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2 years ago

What is the length of a leg of a right triangle if the hypotenuse is 9 inches and the other leg is 8 inches.

Mathematics

1 answer:

adelina 88 [10]2 years ago

5 0

Answer:

√17 or 4.12 inches

Step-by-step explanation:

√9²-8²=√81-64=√17 inches

or 4.12 inches

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The cost of a babysitting on a cruise is 10 for the first hour, and 12 for each additional hour. If the total cost of baby Aaron

Sliva [168]

Answer:

5 hours was Aaron at the sitter

Explanation:

Cost of baby sitting for the first hour: 10

Cost of baby sitting for additional hour= 12

Total cost of babysitting= 58

Since the cost of first hour is 10

Hence the remaining cost after first hour

= 54-10

=48

Which means 1 hour is consumed in the first hour

Now to calculate the remaining hours for every additional hour

= $\frac{48}{12}$

=4 hours

Hence the total hour Aaron was with the sitter

= 1 hour + 4 hours

= 5 hours

4 0

3 years ago

Integrate 1 - x / x(x2 + 1) d x by partial fractions.

solniwko [45]

Answer:

$log x-\frac{log(x^{2}+1) }{2}-tan^{-1} x$

Step-by-step explanation:

step 1:- by using partial fractions

$[tex]\frac{1-x}{x(x^{2}+1) } =\frac{A(x^{2}+1)+(Bx+C)(x }{x(x^{2}+1) }$ ......(1)

step 2:-

solving on both sides

$1-x=A(x^{2} +1)+(Bx+C)x......(2)$

substitute x =0 value in equation (2)

1=A(1)+0

A=1

comparing x^2 co-efficient on both sides (in equation 2)

0 = A+B

0 = 1+B

B=-1

comparing x co-efficient on both sides (in equation 2)

-1 = C

step 3:-

substitute A,B,C values in equation (1)

now

$\\\int\limits^ {} \, \frac{1-x}{x(x^{2}+1) } d x =\int\limits^ {} \frac{1}{x} d x +\int\limits^ {} \frac{-x}{x^{2}+1 } d x -\int\limits \frac{1}{x^{2}+1 } d x$

by using integration formulas

i) by using $\int\limits \frac{1}{x} d x =log x+c........(a)\\\int\limits \frac{f^{1}(x) }{f(x)} d x= log(f(x)+c\\$ .....(b)

$\int\limits tan^{-1}x dx =\frac{1}{1+x^{2} } +C$ .....(c)

step 4:-

by using above integration formulas (a,b,and c)

we get answer is

$log x-\frac{log(x^{2}+1) }{2}-tan^{-1} x$

6 0

3 years ago

Candice spent 5 1/4 hours doing her homework. Her brother, Ronald, spent 1/2 that number of hours doing his homework. How many h

Elden [556K]

Let

x-----> the number of hours that Candice spent doing her homework

y-----> the number of hours that Ronald spent doing his homework

we know that

$x=5\frac{1}{4}\ hours$

convert mixed number to an improper fraction

$5\frac{1}{4}\ hours=\frac{5*4+1}{4}= \frac{21}{4}\ hours$

$x=\frac{21}{4}\ hours$ -------> equation A

$y=\frac{1}{2}x$ ------> equation B

Substitute equation A in equation B

$y=\frac{1}{2}*\frac{21}{4}=\frac{21}{8}\ hours$

convert an improper fraction to a mixed number

$\frac{21}{8}\ hours=2.625=2+0.625=2+\frac{5}{8}=2\frac{5}{8}\ hours$

therefore

the answer is the option B

$2\frac{5}{8}\ hours$

5 0

2 years ago

Read 2 more answers

Complete the missing parts of the paragraph proof.

mariarad [96]

THANK YOU FOR YOUR HELP.

4 0

3 years ago

Read 2 more answers

Factor -12x^6-60x^5-75x^4

lesya [120]

-12x^6 - 60x^5-75x^4.......GCF = 3x^4
3x^4(-4x^2 - 20x - 25)
3x^4(-2x - 5)(2x + 5) <==

6 0

3 years ago