All categories

2 years ago

Find a line that lies entirely in the set defined by the equation x2 + y2 − z2 = 1.

Mathematics

1 answer:

RUDIKE [14]2 years ago

8 0

Answer:

$x=1\,,\,y=t\,,\,z=t$

Step-by-step explanation:

A line is a one-dimensional figure that has no thickness and extends infinitely in both directions.

A line segment is a line that has two end-points and a ray is a line that has one end-point.

Given equation is $x^2+y^2-z^2=1$

To find : a line that lies entirely in the set defined by the given equation.

Solution:

Take $x=1\,,\,y=t\,,\,z=t$

Check:

$L.H.S=1^2+t^2-t^2=1+0=1=R.H.S$

Therefore, $x=1\,,\,y=t\,,\,z=t$ satisfy the given equation.

You might be interested in

The floor of a canyon has an elevation of −14.5−14.5 feet. Erosion causes the elevation to change by −1.5−1.5 feet per year. How

Alona [7]

The canyon starts at an elevation of (-14.5). After each year, the elevation drops by (-1.5). The equation that could be written for this, then, would be (-14.5 - 1.5x = -31). First, we could add 14.5 to both sides of the equation to isolate the unknown. This would leave -1.5x = -16.5. Next, we can remove the negative signs so both sides of the equation are positive and easier to work with. This leaves 1.5x = 16.5. Finally, dividing both sides by 1.5 gives us "x = 11", which means that after 11 years, the canyon floor will be at -31 feet.

4 0

2 years ago

The position of a particle moving to the right on the x-axis is given by x(t), where x(t) is measured in inches and t is measure

wlad13 [49]

Answer:

No options

Step-by-step explanation:

Knowing that V=in/min = x(t)/t and according to the graph,

V=20in/20min=in/min, so

No options since speed is not inches per minute, spedd (V) = inches over minutes

8 0

2 years ago

Read 2 more answers

Sanjay consulted three electricians about upgrading the wiring in his home. Each electrician uses a linear formula that incorpor

Reptile [31]

Answer:
b.Each electrician charges a different base fee:

Explanation:
Each of the equations has two parts:
1- base fee that is independent of any variable (this would be the number that has no variable next to it)
2- an hourly rate depending on the number of hours x (this would be the number that has an x next to it)

For the first electrician:
y = 25x + 30
base fee = $30
hourly rate = $25

For the second electrician:
y = 30x + 25
base fee = $25
hourly rate = $30

For the third electrician:
y = 25x + 20
base fee = $20
hourly rate = $25

Now, let's check the choices:
a.Each electrician charges a different hourly rate:
This is incorrect as electricians 1 and 3 charge the same hourly rate ($25)

b.Each electrician charges a different base fee:
This is correct as all three base fees are different ($30, $20 and $25)

c.All three electricians charge the same hourly rate:
This is incorrect as electrician 2 has a different hourly rate

d. All three electricians charge the same base fee:
This is incorrect as the base fees for the three electricians are different ($30, $25 and $20)

Hope this helps :)

4 0

2 years ago

Read 2 more answers

In one baseball season Peter hit twice the difference of the number of home runs Alice hit and 6. altogether,they hit 18 home ru

Viktor [21]

In a baseball season:
Peter hit = 2 (x - 6)
Total = 19 hits

X= Alex’s hit
Y = Peter’s Hit

=> Y = 2(x - 6)
=> x + y = 18
Let’s start from the second given equation:
=> x + y =18
=> y = 18 – x
Now, let’s use the first given equation to solve:
=> 18 – x = 2 (x - 6)
=> 18 – x = 2x – 12
=> -3x = -30
x = 10

Now, Let’s try:
=> Y = 2(x - 6)
=> y = 2 (10 - 6)
=> y = 2 (4)
=> y = 8

Thus, Peter hit 8 and Alice hit 10.

4 0

2 years ago

The heights of students in a class are normally distributed with mean 55 inches and standard deviation 5 inches. Use the Empiric

maks197457 [2]

Answer: c)[50,60]

Step-by-step explanation:

The Empirical rule says that , About 68% of the population lies with the one standard deviation from the mean (For normally distribution).

We are given that , The heights of students in a class are normally distributed with mean 55 inches and standard deviation 5 inches.

Then by Empirical rule, about 68% of the heights of students lies between one standard deviation from mean.

i.e. about 68% of the heights of students lies between $\text{Mean}\pm\text{Standard deviation}$

i.e. about 68% of the heights of students lies between $55\pm5$

Here, $55\pm5=(55-5, 55+5)=(50,60)$

i.e. The required interval that contains the middle 68% of the heights. = [50,60]

Hence, the correct answer is c) (50,60)

4 0

2 years ago