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3 years ago

Divide. Write your answer as a fraction in simplest form. 9/10÷(−6/5)=

Mathematics

1 answer:

hoa [83]3 years ago

6 0

Put (9/10) ÷ (-6/5) into a calculator and you get -. 75 (aka - 1/4)

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I know you’re supposed to change the bounds and break up the integral, but for some reason, I can’t get the 44/3. Can someone ex

tatyana61 [14]

First, look for the zeroes of the integrand in the interval [0, 6] :

x² - 6x + 8 = (x - 4) (x - 2) = 0 ⇒ x = 2 and x = 4

Next, split up [0, 6] into sub-intervals starting at the zeroes we found. Then check the sign of x² - 6x + 8 for some test points in each sub-interval.

• For x in (0, 2), take x = 1. Then

x² - 6x + 8 = 1² - 6•1 + 8 = 3 > 0

so x² - 6x + 8 > 0 over this sub-interval.

• For x in (2, 4), take x = 3. Then

x² - 6x + 8 = 3² - 6•3 + 8 = -1 < 0

so x² - 6x + 8 < 0 over this sub-interval.

• For x in (4, 6), take x = 5. Then

x² - 6x + 8 = 5² - 6•5 + 8 = 3 > 0

so x² - 6x + 8 > 0 over this sub-interval.

Next, recall the definition of absolute value:

$|x| = \begin{cases}x & \text{for }x \ge0 \\ -x & \text{for }x < 0\end{cases}$

Then from our previous analysis, this definition tells us that

$|x^2 - 6x + 8| = \begin{cases}x^2 - 6x + 8 & \text{for }0$

So, in the integral, we have

$\displaystyle \int_0^6 |x^2-6x+8| \, dx = \left\{\int_0^2 - \int_2^4 + \int_4^6\right\} (x^2 - 6x + 8) \, dx$

Then

$\displaystyle \int_0^2 (x^2 - 6x + 8) \, dx = \left(\frac13 x^3 - 3x^2 + 8x\right) \bigg|_0^2 = \frac{20}3 - 0 = \frac{20}3$

$\displaystyle \int_2^4 (x^2 - 6x + 8) \, dx = \left(\frac13 x^3 - 3x^2 + 8x\right) \bigg|_2^4 = \frac{16}3 - \frac{20}3 = -\frac43$

$\displaystyle \int_4^6 (x^2 - 6x + 8) \, dx = \left(\frac13 x^3 - 3x^2 + 8x\right) \bigg|_4^6 = 12 - \frac{16}3 = \frac{20}3$

and the overall integral would be

20/3 - (-4/3) + 20/3 = 44/3

3 0

3 years ago

Which of these could be measured using milliliters? A) The cost of a 2-liter of soda B) The amount of time it takes to blink C)

lys-0071 [83]

Answer: C

Step-by-step explanation: A would be measured in money, B would be measured in time, D would be measured in distance, milliliters is used for liquid so the answer would be the eye drops

4 0

3 years ago

Read 2 more answers

Multi step equation that equal 27 when solved

Ksenya-84 [330]

Sample Equation: 3x - 3 = 27

Multiple step:

3x - 3 =    27
<u>    + 3    +3</u> Step1. Remove the -3 by adding 3 to both sides
3x =   30
<u>÷3 ÷ 3</u> Step2. Remove the multiplicand 3 by dividing both sides by 3
x = 10

To check: substitute x by its value

3x - 3 = 27
3(10) - 3 = 27
30 - 3 = 27
27 = 27

6 0

3 years ago

Rewarding BraiNly

Salsk061 [2.6K]

Answer:

Step-by-step explanation:

I counted how many thirty-fives there were in the set of data.

I hope this helps, have a nice day.

3 0

3 years ago

Read 2 more answers

Which is greater 34/18 or 1 5/6

Alisiya [41]

34/18 = 1.89
1 5/6 = 1.83

34/18 is greater then 1 5/6

8 0

3 years ago