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2 years ago

Parallel lines What is the segment

Mathematics

2 answers:

Helga [31]2 years ago

8 0

Answer:

Step-by-step explanation:

aev [14]2 years ago

6 0

A segment means: each of parts into which something is or may be divided.

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Consider F and C below. F(x, y, z) = yz i + xz j + (xy + 6z) k C is the line segment from (2, 0, −2) to (5, 4, 2) (a) Find a fun

WITCHER [35]

Answer:

Required solution (a) $f(x,y,z)=xyz+3z^2+C$ (b) 40.

Step-by-step explanation:

Given,

$F(x,y,z)=yz \uvec i +xz\uvec j+(xy+6z)\uvex k$

(a) Let,

$F(x,y,z)=yz \uvec i +xz\uvec j+(xy+6z)\uvex k=f_x \uvec{i} +f_y \uvex{j}+f_z\uvec{k}$

Then,

$f_x=yz,f_y=xz,f_z=xy+6z$

Integrating $f_x$ we get,

$f(x,y,z)=xyz+g(y,z)$

Differentiate this with respect to y we get,

$f_y=xz+g'(y,z)$

compairinfg with $f_y=xz$ of the given function we get,

$g'(y,z)=0\implies g(y,z)=0+h(z)\implies g(y,z)=h(z)$

Then,

$f(x,y,z)=xyz+h(z)$

Again differentiate with respect to z we get,

$f_z=xy+h'(z)=xy+6z$

on compairing we get,

$h'(z)=6z\implies h(z)=3z^2+C$ (By integrating h'(z)) where C is integration constant. Hence,

$f(x,y,z)=xyz+3z^2+C$

(b) Next, to find the itegration,

$\int_C \vec{F}.dr=\int_C \nabla f. d\vec{r}=f(5,4,2)-f(2,0,-2)=(52+C)-(12+C)=40$

3 0

3 years ago

The population of a city in 2005 was 15,000. By 2015, the city's population had grown to 45,000 people. Assuming that the popula

Ede4ka [16]

Answer:

The population of the city in the year 2025 will be 85,000.

Step-by-step explanation:

The population of the city in year 2005 = 15,000

The population of the city in the year 2015 = 45,000

⇒ The change in population in 10 years

= Population in year 2015 - Population in the year 2005

= 45,000 - 15, 000

= 30,000

⇒ The change in population in 10 years = 30,000

Now, the population in the year 2015 = 45, 000

Let us assume the number of population in the year 2025 = m

Here, according to the question:

Since, the CHANGE OF RATE is a linear growth since 2005.

⇒ The change in population in each 10 years = 30,000

⇒ The change in population in next 10 years

= Population in year 2025 - Population in the year 2015

or, 30, 000 = m - 45, 000

⇒ m = 30,000 + 45,000 = 85,000

or, m = 85,000

Hence, the population of the city in the year 2025 will be 85,000.

3 0

3 years ago

(X+2) (x+8) <br> expand and simplify

Nutka1998 [239]

Answer:

X+2=2x

x+8=8x

(2x).(8x)=16x

8 0

2 years ago

Sari drives 55 miles per hour. Which equation shows the proportional relationship between hours (h) and miles (m)?

Finger [1]

Answer:

$m=55h$

Step-by-step explanation:

we know that

A relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form $k=\frac{y}{x}$ or $y=kx$

In a proportional relationship the constant of proportionality k is equal to the slope m of the line and the line passes through the origin

Let

m ----> the distance in miles (y-coordinate)

h ----> the time in hours (x-coordinate)

In this problem the constant of proportionality k is given and is equal to

$k=55\ \frac{miles}{hour}$ ----> the speed

substitute

$m=55h$

8 0

3 years ago

Function g is shown on the graph.

kvv77 [185]

Answer:

the third one

Step-by-step explanation:

8 0

3 years ago