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2 years ago

Q4H: The question is in the picture below (please show work) :

Mathematics

1 answer:

Ipatiy [6.2K]2 years ago

4 0

-3x-5=16
-3x-5(+5)=16+5
-3x=21
-3x/-3=21/-3
x=-7

-4(y-2)=12
-4y+8=12
-4y=4
y=-1

8.88=4.44(x-7)
8.88=4.44x-31.08
39.96=4.44x
9=x

5(y+2/5)=-13
5y+2=-13
5y=-15
y=-3

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Compute the surface area of the portion of the sphere with center the origin and radius 4 that lies inside the cylinder x^2+y^2=

Tom [10]

Answer:

16π

Step-by-step explanation:

Given that:

The sphere of the radius = $x^2 + y^2 +z^2 = 4^2$

$z^2 = 16 -x^2 -y^2$

$z = \sqrt{16-x^2-y^2}$

The partial derivatives of $Z_x = \dfrac{-2x}{2 \sqrt{16-x^2 -y^2}}$

$Z_x = \dfrac{-x}{\sqrt{16-x^2 -y^2}}$

Similarly;

$Z_y = \dfrac{-y}{\sqrt{16-x^2 -y^2}}$

∴

$dS = \sqrt{1 + Z_x^2 +Z_y^2} \ \ . dA$

$=\sqrt{1 + \dfrac{x^2}{16-x^2-y^2} + \dfrac{y^2}{16-x^2-y^2} }\ \ .dA$

$=\sqrt{ \dfrac{16}{16-x^2-y^2} }\ \ .dA$

$=\dfrac{4}{\sqrt{ 16-x^2-y^2} }\ \ .dA$

Now; the region R = x² + y² = 12

Let;

x = rcosθ = x; x varies from 0 to 2π

y = rsinθ = y; y varies from 0 to $\sqrt{12}$

dA = rdrdθ

∴

The surface area $S = \int \limits _R \int \ dS$

$= \int \limits _R\int \ \dfrac{4}{\sqrt{ 16-x^2 -y^2} } \ dA$

$= \int \limits^{2 \pi}_{0} } \int^{\sqrt{12}}_{0} \dfrac{4}{\sqrt{16-r^2}} \ \ rdrd \theta$

$= 2 \pi \int^{\sqrt{12}}_{0} \ \dfrac{4r}{\sqrt{16-r^2}}\ dr$

$= 2 \pi \times 4 \Bigg [ \dfrac{\sqrt{16-r^2}}{\dfrac{1}{2}(-2)} \Bigg]^{\sqrt{12}}_{0}$

$= 8\pi ( - \sqrt{4} + \sqrt{16})$

= 8π ( -2 + 4)

= 8π(2)

= 16π

4 0

2 years ago

Jose earned 45$ working at his job for 5 hours . how much would he earn for 7 hours

telo118 [61]

63$

five hours = 45$
1 hour = 9$
7 hours = 63$

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2 years ago

Read 2 more answers

How far apart were the closest marks on the ruler that was used to make a measurement of 23.435 m?

qwelly [4]

The closest marks on the ruler that was used to make a measurement of 23.435m is 0.01m apart.

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

This refers to a tool which is used to measure distances of two points or area and has standard markings.

Since the thousandth digit is uncertain and the significant figures are digits which are read from the measuring instrument plus one doubtful number on the ruler then the most appropriate choice will be 0.01m.

Read more about Ruler here brainly.com/question/18558504

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1 year ago

Find the y-intercept(s), if any for the equation: y=x^2-16

Murrr4er [49]

The Y-int would be <u>-16</u>

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2 years ago

Plz give me brainliest. I am good answerer. Please

Katen [24]

Uhm what? sir your asking a question, and not giving someone else an answer

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2 years ago