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zavuch27 [327]
4 years ago
11

Simplify the following expression. 4/72

Mathematics
2 answers:
ryzh [129]4 years ago
8 0

Answer:

1/18

Step-by-step explanation:

Ⓗⓘ ⓣⓗⓔⓡⓔ

Well, 4/4=1 and 72/4=18.

Hence, 4/72=1/18

(っ◔◡◔)っ ♥ Hope this helped! Have a great day! :) ♥

dimaraw [331]4 years ago
5 0

Answer:

1/18

Step-by-step explanation:

1. Write down the factors for the numerator and the denominator.

2. Determine the largest factor that is common between the two.

3. Divide the numerator and denominator by the greatest common factor.

4. Write down the reduced fraction.

Hopefully these steps i've provided help your fraction simplifying needs

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A box is 12 centimeters wide ,12 centimeters long, and 15 centimeters tall. What is the total surface area of 4 such boxes?
Grace [21]
First you want to find the surface area of one box
SA=2(l*w)+2(h*l)+2(h*w)
SA=2(12*12)+2(15*12)+2(15*12)
SA=2(144)+2(180)+2(180)
SA=288+360+360
SA=1008 cm² is for one box
Multiply by 4 to get for 4 boxes
4*1008=4032 cm²
4 0
3 years ago
Lim x-> vô cùng ((căn bậc ba 3 (3x^3+3x^2+x-1)) -(căn bậc 3 (3x^3-x^2+1)))
NNADVOKAT [17]

I believe the given limit is

\displaystyle \lim_{x\to\infty} \bigg(\sqrt[3]{3x^3+3x^2+x-1} - \sqrt[3]{3x^3-x^2+1}\bigg)

Let

a = 3x^3+3x^2+x-1 \text{ and }b = 3x^3-x^2+1

Now rewrite the expression as a difference of cubes:

a^{1/3}-b^{1/3} = \dfrac{\left(a^{1/3}-b^{1/3}\right)\left(a^{2/3}+a^{1/3}b^{1/3}+b^{2/3}\right)}{\left(a^{2/3}+a^{1/3}b^{1/3}+b^{2/3}\right)} \\\\ = \dfrac{a-b}{a^{2/3}+a^{1/3}b^{1/3}+b^{2/3}}

Then

a-b = (3x^3+3x^2+x-1) - (3x^3-x^2+1) \\\\ = 4x^2+x-2

The limit is then equivalent to

\displaystyle \lim_{x\to\infty} \frac{4x^2+x-2}{a^{2/3}+(ab)^{1/3}+b^{2/3}}

From each remaining cube root expression, remove the cubic terms:

a^{2/3} = \left(3x^3+3x^2+x-1\right)^{2/3} \\\\ = \left(x^3\right)^{2/3} \left(3+\dfrac3x+\dfrac1{x^2}-\dfrac1{x^3}\right)^{2/3} \\\\ = x^2 \left(3+\dfrac3x+\dfrac1{x^2}-\dfrac1{x^3}\right)^{2/3}

(ab)^{1/3} = \left((3x^3+3x^2+x-1)(3x^3-x^2+1)\right)^{1/3} \\\\ = \left(\left(x^3\right)^{1/3}\right)^2 \left(\left(3+\dfrac3x+\dfrac1{x^2}-\dfrac1x\right)\left(3-\dfrac1x+\dfrac1{x^3}\right)\right)^{1/3} \\\\ = x^2 \left(9+\dfrac6x-\dfrac1{x^3}+\dfrac4{x^4}+\dfrac1{x^5}-\dfrac1{x^6}\right)^{1/3}

b^{2/3} = \left(3x^3-x^2+1\right)^{2/3} \\\\ = \left(x^3\right)^{2/3} \left(3-\dfrac1x+\dfrac1{x^3}\right)^{2/3} \\\\ = x^2 \left(3-\dfrac1x+\dfrac1{x^3}\right)^{2/3}

Now that we see each term in the denominator has a factor of <em>x</em> ², we can eliminate it :

\displaystyle \lim_{x\to\infty} \frac{4x^2+x-2}{a^{2/3}+(ab)^{1/3}+b^{2/3}} \\\\ = \lim_{x\to\infty} \frac{4x^2+x-2}{x^2 \left(\left(3+\dfrac3x+\dfrac1{x^2}-\dfrac1{x^3}\right)^{2/3} + \left(9+\dfrac6x-\dfrac1{x^3}+\dfrac4{x^4}+\dfrac1{x^5}-\dfrac1{x^6}\right)^{1/3} + \left(3-\dfrac1x+\dfrac1{x^3}\right)^{2/3}\right)}

=\displaystyle \lim_{x\to\infty} \frac{4+\dfrac1x-\dfrac2{x^2}}{\left(3+\dfrac3x+\dfrac1{x^2}-\dfrac1{x^3}\right)^{2/3} + \left(9+\dfrac6x-\dfrac1{x^3}+\dfrac4{x^4}+\dfrac1{x^5}-\dfrac1{x^6}\right)^{1/3} + \left(3-\dfrac1x+\dfrac1{x^3}\right)^{2/3}}

As <em>x</em> goes to infinity, each of the 1/<em>x</em> ⁿ terms converge to 0, leaving us with the overall limit,

\displaystyle \frac{4+0-0}{(3+0+0-0)^{2/3} + (9+0-0+0+0-0)^{1/3} + (3-0+0)^{2/3}} \\\\ = \frac{4}{3^{2/3}+(3^2)^{1/3}+3^{2/3}} \\\\ = \frac{4}{3\cdot 3^{2/3}} = \boxed{\frac{4}{3^{5/3}}}

8 0
3 years ago
A box of in cooked spaghetti cost0.1369 per ounce how much is this cost to the nearest cent
AleksAgata [21]
I think u can just divide by 16 to get it because each ounce is 16
8 0
3 years ago
Read 2 more answers
-3x-8/4=10<br><br> What’s is value of x
dlinn [17]

Answer:

x= -16

Step-by-step explanation:

-3x-8/ 4 = 10

Here we can try to isolate x and so we have to first multiply 4 on each side.

-3x-8= 40

Then we can add the 8 to each side.

-3x= 48

Next, divide the -3 onto each side and we can get the answer!

x= -16

6 0
3 years ago
If 3t − 7 = 5t , then 6t
klemol [59]
3t-7=5t
-3t     -3t
-7 = 2t
/2     /2
t = -7/2

Plug it in to 6t, so it is 6(-7/2) = -21
5 0
3 years ago
Read 2 more answers
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