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3 years ago

Show that <1+<2+<3=180, if line l and m are parallels cut by two transversals.

Mathematics

1 answer:

Svet_ta [14]3 years ago

7 0

Step-by-step explanation:

Angle 1 2 and 3 are angles that are in a triangle and all the angles in a triangle always add up to 180

so <1 +<2 +<3=180

Hope that helps :)

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Find the area of the surface. the part of the hyperbolic paraboloid z = y2 − x2 that lies between the cylinders x2 + y2 = 4 and

Nadusha1986 [10]

Call the surface $S$ ; then the area of $S$ is given by the surface integral

$\displaystyle\iint_S\mathrm d\mathbf S$

Parameterize the surface by

$\mathbf r(u,v)=\begin{cases}x(u,v)=u\cos v\\y(u,v)=u\sin v\\z(u,v)=u^2\cos^2v-u^2\sin^2v=u^2\cos2v\end{cases}$

with $2\le u\le4$ and $0\le v\le2\pi$ . The surface element is given by

$\mathrm d\mathbf S=\|\mathbf r_u\times\mathbf r_v\|\,\mathrm du\,\mathrm dv$
$\mathrm d\mathbf S=u\sqrt{1+4u^2}\,\mathrm du\,\mathrm dv$

So the area is

$\displaystyle\iint_S\mathrm d\mathbf S=\int_{v=0}^{v=2\pi}\int_{u=2}^{u=4}u\sqrt{1+4u^2}\,\mathrm du\,\mathrm dv$
$=\displaystyle2\pi\int_{w=17}^{w=65}\sqrt w\,\frac{\mathrm dw}8$

where $w=1+4u^2\implies\mathrm dw=8u\,\mathrm du$

$=\displaystyle\frac\pi4\frac23w^{3/2}\bigg|_{w=17}^{w=65}$
$=\dfrac\pi6\left(65^{3/2}-17^{3/2}\right)\approx237.69$

8 0

3 years ago

PLS HELP.<br> YOU WILL GET A GOOD DEED :)

qaws [65]

Answer:

a, 17.5

b, 16.2

do it with reciprocal

3 0

3 years ago

What is the equation of the line that passes through the points (-7,-7) and (-7,4)

musickatia [10]

Answer:

Step-by-step explanation:

The equation of a line

y = mx + c

y - intercept point y

m - slope of the line

x - intercept point x.

c - intercept of the line

Step 1: find the slope

m = y2 - y1 / x2 - x1

Given two points

( -7 , -7) ( -7 , 4)

x1 = -7

y1 = -7

x2 = -7

y2 = 4

Insert the values into the equation

m = 4 - (-7) / -7 -(-7)

m = 4 + 7 / -7 + 7

m = 11/ 0

Step 2: sub any of the two points given into the equation

y= mx + c

y = 11/0x + c

(-7 ,4 )

x = -7

y = 4

4 = 11/0(-7) + c

4 = -77/0 +c

-77/0 is math error which means that the points are not correct

4 0

3 years ago

Identify the variable(s), set up your equation(s), and solve. Richard has an elder sister who is twice his age and a younger sis

alexdok [17]

Answer:

7 years

Step-by-step explanation:

Given that:

Let Richard's age = x

Elder sister's age = 2x

Youngwr sister's age = x - 2

Product of sisters ages = 70

2x * (x - 2) = 70

2x² - 4x = 70

2x² - 4x - 70 = 0

x² - 2x - 35 = 0

x² - 7x + 5x - 35 = 0

x(x - 7) +5(x - 7) = 0

(x - 7) or (x + 5) = 0

x = 7 or x = - 5

X can't be negative

Hence, x = 7

Richard is 7 years

3 0

3 years ago

the freeze club ordered 16 pizzas for a party. Each pizza had 6 slices. I ate 9 of the slices. How many slices were left for the

GREYUIT [131]

Answer:

267 slices of pizza

Step-by-step explanation:

16 x 6 = 276

276 - 9 = 267

5 0

2 years ago