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3 years ago

10. Find a third number so that the three numbers form a right triangle: i) 9, 41

Mathematics

2 answers:

vazorg [7]3 years ago

5 0

Answer:

40
41.9762

Step-by-step explanation:

There are two possibilities here:

1) The two numbers are the legs of the right triangle. Then the hypotenuse is ...

√(9^2 +41^2) = √1762 ≈ 41.9762

2) The length 41 is the hypotenuse. Then the other leg is ...

√(41^2 -9^2) = √1600 = 40

_____

<em>Comment on Pythagorean triples</em>

I find it somewhat interesting that for any odd number n, one Pythagorean triple involving that number is ...

(n, (n^2 -1)/2, (n^2 +1)/2)

For n=9, the triple is (9, 80/2, 82/2) = (9, 40, 41).

Along these lines, ones commonly seen in math problems are ...

(3, 4, 5), (5, 12, 13), (7, 24, 25), (9, 40, 41), (11, 60, 61)

Travka [436]3 years ago

3 0

Answer:

The third number is 40.

Step-by-step explanation:

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iragen [17]

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3 years ago

Use the ordinary division of polynomials to find the quotient and remainder when the first polynomial is divided by the second.

Vanyuwa [196]

The quotient and remainder when the first polynomial is divided by the second are -4w^2 - 7w - 21 and -71 respectively

<h3>How to determine the quotient and remainder when the first polynomial is divided by the second?</h3>

The polynomials are given as:

-4w^3 + 5w^2 - 8, w - 3

Set the divisor to 0.

So, we have

w - 3 = 0

Add 3 to both sides

w = 3

Substitute w = 3 in -4w^3 + 5w^2 - 8 to determine the remainder

-4(3)^3 + 5(3)^2 - 8

Evaluate the expression

-71

This means that the remainder when -4w^3 + 5w^2 - 8 is divided by w - 3 is -71

The quotient (Q) is calculated as follows:

Q = [-4w^3 + 5w^2 - 8]/[w - 3]

The numerator can be expressed as follows:

Numerator = -4w^3 + 5w^2 - 8

Subtract the remainder.

So, we have:

Numerator = -4w^3 + 5w^2 - 8 + 71

This gives

Numerator = -4w^3 + 5w^2 + 61

So, the quotient becomes

Q = [-4w^3 + 5w^2 + 61]/[w - 3]

Expand

Q = [(w - 3)(-4w^2 - 7w - 21)]/[w - 3]

Evaluate

Q = -4w^2 - 7w - 21

Hence, the quotient and remainder when the first polynomial is divided by the second are -4w^2 - 7w - 21 and -71 respectively

Read more about polynomials at:

brainly.com/question/4142886

#SPJ1

6 0

2 years ago

Thaddeus shakes his head as he pays $12.37 to the clerk for lunch. Complaining to a friend, Thaddeus says, “Do you realize that

atroni [7]

his income must be "x" which is the 100%, and we would know that 0.2% of that is 12.37.

$\begin{array}{ccll} amount&\%\\ \cline{1-2} x&100\\ 12.37&0.2 \end{array}\implies \cfrac{x}{12.37}=\cfrac{100}{0.2}\implies 0.2x=1237 \\\\\\ x=\cfrac{1237}{0.2}\implies x=61.85$

his income must be "x" which is the 100%, and we would know that 2% of that is 12.37.

$\begin{array}{ccll} amount&\%\\ \cline{1-2} x&100\\ 12.37&2 \end{array}\implies \cfrac{x}{12.37}=\cfrac{100}{2}\implies 2x=1237 \\\\\\ x=\cfrac{1237}{2}\implies x=618.5$