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4 years ago

Given the figure below, find the values of x and z.

Mathematics

2 answers:

Lera25 [3.4K]4 years ago

5 0

Answer:

z=98 and 5x+57 and z are supplementary.

Step-by-step explanation:

vertical angles theorem

telo118 [61]4 years ago

5 0

Answer:

X = 5. Z = 98

Step-by-step explanation:

180 minus 98 is 82

5x+57=82

5x=25

5÷25

x=5

and for Z, well 98 is vertical to Z so that's what that is

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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

Point J is located at (2,5)(2,5) and point K is located at (4,19)(4,19).

Anni [7]

We have the coordinates
J (2,5)
K (4,19)

Since we are to find the point that partitions the line segment into 3:2 ratio, we have 5 equal parts of the line segment. So,

Get the horizontal distance:
4 - 2 = 2
Divide by 5
2/5
Multiply by 3
2/5 x 3 = 1.2
Add this to the x coordinate of J
2 + 1.2 = 2.2

Get the vertical distance:
19 - 5 = 14
Divide by 5
14/5
Multiply by 3
14/5 x 3 = 8.4
Add this to the y coordinate of J
5 + 8.4 = 13.4

The coordinates of the point is
(2.2,13.4)

5 0

3 years ago

What is the image point of (0,-6) after the transformation D 1/2 or y-axis?

rewona [7]

I think you multiply 1/2 by the x and y point

1/2(0)= 0
1/2(-6)= -3

(0,-3)

6 0

3 years ago

Ruby baked fried apple pies for a bake sale if each pie contains 12 apples how many total apples did reviews

Neko [114]

Doesn't say how any pies she fried

8 0

3 years ago

Read 2 more answers

Melanie has a bag that contains orange chews, cherry chews, and peach chews. She performs an experiment. Melanie randomly remove

adoni [48]

Answer:

0.30

Step-by-step explanation:

Given that:

Total number of trials = 61

Number of orange chews = 38

Number of cherry chews = 5

Number of peach chews = 18

Probability that next chew removed will be a peach chew ;

This is an experimental probability problem ;

Using the relation :

Experimental probability of A;

Number of successes (A) / total number of trials

Hence, Probability that next chew removed will be a peach chew ;

Experimental probability of peach chew :

Number of trails = 61 ; number of successes (peach chew) = 18

P(peach chew) = 18 / 61

P( peach chew) = 0.2950819

= 0.30 ( nearest hundredth)

4 0

3 years ago