the slope-intercept form is : y = a x + b. This equation is: y = 2.25 x - 3.15. The slope: a = 2.25 and the y-intercept is: b = -3.15. Answer: a = 2.25 and b = - 3.15.</span>
148 is the answer because
8,120+64,100=72,220
72,220 divide by 488 = 147.991803
rounded is 148
Answer:
$9.62
Step-by-step explanation:
15.50 + 3.74 = 19.24
19.24 / 2 = 9.62
so Mindy must pay Nora $9.62