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3 years ago

7. Write 300 as a product of prime factors.

1 answer:

8 0

As the numbers 5 and 2 are both prime numbers, they are counted as prime factors for 300. -Factors of 30: 3 x 10 = 30. As 3 is a prime number, we have found another prime factor of 300.

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Evaluate the integral ∫2−1|x−1|dx

defon

I think you might be referring to the definite integral,

$\displaystyle \int_{-1}^2|x-1|\,\mathrm dx$

Recall the definition of absolute value:

$|x| = \begin{cases}x&\text{if }x\ge0\\-x&\text{if }x$

Then $|x-1|=x-1$ if $x\ge1$ , and $|x-1|=1-x$ is $x$ . So spliting up the integral at <em>x</em> = 1, we have

$\displaystyle \int_{-1}^2|x-1|\,\mathrm dx = \int_{-1}^1(1-x)\,\mathrm dx + \int_1^2(x-1)\,\mathrm dx$

The rest is simple:

$\displaystyle \int_{-1}^2|x-1|\,\mathrm dx = \left(x-\dfrac{x^2}2\right)\bigg|_{-1}^1 + \left(\dfrac{x^2}2-x\right)\bigg|_1^2 \\\\ = \left(\left(1-\frac12\right)-\left(-1-\frac12\right)\right) + \left(\left(2-2\right)-\left(\frac12-1\right)\right) \\\\ = \boxed{\frac52}$

5 0

2 years ago

What is the median of 79,85,86,90,92,93

o-na [289]

THE MEDIAN IS THE MIDDLE NUMBER IS 86 AND 90

7 0

2 years ago

a car generally depreciates 25% of its original value in the first year lonnoes car is worth $27300.00 after the first year. Wha

ivolga24 [154]

First, we convert the percentage to a decimal.
25% - 0.25

Next, we times this by the cars current value.
0.25 x $27,300
= $6,825

Lastly, we add this to our original cost to determine the starting value of the car.
$27,300 + $6,825
= $34,125
Cheers!

3 0

2 years ago

A printer can print 27 pages in 4.5 minutes. How much time does it need to print 324 pages?

oksano4ka [1.4K]

So if the printer can print 27 pages in 4.5 minutes, then how much time does it need to print 324 pages?
The equation looks like this:
4.5/27 = ?/324

To find the value of ? divide 324 divided by 27 which equals 12. Then multiply 12 x 4.5 because to keep the equivalent, you must do the same to the top as you did the bottom. 12 x 4.5= 54

Answer: So, to print 324 pages, 54 minutes is needed.
4.5/27 = 54/324

I hope this helps:)

5 0

2 years ago

A horse named Northen Dancer won the Kentucky Derby with a time of exactly 2 minutes. at this constant rate, how long would it t

forsale [732]

Answer:

Step-by-step explanation:

set up a proportion using minutes/mile:

2/(1 1/4) = x/(1 1/2)

2/(5/4) = x/(3/2)

(5/4)x = (3/2)(2)

(5/4)x = 3

x = 3(4/5)

x = 12/5

x = 2 2/5 minutes

pls mark me the brainliest pls

6 0

3 years ago