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1 month ago

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

Mathematics

1 answer:

zzz [12.3K]1 month ago

8 0

Response:

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

Step-by-step explanation:

A line is defined as a one-dimensional entity that lacks thickness and stretches infinitely in both directions.

A line segment contains two endpoints, while a ray consists of a single endpoint.

The equation given is $x^2+y^2-z^2=1$ .

Objective: to identify a line completely within the set designated by this equation.

Solution:

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

Verification:

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

Thus, $x=1\,,\,y=t\,,\,z=t$ fulfills the criteria of the given equation.

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Ana drew a map of the Panama Canal. In the scale Ana used for the map, 4 centimeters represents 20 kilometers. The actual length

lawyer [12517]

Answer:

According to the map, the length of the canal is 16.4 centimeters.

Step-by-step explanation:

If the real length of Panama Canal = 20 kilometers

and the canal's length on the map = 4 centimeters

Then, the scale factor is $\frac{\text{Length of canal on map}}{\text{Actual length of canal}}$

= $\frac{4}{20}$

= $\frac{1}{5}$

If the actual length of the Panama Canal = 82 kilometers

The length of the canal on the map = Actual length × Scale factor

= $82\times \frac{1}{5}$

= 16.4 centimeters

So, the canal's length on the map is 16.4 centimeters.

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17 days ago

A person flipped a coin 100 times and obtained 73 heads. Can the person conclude that the coin was unbalanced?

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17 days ago

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Which formula can be used to describe the sequence? -2/3,-4,-24,-144...

lawyer [12517]

The formula that describes the sequence is $a_{n}=\frac{-2}{3}(6)^{n-1}$

Step-by-step explanation:

The nth-term formula for a geometric sequence is $a_{n}=a(r)^{n-1}$ , where

a represents the first term of the sequence
r signifies the common ratio between any two consecutive terms
$r=\frac{a_{2}}{a_{1}}$ = $\frac{a_{3}}{a_{2}}$

∵ The sequence is $\frac{-2}{3}$ , -4, -24, -144,.......

∵ The first term is $\frac{-2}{3}$

∵ The second term is -4

∴ $\frac{-4}{\frac{-2}{3}}=6$

∵ The third term is -24

∴ $\frac{-24}{-4}=6$

∵ The fourth term is -144

∴ $\frac{-144}{-24}=6$

∵ $\frac{a_{2}}{a_{1}}$ = $\frac{a_{3}}{a_{2}}$ = $\frac{a_{4}}{a_{3}}$ = 6

∴ There is a consistent ratio between two consecutive terms

∴ The sequence qualifies as a geometric sequence

∵ The formula for the nth term of the geometric sequence is $a_{n}=a(r)^{n-1}$

∵ a = $\frac{-2}{3}$

∵ r = 6

∴ The equation for the sequence is $a_{n}=\frac{-2}{3}(6)^{n-1}$

The formula that can be employed to outline the sequence is $a_{n}=\frac{-2}{3}(6)^{n-1}$

Learn more:

You can explore more about sequences in

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1 month ago

. About 400,000 people visited an art museum in December what could be the exact number of people who visit the art museum

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<span>Considering the visitor count is likely rounded to the nearest hundred thousand, the precise figure could range from 350,000 to 449,999. If rounded to the nearest ten thousand, it would be between 395,000 and 404,999.</span>

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Response:

433.44

Detailed breakdown:

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