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Find the scale factor of 1 inch = 9 feet

tino4ka555 [31]

Answer:

9 ft = 9 × 12 = 108 in

ratio is 1:108

Step-by-step explanation:

7 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

Tate fills a container with 9 1/2 cups of lemonade. Tate drinks 32 fl. oz. of lemonade. How many fluid ounces are left?

iren [92.7K]

Answer:

44 fluid ounces of lemonade are left.

Step-by-step explanation:

Given:

Tate fills a container with 9 1/2 cups of lemonade.

Tate drinks 32 fl. oz. of lemonade.

Now, to find the quantity of fluid ounces left.

So, we convert the unit of cups into fluid ounces.

Tate fill the container of lemonade with = $9\frac{1}{2}\ cups.$

As, 1 cup = 8 fluid ounces.

So, by conversion factor:

$9\frac{1}{2} \times 8$

$=\frac{19}{2} \times 8$

$=9.5\times 8=76\ fl.\ oz.$

Thus, Tate fill the container of lemonade with = 76 fl. oz.

Tate drinks lemonade = 32 fl. oz.

Now, to get the fluid ounces left we subtract the quantity of lemonade Tate drink from the total quantity of lemonade filled in the container:

$76-32$

$=44\ fl.\ oz.$

Therefore, 44 fluid ounces of lemonade are left.

3 0

3 years ago

David is planning to attend a public university after he graduates from high school in 3 years. He is devising a plan to save mo

allochka39001 [22]

Answer:

b. 600

Step-by-step explanation:

subtract money from parents from tuition

divide by months

7 0

3 years ago

He probability of choosing a vowel (a, e, i, o, or u) from a deck of cards containing the 26 letters of the alphabet is shown be

Goryan [66]

The probability is 1/650.

There is 1 a out of 26 letters; P(a) = 1/26

There is 1 e out of 26 letters; however, since it comes after drawing the a and is done without replacement, it is out of 25: 1/25

Together, their probabilities are 1/26(1/25) = 1/650

5 0

3 years ago