What would this problem be factored to ? a^2-b^2

Evaluate the surface integral. s x ds, s is the triangular region with vertices (1, 0, 0), (0, −2, 0), and (0, 0, 12).

aniked [119]

Parameterize the surface by

$\mathbf r(s,t)=(1-s)(0,0,12)+s\bigg((1-t)(1,0,0)+t(0,-2,0)\bigg)$
$\implies\mathbf r(s,t)=(x(s,t),y(s,t),z(s,t))=(s-st,-2st,12-12s)$

where $(s,t)\in(0,1)\times(0,1)$ . We have

$\|\mathbf r_s\times\mathbf r_t\|=\|(1-t,-2t,-12)\times(-s,-2s,0)\|=2\sqrt{181}s$

The surface integral is then

$\displaystyle\iint_Sx\,\mathrm dS=2\sqrt{181}\int_{s=0}^{s=1}\int_{t=0}^{t=1}s(s-st)\,\mathrm dt\,\mathrm ds$
$=\displaystyle2\sqrt{181}\left(\int_{s=0}^{s=1}s^2\,\mathrm ds\right)\left(\int_{t=0}^{t=1}(1-t)\,\mathrm dt\right)$
$=\dfrac{\sqrt{181}}3$

7 0

3 years ago

Zara translates figure p to make figure q. If she translates figure q 4 units to right to make figure r where will figure r be l

Morgarella [4.7K]

Using translation concepts, considering the vertices (x,y) of figure p, the following rule is applied to find the vertices of figure r.

(x,y) -> (x + 4, y).

<h3>What is a translation?</h3>

A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction either in it’s definition or in it’s domain. Examples are shift left/right or bottom/up, vertical or horizontal stretching or compression, and reflections over the x-axis or the y-axis.

When a figure is shifted 4 units to the right, <u>4 is added to the x-coordinate</u>, hence, considering the vertices (x,y) of figure p, the following rule is applied to find the vertices of figure r.

(x,y) -> (x + 4, y).

More can be learned about translation concepts at brainly.com/question/28416763

#SPJ1

7 0

1 year ago

María is making fruto punch for her family reunión. She uses 6 quarts of ginger ale, 8 quarts of lemonade, and 10 quarts of rasp

expeople1 [14]

Answer:

6 gallons of punch makes her recipe.

Step-by-step explanation:

Given:

Quarts of ginger ale (g) = 6

Quarts of lemonade (l) = 8

Quarts of raspberry (r) = 10

Therefore, the total volume of fruto punch is equal to the sum of the volume of each of its ingredients.

So, Total volume = $g+l+r$

Total volume = 6 + 8 + 10 = 24 quarts

Now, we know that,

1 quart = 0.25 gallons

Therefore, from unitary method,

24 quarts = 24 × 0.25 = 6 gallons of punch

Therefore, 6 gallons of punch makes her recipe.

3 0

3 years ago

Read 2 more answers

Which three expressions are equivalent to the expression 3x − 12 − 2(x + 12)?

Sergio039 [100]

Answer:

The answer should be x - 36

Step-by-step explanation:

6 0

3 years ago

Read 2 more answers

Let point L be between M and N on MN. Given that MN=31, ML= h-15 and LN = 2h-8. Find LN

MrRa [10]

Since the distance of MN is 31 and we have a distance of ML of h -15 and LN of 2h – 8, therefore

ML + LN = h -15 + 2h – 8 = 31

h = 18

substituting the value of h to the expression for LN obtaining

LN = 2h – 8

LN = 2(18) – 8

LN = 28

Therefore the length of the segment LN is 28 units

7 0

3 years ago