Is this a function or not a function?

Which best explains whether a triangle with side links 5 cm 13 cm and 12 cm is a right triangle

Genrish500 [490]

Answer:

$5^{2} + 12^{2} = 13^{2}\\25+144=169$

Step-by-step explanation:

Squaring base and adjacent then adding them and finally getting the squareroot of the sum gives hypotenuse of a right angle triangle. In this case, squaring 5 and 12 then getting their square roots gives you 13, proving that it is a right angle

Here is the proof

$5^{2}=25\\12^{2}=144\\13^{2}=169\\25+144=169$

Therefore, the above dimensions are for a right angled triangle.

5 0

3 years ago

Use appropriate algebra and theorem 7. 2. 1 to find the given inverse laplace transform. (write your answer as a function of t.

ollegr [7]

The given function s/(s^2 +3s -4) is proved with the help of inverse Laplace theorem.

According to the statement

we have to find the inverse of the Laplace theorem with the help pf the given theorem in the statement.

So, For this purpose, we know that the

Laplace transformation is a transformation of a function f(x) into the function g(t) that is useful especially in reducing the solution of an ordinary linear differential equation with constant coefficients to the solution of a polynomial equation.

Now, We assume you want to find the inverse transform of $s/(s^2 +3s -4).$

This can be written in partial fraction form as

$\frac{(4/5)}{(s+4)} + \frac{(1/5)}{(s-1)}$

which can be found in a table of transforms to be the transform of

$\frac{4}{5} e^{-4t} + \frac{1}{5} e^t$

There are a number of ways to determine the partial fractions. They all start with factoring the denominator.

$s^2 +3x -4 = (s+4)(s-1)$

After that, you can postulate the final form and determine the values of the coefficients that make it so.

For example:

$\frac{A}{(s+4)} + \frac{B}{s-1} = (A+B)s + \frac{(4B-A)}{(s^2 +3x -4)}$

This gives rise to two equations:

(A+B) = 1

(4B-A) = 0.

So, The given function s/(s^2 +3s -4) is proved with the help of inverse Laplace theorem.

Disclaimer: This question was incomplete. Please find the full content below.

Question:

Use appropriate algebra and theorem 7.2.1 to find the given inverse laplace transform. (write your answer as a function of t.) ℒ−1 s s2 + 3s − 4.

Learn more about Laplace here

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3 0

2 years ago

The probability that an archer hits the target when it is windy is 0.4; when it is not windy, her probability of hitting the tar

stiks02 [169]

Answer:

x = 6

Step-by-step explanation:

The probability that this archer hits her first shot is given by t the probability of being windy and that she hits the shot added to the probability of not being windy and that she hits the shot:

$P(H_{first}) = P(H_w)*P(W)+P(H_{nw})*(1-P(W))\\P(H_{first})=0.4*0.3+0.7*(1-0.3)\\P(H_{first})=0.12+0.49 = 0.61$