hey can someone pls help me out? i don’t understand this. find the surface area of the rectangle prism. thx hun <3

Let c be the curve which is the union of two line segments, the first going from (0, 0) to (4, 4) and the second going from (4,

victus00 [196]

First of all we need to find a representation of C, so this is shown in the figure below.

So the integral we need to compute is this:

$I=\int_c 4dy-4dx$

So, as shown in the figure, C = C1 + C2, so:

$I=\int_{c_{1}} (4dy-4dx)+\int_{c_{2}} (4dy-4dx)=I_{1}+I_{2}$

Computing first integral:

$c_{1}: y-y_{0}=m(x-x_{0}) \rightarrow y=x$

Applying derivative:

$dy=dx$

Substituting this value into $I_{1}$

$I_{1}=\int_{c_{1}} (4dx-4dx)=\int_{c_{1}} 0 \rightarrow \boxed{I_{1}=0}$

Computing second integral:

$c_{2}: y-y_{0}=m(x-x_{0}) \rightarrow y-0=-(x-8) \rightarrow y=-x+8$

Applying derivative:

$dy=-dx$

Substituting this differential into $I_{2}$

$I_{2}=\int_{c_{2}} 4(-dx)-4dx=\int_{c_{2}} -8dx=-8\int_{c_{2}}dx$

We need to know the limits of our integral, so given that the variable we are using in this integral is x, then the limits are the x coordinates of the extreme points of the straight line C2, so:

$I_{2}= -8\int_{4}^{8}}dx=-8[x]\right|_4 ^{8}=-8(8-4) \rightarrow \boxed{I_{2}=-32}$

Finally:

$I=\int_c 4dy-4dx=0-32 \rightarrow \boxed{I=-32}$

4 0

3 years ago

Diego works at a warehouse that ships two types of packages, a red package weighing 4 pounds and a blue package weighing 6 pound

Misha Larkins [42]

Answer:

Step-by-step explanation:

Red =x Blue = y

1) 4x + 6y = 180

2) x + y = 40

solve for x in eq. 2 and plug into eq. 1

2a) x=40-y

1a) 4(40-y) + 6y = 180

160-4y +6y = 180

2y=20

y=10

plug into eq. 2

x + 10 =40

x=30

30 red packages

;) maybe a late Christmas gift.. :D

8 0

3 years ago

What graph best represents the solution to the equality y - 2x > -8

Ne4ueva [31]

Answer:

<h2>In the attachment</h2>

Step-by-step explanation:

$y-2x>-8\qquad\text{add}\ 2x\ \text{to both sides}\\\\y>2x-8\\-------------------------\\\\-\ dotted\ line\\\leq,\ \geq-\ solid\ line\\,\ \geq-\ shading\ above\ the\ line\\-------------------------\\\\y=2x-8-\text{It's a linear function.}\\\text{We only need two points to draw a graph.}\\\text{Choice two arbitrary values of x, substitute to the equation,}\\\text{and calculate the values of y}.\\\\for\ x=4\to y=2(4)-8=8-8=0\to A(4,\ 0)\\for\ x=0\to y=2(0)-8=0-8=-8\to B(0,\ -8)$