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2 years ago

Why must one leg of a triangle that the Pythagorean triple represents need an even-numbered length?

1 answer:

6 0

Most of the square numbers are even.so if we need to find root over we need an even number to convert it to perfect square.

See the example below

$\\ \ast\bull\rm\longmapsto H^2=P^2+B^2$

$\\ \ast\bull\rm\longmapsto H^2=3^2+4^2$

$\\ \ast\bull\rm\longmapsto H^2=9+16$

$\\ \ast\bull\rm\longmapsto H^2=25$

$\\ \ast\bull\rm\longmapsto H=\sqrt{25}$

$\\ \ast\bull\rm\longmapsto H=5$

Some other triplets are

(6,8,10)
(5,12,13)
(8,15,17)

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Police use photographs of various facial features help witnesses identify suspects. One basic identification kit contains 195 ha

Brrunno [24]

Answer: 99 different faces

Step-by-step explanation:

Since a witness can clearly remember the hairline and the eyes and eyebrows of a suspect, and the

basic identification kit contains 195 hairlines, 99 eyes and eyebrows, the number of different faces that can be produced with this information will be 99

5 0

3 years ago

NO LINKS!! Please help me with this problem

iogann1982 [59]

${\qquad\qquad\huge\underline{{\sf Answer}}}$

The given figure shows a vertical hyperbola with its centre at origin, and as we observe the figure, we can conclude that :

Length of transverse axis is :

$\qquad \sf \dashrightarrow \: 2b = 12$

$\qquad \sf \dashrightarrow \: b = 6$

length of conjugate axis is :

$\qquad \sf \dashrightarrow \: 2a = 8$

$\qquad \sf \dashrightarrow \: a = 4$

Equation of hyperbola ~

$\qquad \sf \dashrightarrow \: \cfrac{ {y}^{2} }{ {b}^{2} } - \cfrac{ {x}^{2} }{ {a}^{2} } = 1$

plug in the values ~

$\qquad \sf \dashrightarrow \: \cfrac{ {y}^{2} }{ {6}^{2} } - \cfrac{ {x}^{2} }{ {4}^{2} } = 1$

$\qquad \sf \dashrightarrow \: \cfrac{ {y}^{2} }{ {36}^{} } - \cfrac{ {x}^{2} }{ {16}^{} } = 1$

5 0

1 year ago

Read 2 more answers

Let f(x) = 1/x . Find the number b such that the average rate of change of f on the interval [2, b] is − 1/8

vekshin1

Answer:

b=4

Step-by-step explanation:

So, we have the function $f(x)=1/x$ . We need to find b such that the average rate of change or the slope is -1/8 between the intervel [2, b]. First, let's find f(2).

f(2) = 1/(2) = 1/2

So, we have the point (2, 1/2)

At point b, f(b) = 1/b.

Let's plug this into the slope formula:

$\frac{y_2-y_1}{x_2-x_1}=\frac{.5-\frac{1}{b} }{2-b} =-1/8$

Now, we just need to solve for b. First, let's multiply both the numerator and denominator by b (to get rid of the annoying fraction in the numerator).

$\frac{.5b-1}{2b-b^2} =\frac{-1}{8}$