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3 years ago

David went for a run in his town.

Mathematics

1 answer:

Kazeer [188]3 years ago

5 0

1.2 plus .75 plus 1.34 plus .49 which is 3.78

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Without a calculator how would you solve this?

mina [271]

Answer:

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

Step-by-step explanation:

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

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

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

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

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

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

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

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

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

8 0

3 years ago

Using the table find the value of y when x=2<br>

Tju [1.3M]

Answer:

y = 8 when x = 2

Step-by-step explanation:

y = 4x

6 0

3 years ago

Erin has 60$ in a savings account that earns 5% interest per year. The interest is not compounded. How much interest will she ea

Flauer [41]

Answer:

Step-by-step explanation:

she will earn 12 dollars a year i think

3 0

3 years ago

The school environment club made a poster to celebrate earth day. The poster is 7/8 yard long and 2/3 yard wide. What is the dif

Ronch [10]

7/8 yd -2/3 yd
= 21/24 yd -16/24 yd
= (21 -16)/24 yd
= 5/24 yd . . . . . difference between length and width

_____
This is (5/24)*36 = 7 1/2 inches.

6 0

3 years ago

ANSWER FAST PLEASE

xeze [42]

Answer:16/8

Step-by-step explanation:

8 0

3 years ago