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RUDIKE [14]
2 years ago
12

Without a calculator how would you solve this?

Mathematics
1 answer:
mina [271]2 years ago
8 0

Answer:

the largest number that is less than (2+√3)^6 is 2701

Step-by-step explanation:

\bigstar \ (2+\sqrt{3})^6= \\\\C{}^{0}_{6}2^{6}+C{}^{1}_{6}2^{5}\sqrt{3}^1+C{}^{2}_{6}2^{4}\sqrt{3}^2+C{}^{3}_{6}2^{3}\sqrt{3}^3+C{}^{4}_{6}2^{2}\sqrt{3}^4+C{}^{5}_{6}2^{1}\sqrt{3}^5+C{}^{6}_{6}\sqrt{3}^6

=64+192\sqrt{3}+720 +480\sqrt{3} +540+108\sqrt{3} +27\\=1351+780\sqrt{3}

\bigstar\  (2-\sqrt{3} )^6 =\\\\1351-780\sqrt{3}

\bigstar\  \bigstar\  (2+\sqrt{3} )^6+(2-\sqrt{3} )^6 =\\\\1351+780\sqrt{3}+1351-780\sqrt{3}

\Longrightarrow(2+\sqrt{3} )^6+(2-\sqrt{3} )^6 =2702

\Longrightarrow(2+\sqrt{3} )^6 =2702-(2-\sqrt{3} )^6

0 < \left( 2-\sqrt{3} \right) < 1 \Longrightarrow 0 < \left( 2-\sqrt{3} \right)^{6} < 1 \Longrightarrow-1 < \left( 2-\sqrt{3} \right)^{6} < 0

\Longrightarrow2702-1 < 2702-\left( 2-\sqrt{3} \right)^{6} < 2702+0

\Longrightarrow 2701 < \left( 2+\sqrt{3} \right)^{6} < 2702

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Zanzabum

My calculator shows that

(2.1)/(1.488) = 1.41129

which is approximate. If you want the result to two decimal places, then it would be 1.41 and not 1.40

Try 1.41 and it should work out, assuming your teacher wants two decimal places.

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2 years ago
\text{Emily runs 11 feet per second.}
Stels [109]

Answer:

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2 years ago
The volume of a rectangle prism with length 9 meters, width 4 meters, and height 5 meters.
vovangra [49]

Answer:

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Step-by-step explanation:. Please brainliest!

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5 0
3 years ago
Read 2 more answers
Which unit is not a measurement of volume? cm L ml cm3
Dahasolnce [82]
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cm is 1 dimentional: legnth
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cm is the answer



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3 years ago
Help, please. I just need an answer, so if anyone is bored, for the love of god please... ​
Alla [95]

Answer:B & E

Step-by-step explanation:

We can first rearrange the function to isolate y. Then, we can find the slope as the function is in the form y=mx+b.

3x-4y=7\\-4y=-3x+7\\y=\frac{3}{4}x-\frac{7}{4}

Since parallel lines have the same slope, we can put the slope of 3/4 into the point slope form to get the answer.

<em>For reference, the point-slope form is </em>y-y_1=m(x-x_1)

y+2=\frac{3}{4}(x+4)\\y+2=\frac{3}{4}x+3\\y=\frac{3}{4}x+1

The first line is found in option E, so option E is one of the correct options.

We can also move the x to the other side, as two of the 5 options have both variables on the left (B and C).

-\frac{3}{4}x+y=1

If we multiply the whole equation by -4, we can get rid of the fraction.

-4(-\frac{3}{4}x+y)=-4(1)\\3x-4y=-4

Hence, option B is also correct.

7 0
1 year ago
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